California state prisoner Demetrie La-don Mayfield appeals the district court’s denial of his habeas petition brought pursuant to 28 U.S.C. § 2254 . Mayfield’s petition challenges his 1983 convictions in San Bernardino County on two counts of first degree murder and his subsequent death sentence. In his petition, Mayfield argues that he was denied effective assistance of counsel at both the guilt and penalty phases of his trial, that the jury instructions were unconstitutional, and that California’s death penalty scheme under which he was sentenced violates the Eighth and Fourteenth Amendments. We have jurisdiction pursuant to 28 U.S.C. § 1291 and 28 U.S.C. § 2253 , and we affirm.

In December 1982, Mayfield was arrested while driving a stolen 1968 Pontiac. When arrested, Mayfield claimed that he had recovered the car from the actual thief and was on his way to return it to its rightful owners, his friend Byron Pope and Byron’s mother, Ora Pope. The Popes pressed charges against Mayfield for the theft. On January 14, 1983, he pled guilty to a misdemeanor charge of joyriding and was released on his own recognizance pending sentencing.

On the night of February 2, 1983, May-field went to the Pope residence armed with a sawed off shotgun and two shells. He entered the house by removing the bedroom window with a screwdriver and, once in the house, he loaded and cocked the shotgun. Mayfield went into the living room where Ora Pope and her friend, Edward Moreno, were seated on a couch, drinking and listening to music. Mayfield aimed the shotgun at Ora and confronted her about the car theft charges. During the conversation, Ora got up, either to light a cigarette or to come at Mayfield, and Mayfield, startled by her sudden movement, pulled the shotgun’s “hair” trigger killing Ora. He then reloaded the gun and killed Moreno.

Mayfield dragged the bodies, with Ora still showing signs of life, to an outside storage shed. He hosed the blood off the pavement, retrieved the two spent shells, locked the house, and replaced the bedroom window. Mayfield went to the house of his friend, Patricia Harper, and hid the shotgun. Harper testified that “[h]e said he did it. It slipped. He didn’t mean to. And then he had to.... He had to do the second one.” Before leaving Harper’s house, Mayfield told her that he was “going to go wait for Byron, too,” and going to “get Byron, too.”

To prevent the discovery of his crimes, Mayfield waited outside the Pope residence for Byron carrying a knife. When Byron arrived at the house, Mayfield confronted him and the two fought. After discussing the car theft charges for an extended period, Mayfield succeeded in forcing Byron to leave without entering the house. Mayfield then returned home where the police found him the next morning.

During a lengthy interrogation in which the police confronted Mayfield with the evidence collected against him, Mayfield confessed to the killings. The following day, Mayfield provided a videotaped reenactment of the crimes. In both the confession and the re-enactment, Mayfield admitted to killing Ora and Moreno, but he claimed that the killing of Ora was an accident.

At trial, the prosecution presented evidence describing the crimes and the events that immediately preceded and followed them. Evidence was offered that, on the day of the killings, Mayfield told others that he was going to kill Ora. The prosecution then played for the jury an excerpt from Mayfield’s audiotaped statement to the police and the entire videotaped reenactment of the crime. Defense counsel did not make an opening statement to the jury nor did he present any witnesses. The defense consisted of cross examinations of prosecution witnesses, playing the audiotaped confession for the jury in its entirety, and presenting closing argument. In closing argument, defense counsel conceded that the killing of Ora was at minimum voluntary manslaughter and the killing of Moreno was at minimum second degree murder. He argued, however, that the jury should believe Mayfield’s statements to the police and his friend, Patricia Harper, that the killing of Ora was an accident and therefore did not constitute murder. He further posited that the killing of Moreno may not have amounted to first degree murder because it was possible that Mayfield was not acting with premeditation and deliberation when he shot Moreno. The jury found Mayfield guilty of two counts of first degree murder and found true the special circumstance allegation of multiple murder.

At the penalty phase, the prosecution presented evidence of two incidents of violent criminal conduct — that he fired a rifle into an ex-girlfriend’s house while her family was in the house and that he physically assaulted another ex-girlfriend. Defense counsel again waived opening statement and presented only one witness, Dr. Craig Rath, a clinical psychologist. Dr. Rath described Mayfield’s background including the fact that he was the oldest of five illegitimate siblings, abused drugs and alcohol, and suffered from juvenile-onset diabetes for which he had been hospitalized on numerous occasions. Dr. Rath reported that psychological tests revealed that Mayfield was in the low, average range of intelligence, “emotionally immature, but not psychotic” and suffered from mild or-ganicity.

