ORDER AND AMENDED OPINION

ORDER

A majority of the panel has voted to deny the petition for rehearing and to deny the petition for rehearing en banc. Judge Fletcher votes to grant the petition for rehearing and so recommends with respect to the petition for rehearing en banc, in accord with the attached dissent. The opinion filed on June 24, 2003, shall be amended to incorporate Judge Fletcher’s dissent.

The full court has been advised of the petition for rehearing and rehearing en banc and no judge has requested a vote on whether to rehear the matter en bane. Fed. R.App. P. 35.

The petition for panel rehearing and the petition for rehearing en banc are denied. The mandate shall not issue until it is determined whether, as a result of the amended opinion, any judge of the court desires to call for an en banc rehearing pursuant to General Order 5.4. No further petitions shall be accepted from the parties.

OPINION

Larry David Davis was convicted of first-degree murder and sentenced to death. After exhausting his California state appeals, he filed an amended petition for habeas corpus in federal district court, raising multiple constitutional challenges to both the conviction and sentence. The district court denied the petition. Having reviewed the record, transcript, arguments, and prior decisions, including the extensive opinions of the California Supreme Court and the district court, we affirm.

BacKGround

Davis’s conviction and sentence stem from two events that occurred close in time and proximity in the early hours of August 28, 1988: the attempted rape of Suzanne H. and the death by asphyxiation and apparent kidnapping and sodomy of Dawn Holman. According to Suzanne H.’s trial testimony, she met Davis in a bar on August 26, 1988, and invited him to meet her the next evening for her birthday. She and Davis went out the next night, along with one of her friends. At the end of the evening, Suzanne H. drove her friend home, and then agreed to take Davis to a party ostensibly being given by a friend of his. As they were driving, Davis directed her to a dead-end road, took the keys out of the ignition, and began groping her. She first tried to end his advances by telling him she was a lesbian, but that seemed only to excite him more. She was finally able to persuade him to stop by telling him that she would have sex with him in a motel in town. Davis gave her car keys back to allow her to drive to a motel, and she drove toward town, trying unsuccessfully to attract the attention of police.

Once in town, Suzanne H. told Davis that she needed to get gas before going to the motel. While Davis was pumping gas, she went to the cashier, told him that Davis had tried to rape her, and asked him *635 to call the police. Davis came after her and tried to drag her away, but she elbowed him and screamed “Rape!” and he let her go. When the police arrived, Davis ran away, though not before removing the coil wire from Suzanne H.’s car. Suzanne H. gave a statement to the police, but said she did not wish to participate in a prosecution, saying that she was returning to New York within days. Later that night, one of the police officers who had interviewed Suzanne H. stopped Davis for urinating in public and loitering, but the officer did not connect Davis with the Suzanne H. incident. When asked what he was doing, Davis claimed to be friends with the occupants of a nearby house. The officer awakened the residents of the house, who denied knowing Davis, and the officer told Davis to leave.

After his run-in with the officer, Davis made his way to a nearby Safeway grocery store, and it was there that he met Dawn Holman. At about 3 a.m., he was standing on the sidewalk in front of the store smoking marijuana when a man, later identified as Emanuel Manson, came over and asked for a hit. Davis agreed, and asked him for a ride to Ventura. Manson declined, and later saw Davis asking for a ride from a woman who had just pulled into the parking lot. That woman was Dawn Holman. She agreed to give Davis a ride, and they left alone in Holman’s car.

Holman’s body was found around 5 a.m. by a greenskeeper at a nearby golf course. Her car was partially in a ditch about 265 feet from her body; the front passenger door was heavily damaged, and appeared to have hit a nearby telephone pole. According to the medical examiner, Holman died from asphyxiation from strangulation, likely manual strangulation, but not before suffering extensive external and internal injuries as a result of having been seated in — or partially out of — the passenger seat when the car struck the telephone pole.

The medical examiner testified that Holman’s body showed evidence of sexual assault: her body was found with her bra pulled down below her chest, she was strangled, and her anus was dilated and smeared with fecal matter. The medical examiner also found a large number of sperm in her anal canal and a smaller number in her vaginal canal,, and noted that her skirt was heavily stained with semen and fecal material, suggesting that she had been sodomized. He speculated that the sodomy occurred after she suffered the car crash injuries, perhaps shortly after her death. Moreover, in his "view, if the sex had occurred before her death, she would have been in too much pain from her other injuries to engage in consensual intercourse. He also testified that although the crash injuries were highly disabling and could have resulted in her death, the strangulation was in fact the cause of her death.

Serological testing of the stains on Holman’s skirt revealed that Davis was within the 1% of the population that could have been the source of the semen. Davis’s DNA matched the DNA found , on some of the skirt stains. In addition, a breast swab taken from Holman indicated a high probability of saliva with the same basic blood type as Davis’s, and two hairs found on Holman’s body were consistent with Davis’s hair. Finally, a small piece of glass found in the shirt Davis was wearing on the night of the incident was consistent with broken glass from Holman’s car.

Several days after Holman’s death, two Ventura County-police officers questioned Davis. The questioning focused on the' Suzanne H. incident, but at the end of the conversation the officers mentioned that they were looking into a homicide. Davis told the officers that after leaving Suzanne *636 H., he was stopped for urinating in public, and was picked up by somebody and taken back to his truck, where he sat and drank. The officers arrested Davis for the assault on Suzanne H. and booked him into the Ventura County jail. Soon after, he was arrested and re-booked for Holman’s murder. Criminal charges relating to both events were filed against Davis in December 1988.

Davis ultimately went to trial on six counts: (1) first-degree murder of Holman (Cal.Penal Code § 187(a)) with felony-based special circumstances for kidnapping (Cal.Penal Code §§ 207, 209, 190.2(a)(17)) and sodomy (CaLPenal Code §§ 286, 190.2(a)(17)); (2) sodomy of Holman (Cal.Penal Code § 286(c)); (3) kidnapping of Holman (Cal.Penal Code § 207(a)); (4) sexual battery of Suzanne H. (CaLPenal Code § 243.4); (5) assault of Holman with intent to commit sodomy (CaLPenal Code §§ 261(a)(2), 286); and (6) assault of Suzanne H. with intent to commit rape or sodomy (CaLPenal Code §§ 261(a)(2), 286).

At trial, Davis offered what can only be characterized as a convoluted story, in which he played only a supporting rather than a starring role in the events that led to Holman’s death. He admitted that during his interview with the Ventura County police officers, he lied about his activities the night of the murder, and claimed that he had done so because his life and the lives of his family were “threatened.” He offered a narrative of the evening involving three extra people, including a mysterious “white guy,” an extra car, and Davis as the unlikely hero.

According to Davis, he and Holman left the Safeway in her car, while Manson followed in his. The three parked and smoked some more pot, and then Holman and Davis left together, smoked some more dope, and had consensual sex. They were discovered in the car by Holman’s one-time boyfriend, Ashley Reid, who arrived with Manson and the * anonymous white man. Angered by Holman’s conduct with Davis, Reid got into Holman’s car with her and the others got into Manson’s car. The three men followed Reid and Holman to the golf course, witnessed them fighting in the car on the way, and then saw the car hit a telephone pole while Holman was partially hanging out of the passenger side of the car.

Davis testified that he jumped out of his car, ran to Holman, picked her up, and ran across the golf course with her, but that the “white guy” caught up and told him Reid wanted to speak with him. Davis left Holman where she lay and returned to the car to find Reid pointing a gun at him. Davis kicked the gun out of Reid’s hand, ran away, apparently was hit by some sort of vehicle, and was slapped awake the next morning by a shabbily-dressed old man on the railroad tracks. Because he did not realize anybody had been killed, and because he received some veiled threats from an associate of Reid’s, he did not report the incident to the police.

Both Reid and a man who was identified as potentially being the “white guy” provided alibis for the night in question. At trial, Manson refused to answer most of defense counsel’s questions. The jury found Davis guilty on all counts as charged, with the exception of count 2, sodomy of Holman, on which the jury found Davis guilty of the lesser included offense of attempted sodomy. The jury began the penalty phase six weeks later. After hearing from a number of witnesses for both sides, the jury returned a death verdict. The California Supreme Court affirmed Davis’s conviction and sentence on automatic appeal. People v. Davis, 10 Cal.4th 463, 488 , 41 Cal.Rptr.2d 826 , 896 P.2d 119, 129 (1995), cert. denied sub nom. Davis v. California, 516 U.S. 1121 , 116 *637 S.Ct. 932 , 133 L.Ed.2d 859 (1996). The California courts also rejected Davis’s state petition for writ of habeas corpus filed in March 1995.

Davis initiated his federal action by filing a Request for Appointment of Counsel and for Stay of Execution with the district court on April 5, 1996. He filed a mixed petition for writ of habeas corpus on April 22, 1997. The district court stayed Davis’s habeas case pending exhaustion of the unexhausted claims in state court. Davis then filed a second state habeas petition containing the unexhausted claims, which the California Supreme Court denied after rejecting all claims on the merits. Davis subsequently filed his Amended Petition for Writ of Habeas Corpus, listing seventeen claims, in federal court. The district court granted the state of California’s motion for summary judgment, denied Davis’s cross-motion for partial summary judgment, and denied with prejudice Davis’s petition for writ of habeas corpus. Although the district court denied Davis’s request for an eiddentiary hearing, it is apparent from its 173-page decision that the district court gave careful and thoughtful consideration to the case, exhaustively treating each claim'. We granted a certificate of appealability on ten of Davis’s seventeen claims.

STANDARD OF REVIEW

Davis seeks two forms of relief: an evi-dentiary hearing on the majority of his claims and reversal of the district court’s grant of summary judgment to the state of California on the remaining claims. 1 Because Davis filed only his Request for Appointment of Counsel and for Stay of Execution, not his Amended Petition for Writ of Habeas Corpus, before the effective date of the Antiterrorism and Effective Death Penalty Act (“AEDPA”), AEDPA’s standards of review are applicable to both the merits and procedural aspects of this appeal. See Woodford v. Garceau, 538 U.S. 202 , 123 S.Ct. 1398, 1404 , 155 L.Ed.2d 363 (2003) (“[W]e hold that ... a case does not become ‘pending’ until an actual application for habeas corpus relief is filed in federal court.”); see also Valerio v. Crawford, 306 F.3d 742, 763 (9th Cir.2002) (applying appellate review provisions of AED-PA, 28 U.S.C. § 2253 (c)) (citing Slack v. McDaniel, 529 U.S. 473, 480-82 , 120 S.Ct. 1595 , 146 L.Ed.2d 542 (2000)).

Under AEDPA, we may grant habeas relief only if the state court’s decision (1) “was contrary to, or involved an unreasonable application of, clearly established federal law, as determined by the Supreme Court ...; or (2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254 (d). The first prong applies both to questions of law and to mixed questions of law and fact, Williams v. Taylor, 529 U.S. 362, 407-09 , 120 S.Ct. 1495 , 146 L.Ed.2d 389 (2000), while the second prong'applies to decisions based on factual determinations, Miller-El v. Cockrell, 537 U.S. 322 , 123 S.Ct. 1029, 1041 , 154 L.Ed.2d 931 (2003).

To satisfy the “Unreasonable application” portion of the first prong, the petitioner must demonstrate that the state *638 court’s application of Supreme Court precedent to the facts of his case was not only incorrect but “objectively unreasonable.” Woodford v. Visciotti, 537 U.S. 19 , 123 S.Ct. 357, 360 (2002). “While Supreme Court precedent is the only authority that is controlling under AEDPA, we look to Ninth Circuit case law as ‘persuasive authority for purposes of determining whether a particular state court decision is an “unreasonable application” of Supreme Court law.’ ” Luna v. Cambra, 306 F.3d 954, 960 (9th Cir.2002) (quoting Van Tran v. Lindsey, 212 F.3d 1143, 1154 (9th Cir.2000), overruled in part on other grounds by Lockyer v. Andrade, 538 U.S. 63 , 123 S.Ct. 1166, 1172 , 155 L.Ed.2d 144 (2003)). “Factual determinations by state courts are presumed correct absent clear and convincing evidence to the contrary.” Miller-El, 123 S.Ct. at 1041 ; 28 U.S.C. § 2254 (e)(1). A state court decision “based on a factual determination will not be overturned on factual grounds unless objectively unreasonable in light of the evidence presented in the state-court proceeding.” Miller-El, 123 S.Ct. at 1041 ; 28 U.S.C. § 2254 (d)(2).

We review the district court’s denial of an evidentiary hearing for abuse of discretion, Lawson v. Borg, 60 F.3d 608, 611 (9th Cir.1995), and review the district court’s grant of summary judgment de novo, Lessard v. Applied Risk Mgmt., 307 F.3d 1020, 1023 (9th Cir.2002). The petitioner carries the burden of proving by a preponderance of the evidence that he is entitled to habeas relief. Silva v. Woodford, 279 F.3d 825, 835 (9th Cir.2002).

Guilt Phase

1. Impermissible Joinder

Davis argues that the trial court’s denial of his motion to sever the capital charges related to Holman from the non-capital charges relating to Suzanne H. violated his due process rights. The California Supreme Court held that it was not an abuse of discretion for the trial court to allow all counts to be tried together.

We may grant habeas relief on a joinder challenge only “if the joinder resulted in an unfair trial. There is no prejudicial constitutional violation unless ‘simultaneous trial of more than one offense ... actually rendered] petitioner’s state trial fundamentally unfair and hence, violative of due process.’ ” Sandoval v. Calderon, 241 F.3d 765, 771-72 (9th Cir.2001), cert. denied, 534 U.S. 847 , 122 S.Ct. 112 , 151 L.Ed.2d 69 (2001) and cert. denied, 534 U.S. 943 , 122 S.Ct. 322 , 151 L.Ed.2d 241 (2001) (quoting Featherstone v. Estelle, 948 F.2d 1497, 1503 (9th Cir.1991)) (omissions and modifications in original). The requisite level of prejudice is reached only “if the impermissible joinder had a substantial and injurious effect or influence in determining the jury’s verdict.” Sandoval, 241 F.3d at 772 (citing Bean v. Calderon, 163 F.3d 1073, 1086 (9th Cir.1998)). In evaluating prejudice, the Ninth Circuit focuses particularly on cross-admissibility of evidence and the danger of “spillover” from one charge to another, especially where one charge or set of charges is weaker than another. See, e.g., Sandoval, 241 F.3d at 772 ; Bean, 163 F.3d at 1084 .

As the California Supreme Court noted, Davis “concede[d] [that] the evidence in support of the offenses against Holman and Suzanne H. was cross-admissible on the issues of identity and intent.” 2 Davis, 10 Cal.4th at 508 , 41 Cal.Rptr.2d *639 826 , 896 P.2d at 142 ; see also Cal. Evicl. Code § 1101 (b) (evidence that person committed crime admissible to prove fact other than disposition to commit act). The incidents were similar in nature, occurred only a few hours apart, and were in close geographic proximity.