Dr. Rath then expressed his opinion that the murders were out of character for Mayfield. His opinion was consistent with that of Dr. Hunt, a neurologist, who had also examined Mayfield. Although Dr. Hunt did not testify, Dr. Rath read a portion of a report in which Dr. Hunt concluded that “[ajlthough [Mayfield] has shown rather poor judgment in the past, particularly in earing for himself, the crime of which he is accused is out of character and can be explained only on the basis of definite cerebral impairment due to alcohol and drug abuse.” Dr. Rath further testified that Patricia Harper had told him that Mayfield was a gentle person who had helped her over the years take care of her children. Dr. Rath told the jury that Mayfield had expressed “considerable remorse” for the killings.

In rebuttal, the prosecution called Dr. William Soltz, a psychologist who had examined Mayfield shortly after his arrest. Dr. Soltz testified that Mayfield told him that he was a light drinker, did not use drugs, and that his mind was clear on the day of the killings. Dr. Soltz opined that the killings were “intentional and deliberate” and not the result of a mental problem related to drug use. He found that the killings were consistent with Mayfield’s reactions to other tense situations.

After two days deliberation, the jury found that Mayfield should be sentenced to death. Before sentencing Mayfield, the trial court held a hearing, pursuant to Cal. Pen.Code § 190.4(e), to rule on Mayfield’s automatic motion for modification of the death verdict to life without parole. The judge stated that he was troubled by having to impose a death sentence on May-field; that he had perceived this case as a “different type of case” than other death penalty cases he had tried. He also stated that he was troubled by Mayfield’s young age and that “[h]is lack of criminal activity in the past [was] of merit or [had] been— there has been some relatively minor incidents of violence.” He noted, however, that apart from Dr. Rath’s testimony, which he did not find compelling, the defense had offered no other evidence in mitigation. Despite his hesitation, the trial judge denied the motion to reduce the sentence because he found that “the factors in aggravation beyond a reasonable doubt outweigh those in mitigation.”

The California Supreme Court affirmed Mayfield’s conviction and sentence on direct appeal. People v. Mayfield, 5 Cal.4th 142 , 19 Cal.Rptr.2d 836 , 852 P.2d 331 (1993), cert. denied, 512 U.S. 1253 , 114 S.Ct. 2780 , 129 L.Ed.2d 892 (1994). While his direct appeal was pending, Mayfield filed a habeas corpus petition in state court. The California Supreme Court appointed a referee to take evidence and make findings of fact regarding Mayfield’s claim of ineffective assistance of counsel at the guilt and penalty phases of the trial.

At the reference hearing, Mayfield presented several witnesses who could have testified on his behalf, including family members, friends, and medical experts. If Mayfield’s family and friends had been called, the jury would have heard additional evidence about Mayfield’s disadvantaged background, about his struggles with diabetes and substance abuse, and his general psychological decline in the time immediately preceding the crimes. The referee found, however, that “some of them would have given negative as well as positive information to the jury.” For example, Mayfield’s mother, may have told the jury negative things about Mayfield if called to testify, including that “she caught petitioner trying to ‘have sex’ with his sister when she was only four or five months old” and that she had engaged in physical altercations with Mayfield in the past.

The medical experts could have offered additional evidence relating to Mayfield’s insulin-dependent diabetic condition and his ingestion of PCP, and their possible side effects on his behavior at the time of the crimes. For example, Dr. Clinton Young, an endocrinologist, testified at the reference hearing that a diabetic with a blood-sugar level of 371, Mayfield’s level following his arrest, may experience blurred vision, impaired reasoning, dehydration, confusion, headaches, nausea and fatigue. On cross-examination, Dr. Young admitted that he could not extrapolate what Mayfield’s blood-sugar level was at the time of the crimes. He further admitted that diabetes does not normally impair reasoning to the extent that it causes a person to do something he would not otherwise do. Dr. David Smith, a toxicologist, testified about the general effects of PCP consumption and the particular effects that it can have on diabetics. Dr. Smith expressed the view that Mayfield’s reasoning process and impulse control at the time of the shootings may have been impaired due to a combination of PCP abuse and flashbacks, alcohol abuse, out-of-control diabetes, and depression. Dr. Rita Hargrave, a psychiatrist, testified about the psychological trauma that Mayfield suffered as a result of his chronically out-of-control juvenile-onset diabetes. She opined that the combination of Mayfield’s mental disorders, diabetes, and abuse of PCP, may have caused mental impairments at the time of the crimes.