Moreover, the State did not join “a strong evidentiary case with a much weaker case in the hope that the cumulation of the evidence would lead to convictions in both cases.” Sandoval, 241 F.3d at 772 . The weight of evidence in the Holman and Suzanne H. cases was roughly equivalent. The Holman case turned entirely on circumstantial evidence, although the physical evidence against Davis — including the serological results and the shard of windshield found in his shirt pocket — was very strong. The Suzanne H. charge rested on Suzanne H.’s own direct testimony — a narrative that the jury found more credible than Davis’s. If anything, the physical evidence made for a stronger case on the Holman capital charges than on the non-capital charges involving Suzanne H.

Notably, any prejudice was further limited through an instruction directing the jury to consider each count separately. See United States v. Lane, 474 U.S. 438 , 450 n. 13, 106 S.Ct. 725 , 88 L.Ed.2d 814 (1986) (concluding, in a case regarding misjoinder of defendants, that a “carefully crafted limiting instruction” may reduce prejudice “to the minimum” and that”[w]e cannot necessarily assume that the jury misunderstood or disobeyed such instructions” (internal citations and quotation marks omitted)). Although such jury instructions can pose difficulties by asking juries to “compartmentalize damaging information about one defendant derived from joint counts,” the instructions have a better chance of' effectiveness “when the evidence of each crime is simple and distinct, even in the absence of cross-admissibility.” Bean, 163 F.3d at 1084-85 . The same holds true where two , different charges are joined for trial. The evidence here was not. only cross-admissible, but distinct and straightforward. The two counts were not improperly joined.

II. Sufficiency of the Evidence on Premeditation

Davis next challenges his conviction on due process grounds, claiming that there was insufficient evidence of premeditation and deliberation to support a first-degree murder conviction. Davis faces a considerable hurdle on this claim. The jury’s finding must stand if, “after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 319 , 99 S.Ct. 2781 , 61 L.Ed.2d 560 (1979). Significantly, our court, “faced with a record of historical facts that supports conflicting inferences must presume — even if it does not affirmatively appear in the record — that the trier of fact resolved any such conflicts in favor of the prosecution, and must defer to that resolution.” Id. at 326 , 99 S.Ct. 2781 .

We apply the Jackson standard “with explicit reference to the substantive elements of the criminal offense as defined by state law.” Id. at 324 n. 16, 99 S.Ct. 2781 . Under California law, “[a] verdict of murder in the first degree ... is proper only if the slayer killed ‘as a result of careful thought and weighing of considerations; as a deliberate judgment or plan; carried on coolly and steadily, [especially] according to a preconceived design.’ ” People v. Caldwell, 43 Cal.2d 864, 869 , 279 P.2d 539, 542 (1955) (citations omitted). “Deliberation” and “premeditation” must be construed to require “more reflection than may be involved, in the mere forma *640 tion of a specific intent to kill.” People v. Anderson, 70 Cal.2d 15, 26 , 73 Cal.Rptr. 550 , 447 P.2d 942, 949 (1968).

Anderson explains that in reviewing verdicts of first-degree murder, the court looks to evidence of (1) planning, (2) motive, and (3) facts “from which the jury could infer that the manner of killing was so particular and exacting that the defendant must have [had] ... a ‘preconceived design’ ” that the jury may infer from either motive or planning. 70 Cal.2d at 26-27 , 73 Cal.Rptr. 550 , 447 P.2d at 949 . Such verdicts are typically sustained “when there is evidence of all three types”; otherwise, there must be “at least extremely strong evidence of (1) or evidence of (2) in conjunction with either (1) or (3).” 3 70 Cal.2d at 27 , 73 Cal.Rptr. 550 , 447 P.2d at 949 .

In accord with California law, the trial judge instructed the jury almost verbatim from the California model jury instructions:

Although the jury certainly could have found that the crime did not rise to the level of first-degree murder, we cannot say under the Anderson framework that no rational trier of fact could have found that the Holman murder was deliberate and premeditated.

We focus first on the manner of killing — strangulation. Under California law, “when manner-of-killing evidence strongly suggests premeditation and deliberation, that evidence is enough, by itself, to sustain a conviction for first-degree murder.” Drayden v. White, 232 F.3d 704, 709 (9th Cir.2000) (citing Hawkins, 10 Cal.4th at 957 , 42 Cal.Rptr.2d 636 , 897 P.2d at 595 ).

The unrefuted medical evidence on this point is compelling. Holman’s injuries from the crash were extremely serious but were not the cause of her death. Even after the debilitating crash, she was apparently able to escape from the car. Her ultimate demise resulted from strangulation. To render her unconscious, Davis would have had to apply pressure deliberately and steadily for up to two minutes. Even in her weakened state, death by strangulation would have taken three to five minutes of continuous pressure. A rational juror could infer that there was nothing casual or accidental about the death and that the intent to keep Holman from escaping from the car plus the strangulation evidenced premeditation and deliberation. Whether viewed in isolation or in conjunction with the other evidence, the manner of killing evidence was sufficient to sustain the verdict. See Anderson, 70 Cal.2d at 27 , 73 Cal.Rptr. 550 , 447 P.2d at *641 949 (noting that evidence of a preconceived design coupled with a motive is sufficient to sustain first-degree murder verdict).

As the district court observed, this case also involves evidence falling within the other two Anderson categories — planning and motive. Evidence of planning arises from Davis’s engineering the assaults on both Suzanne H. and Holman in isolated areas where they could not easily escape or seek help. A jury could also believe that Davis got into the car intending to have sex with Holman and, when she refused, devised a plan to forcibly rape, sodomize, and kill her.

As for motive, in discussing the topic of sex with “a dead girl,” Davis reportedly told a jailhouse informant, “You got to get ‘em before the body gets cold.” A jury that believed the informant’s testimony could infer that Davis intended to kill Holman so that he could have sex with her dead body or to eliminate the possibility of her reporting the rape or testifying against him. Given the evidence supporting all three Anderson factors, the district court did not err in concluding that there was sufficient evidence to sustain the Special finding of premeditation.

III. Ineffective Assistance of Counsel

Davis seeks an evidentiary hearing on four claims of ineffective assistance of counsel in the guilt phase. We address each in turn and affirm the district court’s denial of a hearing because Davis has not demonstrated that he is entitled to relief on any claim. See Phillips v. Woodford, 267 F.3d 966, 973 (9th Cir.2001) (“A habeas petitioner is entitled to an evidentiary hearing if [ ] the allegations in his petition would, if proved, entitle' him to relief....”).

Under Strickland v. Washington, 466 U.S. 668 , 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984), to prevail on a claim of ineffective assistance of counsel, Davis must show that counsel’s performance was deficient— that is, that it fell below an objective standard of reasonableness — and that “counsel’s errors were so serious as to deprive the defendant of a fair trial.” Id. at 687 , 104 S.Ct. 2052 .

A. Failure to Impeach Prosecution Witness

Davis first attacks defense counsel’s failure to impeach Emanuel .Manson. During cross-examination, Davis’s counsel asked Manson whether he had been convicted of lying to a police officer. Manson admitted, outside the presence of the jury, that two years earlier he had lied to a police officer in connection with a misdemeanor traffic ticket. The trial judge sustained the prosecutor’s objection because misdemeanor convictions are not admissible for impeachment purposes under California law. Davis’s counsel could then have asked for permission to impeach Manson with the conduct underlying the misdemeanor, which was admissible, but he failed to do so. Both sides acknowledge that this mistake constituted ineffective assistance of counsel, violating the first prong of Strickland . The only issue is whether the mistake denied Davis a fair trial. We hold that it did not.

Defense counsel did impeach Manson’s credibility on many other grounds, including inconsistencies in his testimony and his inability to remember whether he had been drinking on-the night he saw Davis at the Safeway. When Manson refused to answer several questions, the judge instructed the jury that “you can draw whatever inferences regarding his credibility or lack of it from his refusal to answer a direct order from me to answer what I feel to be a relevant question in this trial.” The jury was thus on notice that Manson’s credibility was at issue and defense coun *642 sel further highlighted that fact through effective questioning.

More importantly, it is almost impossible to believe that a jury — already aware that Manson’s credibility was an issue— would have decided the guilt phase differently had it known that Manson lied in connection with a traffic ticket issued a year before the murder occurred and two years before Davis’s trial. We therefore conclude that counsel’s failure to introduce Manson’s conduct did not prejudice the outcome of Davis’s trial.

B.FailuRE to Introduce Davis’s Statement to Investigators

Before trial, Davis recounted his version of the events in a tape-recorded statement to defense investigators. At trial, Davis testified that he had spoken with the investigators, and defense counsel pointed out in his closing argument that Davis “had already told his story” and thus did not invent his explanation after hearing the prosecution’s testimony. However, defense counsel never introduced into evidence Davis’s statement or any other testimony that the statement had been given. The prosecutor thus was able to point out in rebuttal that defense counsel’s claim was uncorroborated.

Whether or not counsel’s failure to introduce this evidence constituted ineffective assistance, it did not prejudice the trial. As documented by the sequence of other evidence, Davis gave his statement to investigators after both hearing the prosecution arguments at the preliminary hearing and seeing a police report about the murder. Even if the statement and its timing were in evidence, the prosecution could have rebutted it by pointing out that Davis already knew the broad outlines of the prosecution’s case by the time he made his statement. Davis’s Strickland claim therefore fails.

C. Presentation of “Irrelevant” Testimony

The first two witnesses for the defense were Tammy Kay Thompson and Cecilia Taylor. Each testified that, in the spring or summer of 1989, she had been harassed or assaulted by a black man; based on composite sketches of Davis, each woman testified that he could have been the perpetrator. Both incidents, however, occurred while Davis was in custody. Defense counsel used the witnesses to emphasize that victims often make mistakes in identification. Davis claims that his counsel was ineffective for offering these witnesses because the identification issue was irrelevant to his defense. He argues that this strategy made the defense appear “desperate” and opened up the testimony to potshots from the prosecution.

This claim fails under the first prong of Strickland . In addition to arguing that sex crime victims often make mistakes in identifying their assailants,, defense counsel argued in closing that witnesses “can also be mistaken about all kinds of other things that [they] see and hear” and he gave examples of some of the mistakes that various witnesses might have made. Counsel’s presentation of this pair of witnesses was part of a reasonable trial strategy, albeit one subject to criticism and after-the-fact second-guessing. See Siripongs v. Calderon, 133 F.3d 732, 736 (9th Cir.1998) (holding that “the relevant inquiry under Strickland is not what defense counsel could have pursued, but rather whether the choices made by defense counsel were reasonable”).

D. Failure to Exercise Peremptory Challenges

Davis’s final ineffective assistance of counsel claim stems from defense counsel’s decision not to challenge the seating *643 of two jurors despite having unused peremptory challenges. Establishing Strickland prejudice in the context of juror selection requires a showing that, as a result of trial' counsel’s failure to exercise peremptory challenges, the jury panel contained at least one juror who was biased. United States v. Quintero-Barraza, 78 F.3d 1344, 1349 (9th Cir.1995). “The Supreme Court has suggested that the relevant test for determining whether a juror is biased is ‘whether the juror[] .... had such fixed opinions that [he] could not judge impartially the guilt of the defendant.’ ” Id. (quoting Patton v. Yount, 467 U.S. 1025, 1035 , 104 S.Ct. 2885 , 81 L.Ed.2d 847 (1984)) (alterations in original).

The jurors’ answers to the voir dire questions demonstrate that they did not hold fixed views on the death penalty or on Davis’s guilt. Each professed- a belief in the presumption of innocence and a willingness to follow the judge’s instructions and decide the case impartially. One of the jurors, an FBI fraud investigator, said that he believed in the death penalty under certain circumstances but had “mixed emotions” about it. He stated that he could be honest and could be a critic of law enforcement handiwork, but also said that he had “a lot of admiration for the various law enforcement officers.” The other juror, an emergency-room nurse, related that her daughter was addicted to cocaine and had been raped seven months before trial, and that her son had been raped three years earlier. She also revealed “what I consider to be ambivalent feelings about the death penalty,” and agreed that the burden of proof “is and ought to be on the accuser in a case like this.”

These statements do not demonstrate actual or implied jury bias. Rather, the comments reflect that the jurors were, appropriately, grappling with their feelings about the death penalty, and that they intended to approach the evidence with an understanding of the proper allocation of burdens in a criminal case. We cannot say thát counsel was deficient in declining to exercise peremptory challenges.

IV. Prosecutorial Vouching

Finally, Davis alleges that the prosecutor improperly vouched for a witness’s credibility. Fernando Moreno, an inmate trustee at the jail where Davis was housed awaiting trial, testified that he had a conversation with Davis in which Davis made statements implying that he was involved in Holman’s murder and that he preferred anal sex — the kind apparently forced upon Holman — to vaginal intercourse. In exchange for his testimony, Moreno entered into a plea agreement and received a recommendation that he be allowed to attend the birth of his second son.

The prosecution introduced the unre-dacted plea agreement, which read in part: “Based on our interview with Fernando Moreno, careful consideration of his prospective testimony and belief that the information he has provided is truthful and accurate, we would like to use him as a witness in the forthcoming trial of People versus Larry Davis” (emphasis added).

During a recess in the trial, Davis’s lawyer objected to the phrase “and belief that the information he has provided is truthful and accurate.” He acknowledged that the jury had already heard the phrase, but asked that it be redacted -from the exhibit that would be in the jury room. At the end of the day’s testimony, the judge gave a curative instruction, referring the jury to the offending language and telling them, “I am actually going to just line it out and admonish you to disregard or delete that portion of the memorandum from the testimony and from the exhibit from [] your *644 mind, not to be considered as evidence by you as to what the parties believed.”

To warrant habeas relief, prosecutorial misconduct must “so infect[] the trial with unfairness as to make the resulting conviction a denial of due process.” Darden v. Wainwright, 477 U.S. 168, 181, 106 S.Ct. 2464 , 91 L.Ed.2d 144 (1986) (citation and internal quotations omitted). Here we need not get tangled in the issue of whether use of the unredacted agreement rises to the level of vouching. Although counsel’s initial failure to object may have been an unfortunate lapse, it was without significant consequence. Counsel did in fact object at the next break, and the trial judge not only redacted the offending language from the exhibit but gave a curative instruction. This was not a case in which there was an “overwhelming probability that the jury[would] be unable to follow the court’s instructions” and “a strong likelihood that the effect of the evidence would be devastating to the defendant.” Greer v. Miller, 483 U.S. 756 , 766 n. 8, 107 S.Ct. 3102 , 97 L.Ed.2d 618 (1987) (citations and internal quotation marks omitted). Davis has not succeeded in demonstrating that the prosecutor’s reading of the plea agreement rendered his trial fundamentally unfair.