The referee found that Mayfield’s trial counsel failed to fully investigate the defense of lack of intent by reason of intoxication or disease and failed to interview witnesses who could have possibly helped Mayfield’s defense in both the guilt and penalty phases of his trial. He described trial counsel’s preparation as “scanty.” The referee found that Mayfield’s counsel should have interviewed Mayfield’s family and friends to gather helpful information. Because there was a risk that cross-examination of some of these witnesses might have produced damaging testimony, May-field’s counsel could have fed the helpful information to Dr. Rath so that he could use it as a basis for his opinions and get it before the jury without cross-examination. The referee also concluded that Mayfield’s counsel should have consulted endocrinologists, toxicologists and psychiatrists for their assistance at the penalty phase. He did not reach the question of whether evidence from these medical experts would have made a difference in the outcome, leaving that question for the California Supreme Court.

The California Supreme Court accepted the referee’s findings of fact but denied the petition for habeas corpus because it found that Mayfield failed to establish that he was prejudiced by counsel’s performance. Thereafter, the United States Supreme Court denied Mayfield’s petition for writ of certiorari.

On June 21, 1995, Mayfield filed a petition for writ of habeas corpus in the federal district court. The district court found that Mayfield had not presented any claim which warranted relief and therefore denied his petition.

Mayfield filed a timely appeal on November 25, 1997. On December 1, 1997, the district court issued a certificate of probable cause (“CPC”), finding that May-field “has made at least one claim in his petition for writ of habeas corpus which makes a substantial showing of the denial of a federal constitutional right and which presents a question of some substance.”

We review de novo the district court’s decision to deny Mayfield’s habeas petition. See Smith v. Stewart, 140 F.3d 1263, 1267 (9th Cir.1998). Because May-field filed his habeas petition on June 6, 1995, prior to the effective date of the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”), the Act’s more stringent standards for issuance of a writ of habeas corpus do not apply. See Lindh v. Murphy, 521 U.S. 320, 327 , 117 S.Ct. 2059 , 138 L.Ed.2d 481 (1997).

However, because Mayfield initiated his habeas appeal on November 25, 1997, after AEDPA’s effective date, his right to appeal is governed by the certificate of appealability (“COA”) requirements of AEDPA. Slack v. McDaniel, — U.S. -, -, 120 S.Ct. 1595, 1603 , 146 L.Ed.2d 542 (2000). The CPC issued by the district court does not suffice. Rather, we treat Mayfield’s notice of appeal as an application for a COA and then determine whether Mayfield has met the requirements for a COA. Id. (citing Fed. Rule App. Proc. 22(b) and Fed. Rule Civ. Proc. 8(f)). “Under AEDPA, a COA may not issue unless ‘the applicant has made a substantial showing of the denial of a constitutional right.’ ” Id. (quoting 28 U.S.C. § 2253 (c)). Where, as here, the district court has rejected a petitioner’s constitutional claims on the merits, “the showing required to satisfy § 2253(c) is straightforward: The petitioner must demonstrate that reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.” Id. at 1604.

Ill

We have reviewed the record and the district court’s well-written and thorough order denying the petitioner’s writ of ha-beas corpus and also Mayfield’s numerous challenges to the district court’s order dismissing his habeas petition. We conclude based upon the district court’s findings and reasoning in its order that Mayfield has demonstrated that “reasonable jurists would find the district court’s assessment ... debatable” with respect to only the issue of ineffective assistance of counsel at the penalty phase of the trial. We therefore grant the COA with respect to that issue alone and deny the COA with respect to all other issues raised by Mayfield’s petition, including: (1) the claim of ineffective assistance of counsel at the guilt phase of the trial; (2) the claim of ineffective assistance of counsel due to conflicts of interest; (3) the claim that the guilt phase jury instructions violated the Constitution; (4) the claim that penalty phase jury instructions violated the Constitution; and (5) the claim that California’s death penalty scheme is unconstitutional.