Penalty Phase

I. Failure to Hold a Competency Hearing

Davis makes three claims related to his competency during the penalty phase: He argues that the trial court erred in not sua sponte holding a competency hearing at the penalty phase (a procedural incompetence claim); that he was actually incompetent at the time of the penalty phase (a substantive incompetence claim); and that his trial counsel rendered ineffective assistance of counsel by not requesting a competency hearing. We hold that because the trial court did not err in declining to hold a competency hearing and because Davis was in fact competent, the district court did not abuse its discretion in declining to hold an evidentiary hearing on the issues and counsel did not err in failing to request a competency hearing.

A. Procedural Incompetence

Over a quarter of a century ago, we offered a succinct benchmark for review of the precise issue raised by Davis: “The question to be asked by the reviewing court is whether a reasonable judge, situated as was the trial court judge whose failure to conduct an evidentiary hearing is being reviewed, should have experienced doubt with respect to competency to stand trial.” de Kaplany v. Enomoto, 540 F.2d 975, 983 (9th Cir.1976) (en banc). A defendant must show that there was “substantial evidence” that he was mentally incompetent to stand trial. Moore v. United States, 464 F.2d 663, 666 (9th Cir.1972). Only when “the evidence raises a ‘bona fide doubt’ ” about the defendant’s competence to stand trial must a trial judge sua sponte conduct an evidentiary hearing. Pate v. Robinson, 383 U.S. 375, 385 , 86 S.Ct. 836 , 15 L.Ed.2d 815 (1966). “The state trial and appellate courts’ findings that the evidence did not require a competency hearing under Pate are findings of fact to which we must defer unless they are ‘unreasonable’ within the meaning of 28 U.S.C. § 2254 (d)(2).” Torres v. Prunty, 223 F.3d 1103, 1105 (9th Cir.2000) (citing Maggio v. Fulford, 462 U.S. 111, 117 , 103 S.Ct. 2261 , 76 L.Ed.2d 794 (1983) (per curiam)).

“To be competent to stand trial, a defendant must demonstrate an ability to consult with his lawyer with a reasonable degree of rational understanding and a rational as well as factual understanding of *645 the proceedings against him.” Douglas v. Woodford, 316 F.3d 1079, 1094 (9th Cir.2003). In reviewing whether a state trial judge should have sua sponte conducted a competency hearing, we may consider only the evidence that was before the trial judge. Williams v. Woodford, 306 F.3d 665, 702 (9th Cir.2002); see also id. (“Although no particular facts signal a defendant’s incompetence, suggestive evidence includes the defehdant’s demeanor before the trial judge, irrational behavior of the defendant, and available medical evaluations of the defendant’s competence to stand trial.”). Because the trial judge was not faced with substantial evidence of Davis’s incompetence — and in fact had good reason to think that Davis was competent — he did not err in failing to hold a competency hearing.

1. Beginning of Penalty Phase

Although there is little doubt that Davis was recalcitrant and acted in ways that were detrimental to his case, his interactions with the trial judge indicated that he understood what was at stake during the penalty phase and could make informed decisions.

On the first day of the penalty phase, Davis’s counsel informed the judge that Davis had waived his right to be present for the penalty phase. When the judge objected to such a blanket waiver, Davis told the judge that, according to his research in the jail law library, “[the law] only says I have to be present at court, not present and at counsel table at any time of my hearing or during the trial.” The judge agreed to allow him to sit in the doorway of the courtroom with one of his attorneys.

The next day, the judge began the proceedings by soliciting and getting Davis’s explicit waiver of his right to sit at the counsel table and to confront witnesses from the counsel table. When Davis’s counsel informed the judge that Davis refused to wear civilian clothes or to sit in the courtroom, the judge asked Davis whether he was rejecting his attorneys’ advice. Davis responded that he was doing so intentionally because “I don’t like sitting here listening to lies* about me. I feel if I sit over there [in the doorway], the[re] will be less problems and T am happy to sit over there so [the jurors] don’t sit here and look' at me getting mad because I have to listen to the lies.... ”

The judge told Davis that he was particularly concerned that Davis’s absence from the counsel table would make it easier for the prosecutor to convince the jury to impose the death penalty. Davis responded that he had been thinking about that issue, and that

When the judge acknowledged that it would be‘“devastating” if Davis did something in front of the jury that could be construed as violent, Davis repeated that “I just want to try and avoid problems. That is all I am trying to do.”

Davis’s decision not to wear civilian clothes and to remain in the doorway of the courtroom rather than facing the prosecution witnesses may seem an unreasonable decision for someone on trial for his life. He was evidently aware of the risks of his behavior, however, and rationally weighed those risks against the likelihood *646 that, if he remained in the courtroom, he would do something to increase further his chances of being sentenced to death. See Douglas, 316 F.3d at 1094 (concluding that defendant’s “coheren[ee][and] responsiveness]” and understanding of “the significance of the ... penalty phase” during colloquy with trial judge indicated that defendant was competent during trial). We conclude that the trial judge did not err in proceeding without a competency hearing at the beginning of the penalty phase.

2. DuRing Penalty Phase

Davis also argues that a hearing should have been held during the penalty phase because his mental status deteriorated during that time. The trial court judge was in a position to gauge whether a competency hearing would be in order. The judge continued to interact with Davis every morning and every afternoon, asking whether Davis still wanted to be in the doorway or if he wanted to join his attorneys at the counsel table. Several times Davis did choose to sit at the counsel table rather than in the doorway, affording the judge a closer look and the opportunity to determine whether Davis was able to make rational choices about his participation in his own trial. The judge’s “ability] to observe[Davis] in the context of the trial” therefore allowed him “to gauge from [Davis’s] demeanor [that Davis] was able to cooperate with his attorney[s] and to understand the nature and object of the proceedings against him.” Drope v. Missouri, 420 U.S. 162, 181 , 95 S.Ct. 896 , 43 L.Ed.2d 103 (1975).

Moreover, although the Supreme Court cautioned in Pate against relying on “demeanor at trial ... to dispense with a hearing” on competence, 383 U.S. at 386 , 86 S.Ct. 836 , the Court was faced in that case with a defendant who, among other things, had had a brick dropped on his head when he was young, often stood “in a daze,” and, according to his mother, “lost his mind.” Id. at 378-79 , 86 S.Ct. 836 ; see also Odle v. Woodford, 238 F.3d 1084, 1089-90 (9th Cir.2001) (holding that it was error not to conduct competency hearing where petitioner had suffered severe trauma to his brain as a result of a car accident and had a 3 x 3 x 4-ineh piece of his brain removed, and had a long subsequent history of psychiatric hospitalization and bizarre behavior); Torres, supra (concluding that district court erred by not holding competency hearing where court-appointed psychiatrist had diagnosed the petitioner as having a severe delusional (paranoid) disorder, testing indicated that the petitioner had brain damage resulting from head trauma, and petitioner had disruptive outbursts in court). Davis may have been depressed, but his history, statements, and conduct did not approach the overwhelming indications of incompetence present in Pate, Odle, and Torres . The judge was not confronted with “substantial evidence” that Davis was incompetent to stand trial, Moore, 464 F.2d at 666 , nor was there evidence to suggest that the judge “should have experienced doubt with respect to competency to stand trial,” de Kaplany, 540 F.2d at 983 . We therefore conclude that the trial judge did not err in declining to hold a competency hearing.

B. Substantive Incompetence

Davis’s Sixth Amendment right to a fair trial would nevertheless have been implicated if he had actually been incompetent during the penalty phase. See Cacoperdo v. Demosthenes, 37 F.3d 504, 510 (9th Cir.1994) (holding that conviction of legally incompetent defendant violates due process, but no competency hearing required unless court has good faith doubt concerning competence). For much the same reason that the trial court had no *647 substantial evidence of incompetence, we cannot glean evidence from the record to support actual incompetence. Davis’s behavior reflects that he had the present ability to consult with his attorneys. He also understood the nature of the proceedings; he was able to weigh the danger of absence from the jury against the danger of the jury’s observing his demeanor, and he understood that he was going to be sentenced to life without parole or to death.

Davis argues that several events during the penalty phase are evidence of his incompetence. First, he insisted on attending the penalty phase proceedings in a wheelchair, despite no apparent physiological cause for his inability to walk. Second, he claimed that his depression was further exacerbated by abuse allegedly suffered at the hands of the jail deputies. The evidence, however, fails to bear out his claims that either fact evidenced or caused incompetence during the penalty phase.

First, although his court-appointed psychiatrist, Dr. William Vicary, testified that Davis had a hysterical conversion disorder — in which Davis’s anxiety about being on trial was being transferred into a belief that he could not get out of his wheelchair — and that he and the jail physician had discussed putting Davis on psychiatric medication, Dr. Vicary gave no indication that he thought Davis was not competent to participate in the proceedings. In addition, although Davis’s penalty phase consultant, with whom Davis had a poor rapport, stated in her post-trial deposition testimony that Davis became “hysterical and unfocusable” near the end of their interviews, her testimony reflects that his behavior probably resulted from his anger towards her, his attorneys, and the entire process. It did not reflect on his competency.

Davis also points to a declaration Dr. Vicary submitted seven years after the trial in which he stated that Davis’s appearance in court was “terrible” and that due to Davis’s lack of cooperation with counsel, he “viewed Mr. Davis as marginal, in the gray area between competency and incompetency.” Dr. Vicary went on to add that “if several psychiatrists had examined Mr. Davis during the penalty phase, at least a few of them would have found Mr. Davis to be incompetent.” Significantly, however, Vicary did not see fit to place himself within the company of those few psychiatrists. His comments must be evaluated for what they are — rank speculation rather than evidence. See also Douglas, 316 F.3d at 1094 (noting the district court’s holding that psychiatric opinions rendered years before and years after trial did not “suffice to raise a ‘real and substantial’ doubt” as to defendant’s competence at the time of trial “in light of other contemporaneous and objective indications of competence”).

In light of our evaluation of the substantive competence claim, Davis’s claim that his trial attorneys rendered ineffective assistance of counsel by failing to move for a competency hearing in the trial court also fails.

II. Ineffective Assistance of Counsel- or. Vicary’s Testimony

Davis argues that defense counsel’s presentation and handling of Dr. Vicary constituted ineffective assistance of counsel. His concerns date from counsel’s initial decision to put Dr. Vicary on the stand. Dr. Vicary cautioned the defense attorneys before the penalty phase that, in order to bolster his credibility with the jury, his practice was to offer candid and possibly damaging information from the stand. That warning, coupled with similar warnings from several other public defend *648 ers, led Davis’s attorneys to request additional time to secure a psychiatrist who would provide less ammunition for the prosecution. When the trial judge refused to grant a continuance, defense counsel chose to use Dr. Vicary rather than forgo any testimony from a psychiatric expert.

On the stand, Dr. Vicary, true to his word, offered extensive and detailed testimony. In answer to several broadly worded questions from defense 'counsel, the psychiatrist volunteered multiple facts about, among other things, the murder, Davis’s criminal background, and his problems in juvenile hall. Dr. Vicary interpreted the results of a psychological evaluation — the Minnesota Multiphasic Personality Inventory (MMPI) — as indicating that Davis had Anti-Social Personality Disorder (ASPD), and characterized Davis as being intense, shallow, impulsive, and prone to violent episodes. Dr. Vicary even testified that he believed, out of respect for the jury’s verdict and after reading thousands of pages of documents, that Davis was lying and did murder Holman.

Dr. Vicary also provided some important and unique mitigating testimony, however. He testified about Davis’s expression of remorse, provided a psychological explanation for Davis’s behavior the night of the murder, detailed a list of mitigating factors, and stated that despite Davis’s ASPD, he would do well in a prison setting that provided him with some structure, in which he could become a model for other prisoners and even a trustee or teacher’s aide.

On cross-examination, the prosecutor made 'some headway in undermining Dr. Vicary’s positive testimony. When the prosecutor asked Dr. Vicary if he wanted to “take" a crack” at listing possible aggravating factors, Davis’s counsel objected only jestingly — so jestingly that the court did not even rule on the objection — and Dr. Vicary listed a number of aggravating elements, including that Holman was “young,” “innocent,” and “didn’t deserve to die.”

On redirect, defense counsel was able to put much of Dr. Vicary’s testimony in perspective. Dr. Vicary agreed that evaluating someone solely on the basis of the MMPI would constitute malpractice. He also agreed that a subject’s performance on the test could be affected by a number of factors, including his comfort with the person administering the examination. Dr. Vicary suggested that Davis might not have committed the murder had his mother’s indifference to her children’s welfare not thwarted appropriate juvenile intervention. Finally, Dr. Vicary testified that Davis could likely be helped by the medication and psychological counseling he would receive in á prison psychological medical unit.

Counsel exercised appropriate professional judgment in choosing to put Dr. Vicary on the stand despite the prospect that he might offer damaging information. When the effort to postpone the penalty phase and bring in a new psychiatric expert failed, defense counsel quite reasonably decided that the risk of a slight unknown was preferable to presenting no psychiatric testimony. Precisely because Davis’s background was susceptible to leverage as a result of abuse, poverty, drugs, or other factors, Davis needed someone who could nevertheless put together the pieces to demonstrate, as Dr. Vicary did, that Davis was not entirely a creature of his own making, that he had psychological problems, and that hope existed for some type of rehabilitation.

The fact that counsel had concerns about what Dr. Vicary might say on the stand is a far cry from the kind of professional incompetence evidenced by initiating contact with a psychiatric expert just days *649 before trial, see Clabourne v. Lewis, 64 F.3d 1373, 1387 (9th Cir.1995) (ultimately holding that counsel’s “representation at the sentencing hearing ‘amount[ed] in every respect to no representation at all’” (citation omitted) (alteration in original)), or asking a defendant to switch into his alternate personality on the stand with no idea what he might offer up, see Wade v. Calderon, 29 F.3d 1312, 1323-24 (9th Cir.1994). Indeed, allowing Dr. Vicary to testify candidly about the negatives may have served to enhance the psychiatrist’s credibility on other points.

Significantly, most of the adverse evidence offered by Dr. Vicary was already in front of the jury. The jury knew that Davis had committed offenses as a juvenile and that he had been involved in domestic violence incidents. The jury itself had already come to the conclusion that Davis killed Holman; that decision was what brought them to the penalty phase. Had Dr. Vicary suggested that their decision was in error, the jury might well have discounted his mitigating testimony.

Dr. Vicary also gave the jurors their only clear sign that Davis might be able to function well in an institutional setting. Although the crime that Davis committed was brutal and sexual in nature, Dr. Vicary testified that Davis could survive and even thrive in a setting in which he was provided with structure and sympathy.