Mayfield’s claim of ineffective assistance of counsel at the penalty phase raises mixed questions of law and fact. Strickland v. Washington, 466 U.S. 668, 698 , 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984). Accordingly, the presumption of correctness given to state court factual findings under former 28 U.S.C. § 2254 (d) does not apply to the ultimate resolution of May-field’s claim. However, we must apply the statutory presumption to the facts underlying the ineffective assistance of counsel claim or explain why the presumption is inapplicable. Burden v. Zant, 498 U.S. 433, 437 , 111 S.Ct. 862 , 112 L.Ed.2d 962 (1991); Sumner v. Mata, 455 U.S. 591, 597 , 102 S.Ct. 1303 , 71 L.Ed.2d 480 (1982). The presumption may be inapplicable if the state court’s factual determination lacks “fair support in the record” or if one of the other enumerated exceptions to § 2254(d) is met. Burden, 498 U.S. at 437 , 111 S.Ct. 862 ; Parker v. Dugger, 498 U.S. 308, 320 , 111 S.Ct. 731 , 112 L.Ed.2d 812 (1991). The presumption of correctness applies to all state court factual findings, whether trial, appellate or post-conviction. Tomlin v. Myers, 30 F.3d 1235, 1242 (9th Cir.1994); Neuschafer v. McKay, 807 F.2d 839, 841 (9th Cir.1987).

Mayfield contends that his trial counsel inadequately investigated and inadequately presented mitigating evidence about his background and mental health at the penalty phase trial. He also argues that, in giving a short perfunctory closing argument, his counsel essentially abandoned him and thereby left him without the Sixth Amendment representation to which he was entitled. He claims that the representation during the penalty phase trial “fell below an objective standard of reasonableness.” Strickland, 466 U.S. at 688 , 104 S.Ct. 2052 .

To prevail on the claim of ineffective assistance, Mayfield must show, in addition to deficient performance, resulting prejudice. To show prejudice at sentencing, Mayfield must show that “there is a reasonable probability that absent the error, the sentencer ... would have concluded that the balance of aggravating and mitigating circumstances did not warrant death.” Strickland, 466 U.S. at 695 , 104 S.Ct. 2052 . The district court found that Mayfield’s counsel provided deficient performance at the penalty phase. It denied relief, however, because it found that “no reasonable probability exists that the jury would have returned a sentence of life without possibility of parole” if the jury had heard the available mitigating evidence.

California’s statutory scheme permits a jury to impose a sentence of death if it finds that the aggravating factors outweigh the mitigating factors. See Cal. Pen. C. § 190.3, CALJIC 8.84.2. Here, the prosecution argued the following aggravating factors were present: the manner in which the murders were carried out, the motives for the murders, and the fact that Mayfield had previously exhibited criminal violent conduct. The mitigating factors presented by the defense through the testimony of Dr. Rath included: May-field’s background as an illegitimate child raised by a single parent; the diagnosis of juvenile-onset diabetes at age nine; his numerous hospitalizations due to inadequate control of the diabetes; the family difficulties which arose as a result of the diabetes; his history of drug abuse; his considerable remorse for the crime; the opinions of Dr. Rath and Dr. Hunt that his crime was out of character; Dr. Hunt’s opinion that the crime can be explained only on the basis of cerebral impairment due to alcohol and drug abuse; and his friend’s description of him as a gentle person. The jury considered all of these aggravating and mitigating factors before sentencing Mayfield to death. We do not address whether Mayfield’s counsel’s performance was constitutionally deficient because we agree with the district court that there is no reasonable probability that, presented with additional mitigating evidence and more effective advocacy, a jury would have found that the aggravating circumstances did not outweigh the mitigating circumstances. See Strickland, 466 U.S. at 694 , 104 S.Ct. 2052 .