Even the ASPD diagnosis was not substantially prejudicial. Any psychiatrist that Davis used would have read the same psychological report and likely come to the same conclusion. Counsel did a reasonable job on redirect of mitigating the effects of the diagnosis.

Davis also argues that Dr. Vicary’s testimony on aggravating factors was inadmissible because there was no foundation for his opinion, the testimony was beyond the scope of the direct, and the evidence was irrelevant. His claim is unavailing. The California Supreme Court found that the testimony was neither beyond the scope of direct examination nor irrelevant. Foundation stemmed from Dr. Vicary’s review of the materials on which he based his mitigating testimony. Because the prosecutor was entitled under California law to elicit Dr. Vicary’s opinion on aggravating factors, defense counsel’s failure to lodge a serious objection to the prosecutor’s question was neither ineffective assistance of counsel nor prejudicial.

Dr. Vicary did a more than adequate job of taking the strands provided by the lay witnesses and weaving together a sympathetic psychiatric portrait. The possibility that cross-examination might diminish the force of his testimony was inevitable. Because Davis’s counsel made an informed choice to put Dr. Vicary on the stand and had access to materials that should have alerted them to his diagnosis, and because Dr. Vicary was able to provide mitigating testimony across a range of areas, the decision to use Dr. Vicary neither constituted ineffective assistance of counsel nor substantially prejudiced the outcome of the penalty phase of Davis’s trial.

III. Other Ineffective Assistance of Counsel Claims

A. Sharon Brubaker’s Testimony

The defense called Davis’s former probation officer, Sharon Brubaker, who had written a diversion report six years before on a domestic violence incident involving Davis and his then wife, Laura King. Brubaker testified that the circumstance was an appropriate one for diversion, whereby Davis would have been shunted to a domestic violence program rather than going through formal proceedings, but that she had recommended that Davis not be diverted due to his prior *650 record, including his juvenile incidents. The prosecutor used Brubaker’s reference to Davis’s criminal record as a platform to recount Davis’s -criminal infractions. Davis contends that the decision to put Brubaker on the stand constituted ineffective assistance of counsel.

On direct and redirect, counsel clarified and minimized Brubaker’s potentially damaging testimony by highlighting her views that the violence toward King was more minor than King reported; that the violent incidents in Davis’s history were few and far between; and that the last offense had occurred five years before Holman’s murder. The main incident that persuaded Brubaker not to divert Davis was one in which he broke a window while drunk— hardly an offense that would persuade a jury to impose death.

Counsel also elicited on redirect that Davis had no felony convictions as an adult; his only adult crimes prior to the murder were the incident for which she evaluated him and the broken window. Brubaker’s report also supported Dr. Vi-cary’s argument that Davis had been deprived of some opportunities to turn his life around since Davis could have received diversion and did not. Finally, the testimony was partially cumulative, as King had already testified about the worst incident — the domestic violence offense, itself — and the jury already knew that Davis had committed juvenile offenses. The tactical decision to call Brubaker cannot be characterized as ineffective assistance of counsel.

, B. Failure to Introduce Additional Lay Witnesses

During the penalty phase, Davis’s counsel introduced fourteen mitigation witnesses. Defense investigators interviewed fifteen other witnesses. Davis faults his counsel for failing to call those additional mitigation witnesses.

The district court chose not to hold an evidentiary hearing on this issue because Davis failed to allege the specific mitigating evidence the witnesses would have presented. Characterizing as “conclusory” Davis’s allegations regarding the additional information that those potential witnesses might offer, the court held that Davis’s notice pleading was insufficient. See O’Bremski v. Maass, 915 F.2d 418, 420 (9th Cir.1990). We agree and further note that even if counsel had called the additional witnesses, their testimony would have been either negative or cumulative. Finally, as to seven of the witnesses, Davis failed to raise this claim in state court, and is therefore precluded from pursuing it here.

C. “Rude and Hostile” Closing Argument

Davis’s two defense attorneys split the closing argument at the end of the penalty phase. Davis maintains that the first closing argument so annoyed and angered the jury that his sentence was affected. We reject his claim, and conclude that counsel’s' actions neither constituted ineffective assistance of counsel nor prejudiced the outcome of the penalty phase.

The first defense attorney began his closing argument by saying, “We will start right out with a comment that I have a strong belief that some of you have already decided this phase of the case to yourselves and to those, probably ... nothing I can say is going to have any particular value.” Counsel took issue with the jury’s decision in the guilt phase, saying, “I would like to talk about Davis [] from a standpoint of someone who does not believe that the evidence in this case was sufficient to justify] your verdict pre *651 viously rendered but with an acceptance that that is the way it is.” Counsel further told jurors, “Now you can poo-poo and shake your head and give me that ‘BS’ look if you wish, and that is fine.” Finally, counsel told the jury, “You’re going to make your decision regardless of what any of us say here and I’d like you to consider a couple of points.”

These statements were part of a closing argument spanning fifty pages. Counsel spent most of his time summarizing the case and asking the jury not to impose the death penalty. Although counsel’s language appeared to denigrate the jurors’ guilt-phase decision, his choice of words could equally have been a legitimate trial strategy of challenging the jurors to recognize the import of their guilt-phase decision and the significance of the determination they were about to make.

In addition, these remarks were countered by co-counsel, who made a point of telling the jury that “I take it that you did your job sincerely and as honestly as you could, as you swore you would do earlier when you were all picked to serve on this jury, and that you followed the law and that’s what you did. And I respect that.” He later added, “I ... disagree with Mr. Maxwell — respectfully so — that I don’t believe any one of you have made up your minds at this point.”

We acknowledge that, however perceived, the strategy may seem unusual on the written record. Nonetheless, in view of the strong evidence in the penalty phase, the legitimate and substantive arguments made by both counsel, and the second counsel’s mitigation efforts, we conclude that the closing argument does not demonstrate the prejudice required under Strickland, 466 U.S. at 695 , 104 S.Ct. 2052 (holding that to demonstrate prejudice, a petitioner must demonstrate “a reasonable probability that, absent the errors, the sentencer ... would have concluded that the balance of aggravating and mitigating circumstances did not warrant death”).

IY. Claimed Jury Bias

After instructing the jury but before deliberations, the court received a note from R.C. Schwartz, the foreman during both phases of the trial. The note read:

[Unrelated seventh question omitted.]

*652 It was not clear whether the note was from Schwartz only or from some larger faction of the jury. Davis’s counsel asked the court to dismiss Schwartz and to inquire whether any of the jurors had discussed the case or the law. The judge denied the request and reasoned that, because the California Supreme Court had in similar situations approved curative instructions, it would be unreasonable to conclude that the note indicated an incurable impropriety. When the jury convened the next morning, prior to the final two closing arguments, the judge briefly mentioned the note and then gave the jury the following comprehensive explanatory instructions, taken directly from People v. Hunter, 49 Cal.3d 957, 981-82 , 264 Cal.Rptr. 367 , 782 P.2d 608, 621-22 (1989) (approving of a trial judge’s decision to answer jury questions with instructions on commutation, the effect of a life sentence, and the jurors’ duties):

Several months after the trial ended, Schwartz wrote a letter to a Ventura County newspaper approving of the outcome in the trial. Davis alleges that the questions Schwartz submitted to the judge in combination with his letter demonstrated a pro death penalty bias. Davis also contends that the use of the pronoun “we” in the questions raised the inference that the jury may have discussed the case before submission. Davis therefore argues that the trial judge should have conducted an inquiry, that the letter established bias, and that the proper remedy is to remand for an evidentiary hearing before the district court or a retrial of the penalty phase.

The Ninth Circuit takes the spectre of jury bias very seriously. We have emphasized that “even a single partial juror violates a defendant’s constitutional right to fair trial.” United States v. Angulo, 4 F.3d 843, 848 (9th Cir.1993). We have also admonished that “[a] court confronted with *653 a colorable claim of juror bias must undertake an investigation of the relevant facts and circumstances.” Dyer v. Calderon, 151 F.3d 970, 974 (9th Cir.1998) (en banc).

Were we to assume that premature deliberations occurred, such an exchange, though not necessarily proper, is not as serious as “private communication, contact, or tampering ... with a juror during a trial [or] ... influence of the press upon the jury,” nor does “every incident of juror misconduct require[ ] a new trial.” United States v. Klee, 494 F.2d 394, 396 (9th Cir.1974) (internal citations and quotation marks omitted). What is crucial is “not that jurors keep silent with each other about the case but that each juror keep an open mind until the case has been submitted to the jury.” Id. Although a hearing might have laid to rest any lingering question about premature deliberations or bias, we do not construe the circumstances as mandating a hearing then or now. The judge’s instructions were sufficient to cure any possible prejudice.

Just three years ago, we addressed virtually the identical issue in Anderson v. Calderon, 232 F.3d 1053 (9th Cir.2000). Prior to deliberations, one of the jurors submitted a note to the judge asking, “Does life without possibility of parole really mean that? Or can Anderson, under the sentence, at some future time be released?” Id. at 1098 . As is the ease here, we first noted that, although there was some evidence that the juror may have discussed the penalty with other jurors, it was not clear whether such communication had actually occurred. Id. Notwithstanding any possible juror misconduct, however, we concluded that Anderson’s claim failed

Id. at 1098-99 (quoting Klee, 494 F.2d at 396 ).

Similarly, we see no evidence in Davis’s case that any of the jurors relied on extrinsic evidence in reaching a death verdict, or .that any of the jurors reached a sentencing determination prematurely. Davis “is entitled to a fair trial, but not a perfect one, for there are no perfect trials.” McDonough Power Equip., Inc. v. Greenwood, 464 U.S. 548, 553 , 104 S.Ct. 845 , 78 L.Ed.2d 663 (1984) (internal citations and quotation marks omitted). The trial court’s decision not to hold a hearing on juror bias is not “inconsistent with substantial justice,” id. (quoting Fed.R.Civ.P. 61), and the district court did not abuse its discretion in denying the request for an evidentiary hearing.

Y. Confrontation Clause

During cross-examination, the prosecutor showed Dr. Vicary a note from a jailhouse informant, which the judge admonished the jury was solely for impeachment purposes. In the note, the informant relayed that he had said to Davis, “Everyone says you killed her because she looked like your wife. Did you [think] it was your wife you were strangling?” According to the note, Davis replied, “Yeah, it should have been,” and the two prisoners laughed. Dr. Vicary agreed that, assuming the note was accurate, Davis’s response might be inconsistent with his feeling remorse over killing Holman. Davis argues that the use of the note — over defense counsel’s objections — violated his Sixth Amendment right to confront witnesses.

*654 This constitutional claim is procedurally barred because Davis raised only an evi-dentiary, not a constitutional, objection at trial. The California Supreme Court noted that Davis was raising his Sixth Amendment claim for the first time on appeal, and held that

People v. Davis, 10 Cal.4th at 531 n. 26, 41 Cal.Rptr.2d 826 , 896 P.2d at 156 n. 26 (internal citations and quotation marks omitted).

When, “a state prisoner has defaulted his federal claim in state court pursuant to an adequate and independent state procedural rule,” federal habeas review is barred. Vansickel v. White, 166 F.3d 953, 957 (9th Cir.1999) (citing Coleman v. Thompson, 501 U.S. 722, 750 , 111 S.Ct. 2546 , 115 L.Ed.2d 640 (1991)). The California Supreme Court’s opinion was the “last reasoned” opinion by a state court, see Ylst v. Nunnemaker, 501 U.S. 797, 803 , 111 S.Ct. 2590 , 115 L.Ed.2d 706 (1991), and its disposition of Davis’s Confrontation Clause claim clearly rests on his procedural error in failing to raise the constitutional issue below. See Harris v. Reed, 489 U.S. 255, 263 , 109 S.Ct. 1038 , 103 L.Ed.2d 308 (1989) (“[A] procedural default does not bar consideration of a federal claim on either direct or habeas review unless the last state court rendering a judgment in the case ‘clearly and expressly’ states that its judgment rests on a state procedural bar.” (citation omitted)).

Because the California Supreme Court held that Davis’s claim was procedurally barred under state law, he must demonstrate cause and prejudice to obtain habeas relief under state law. Wainwright v. Sykes, 433 U.S. 72, 90-91 , 97 S.Ct. 2497 , 53 L.Ed.2d 594 (1977). Davis has demonstrated neither. He offers no explanation for the failure to raise this issue in a timely fashion. In addition, the jury had already determined that Davis murdered Holman, and had heard testimony as damaging as the informant’s note. Davis therefore has not established prejudice of a magnitude resulting in a fundamental “miscarriage of justice.” Schlup v. Delo, 513 U.S. 298, 316 , 115 S.Ct. 851 , 130 L.Ed.2d 808 (1995).

VI. Cumulative Error

Finally, Davis urges us to consider whether defense counsel’s various errors rendered his trial cumulatively unfair, thus requiring reversal of both his conviction and death sentence. It is true that, although individual errors may not rise to the level of a constitutional violation, a collection of errors might violate a defendant’s constitutional rights. Harris v. Wood, 64 F.3d 1432 , 1438 (9th Cir.1995). The cumulative error doctrine does not aid Davis, however, because we are not faced with such a case. As our discussion of the ineffective assistance claims illustrates, Davis has not demonstrated prejudice as to the individual claims, and the nature of the claims does not support a conclusion of cumulative prejudice. Counsel’s few missteps and misjudgments did not render Davis’s trial fundamentally unfair, and the district court therefore did not err in failing to hold an evidentiary hearing on his cumulative error claim.

Because Davis has failed to satisfy AEDPA’s standard for grant of habeas relief, the petition is DENIED.

. Davis requests an evidentiary hearing on: (1) ineffective assistance of counsel in the guilt phase; (2) ineffective assistance of counsel at the penalty phase; (3) ineffective assistance of 'counsel with respect to his expert's testimony; (4) his competence in the penalty phase; (5) juror bias; and (6) cumulative effect of errors. He seeks reversal of, summary judgment on the following bases: (1) denial of severance of the Suzanne H. and Holman charges; (2) sufficiency of the evidence; (3) prosecutorial vouching; and (4) violation of Confrontation Clause rights.

. Although Davis disputes such a concession, he did not argue lack of cross-admissibility to the California Supreme Court and, in any event, the court’s decision rested on the code of evidence rather than the disputed admission.

. We note the California Supreme Court's admonition, however, that the "Anderson analysis was intended only as a framework to aid in appellate review; it did not propose to define the elements of first degree murder .... The Anderson guidelines ... are not a definitive statement of the prerequisites for proving premeditation and deliberation in every case.” People v. Hawkins, 10 Cal.4th 920, 957 , 42 Cal.Rptr.2d 636 , 897 P.2d 574, 595 (1995) (internal citations and quotation marks omitted).