Although this is not a case in which the aggravating factors are so overwhelming that there is little likelihood that mitigating evidence could have made a difference, cf. Bonin v. Calderon, 59 F.3d 815, 836 (9th Cir.1995), Mayfield’s counsel did present several mitigating factors to the jury through Dr. Rath’s testimony, cf. Smith v. Stewart, 140 F.3d 1263, 1269 (9th Cir.1998) (counsel presented no evidence at penalty phase), and the mitigating evidence that counsel failed to introduce at the penalty phase is neither compelling nor exculpatory. See Mak v. Blodgett, 970 F.2d 614, 621-22 (9th Cir.1992) (exculpatory nature of the proffered mitigating evidence is an important factor in Strickland prejudice analysis). Much of the mitigating evidence presented at the reference hearing would have been cumulative of Dr. Rath’s testimony at the penalty phase. See Babbitt v. Calderon, 151 F.3d 1170, 1175 (9th Cir.1998) (no prejudice from failure to call witnesses where testimony would have been cumulative). As the district court found, Mayfield was not prejudiced by his counsel’s failure to call Dr. Hunt or Patricia Harper because Dr. Hunt’s opinion and Harper’s character testimony were provided to the jury through Dr. Rath’s testimony. Although the other medical experts could have testified in greater detail than Dr. Rath about the interaction between Mayfield’s diabetes, his history of drug use and his mental state, Dr. Rath did address each of these individual factors and opined that May-field’s conduct was out of character, implicitly suggesting that his drug use and diabetes played a role in his criminal behavior. Moreover, Dr. Rath read Dr. Hunt’s report for the jury which directly made the connection between the shootings and Mayfield’s “cerebral impairment” from alcohol and drug abuse.

Apart from its cumulative nature, the value of the omitted expert testimony was lessened by the California Supreme Court’s factual finding that none of the medical experts who testified at the reference hearing “could state unequivocally that [Mayfield’s] consumption of food, drugs or alcohol had altered his mental state in a definite or predictable manner.” 5 Cal.4th at 205 , 19 Cal.Rptr.2d 836 , 852 P.2d 331 . Rather, they “could only surmise that his mental state was abnormal when he committed the murders” and such testimony was undermined by “strong evidence to the contrary.” Id. at 208 , 19 Cal.Rptr.2d 836 , 852 P.2d 331 . Because the expert testimony presented by May-field at the reference hearing was largely repetitive of Dr. Rath’s testimony and had little exculpatory value, Mayfield was not prejudiced by its omission.

Nor did Mayfield suffer prejudice as a result of his counsel’s failure to present testimony from his family and friends. At least some of this proposed testimony would have overlapped with Dr. Rath’s description of Mayfield’s childhood, the difficulties arising from the diagnosis of juvenile-onset diabetes and the subsequent hospitalizations, his drug problem, and Patricia Harper’s statements about his gentle nature and his willingness to babysit her children. Further, as the state referee found, the testimony of Mayfield’s family and friends, unless filtered through Dr. Rath, could have opened the door for damaging rebuttal testimony, particularly from Mayfield’s mother. This factor weighs against a finding of prejudice. See Strickland, 466 U.S. at 700 , 104 S.Ct. 2052 (no prejudice in failure to present evidence because the overwhelming aggravating circumstances outweighed the mitigating circumstances and the proffered evidence would have opened the door to harmful and conflicting evidence); Campbell v. Kincheloe, 829 F.2d 1453, 1464 (9th Cir.1987) (failure to present mitigating evidence not prejudicial in part because mitigating evidence could have been met with strong rebuttal evidence).

In addition, as the district court recognized, testimony from Mayfield’s family and friends about his nonviolent nature and love for his family would likely ring hollow if presented to a jury which had already accepted the prosecution’s version of the premeditated killings as evidenced by the guilty verdict. Mayfield’s counsel also understood the danger in parading Mayfield’s family before the jury under such circumstances and indicated at the reference hearing that he had made a tactical choice not to do so. The danger, as summed up by the California Supreme Court, was that “the jury might indignantly or cynically draw a parallel between the victims’ families, devastated in the jurors’ minds by petitioner’s crimes, and petitioner’s own family, which was evidently untouched by murder.” 5 Cal.4th at 208 n. 15, 19 Cal.Rptr.2d 836 , 852 P.2d 331 . Because this mitigating testimony from May-field’s family and friends would have repeated many of the topics discussed by Dr. Rath, opened the door for damaging rebuttal evidence, and risked alienating jurors, Mayfield was not prejudiced by his counsel’s failure to present such evidence at the penalty phase.

AFFIRMED.