Opinion by Judge HAWKINS; Partial Concurrence and Partial Dissent by Judge THOMAS.

Appellant George Lopez (“Lopez”) was convicted in Arizona state court of child abuse and felony murder of his one-year-old son and sentenced to death. In this post-Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”) habeas proceeding, he presents one certified issue: whether the state trial court denied Lopez his rights under the Eighth Amendment by failing to consider mitigation evidence presented at trial. He also seeks to expand the certificate of appealability (“COA”) to include four additional issues, including the Arizona Supreme Court’s review of his death sentence and three ineffective assistance of counsel claims. We affirm in part, reverse in part, and remand for further proceedings.

FACTS AND PROCEDURAL HISTORY

The relevant facts pertaining to the death of Lopez’s son, Anthony, are set forth in the Arizona Supreme Court’s opinion on direct review:

State v. Lopez, 174 Ariz. 131 , 847 P.2d 1078, 1081-83 (1992).

Lopez was indicted on one count of first-degree murder and one count of child abuse, and a jury convicted him on both counts. At an aggravation/mitigation hearing conducted prior to sentencing, Lo *1035 pez put on numerous friends and family members as witnesses, who testified that Lopez was a non-violent person who liked to help people and that he had never acted inappropriately toward their children or his own. Various community members testified concerning Lopez’s service in community organizations and the military, and about his positive employment history. A prison chaplain testified that Lopez was a cooperative and well-behaved inmate who regularly attended Bible study classes and helped other inmates, and could carry out his mission of helping others if given a life sentence. Another prison official testified that Lopez was cooperative and had no disciplinary reports.

The prosecution presented testimony from an expert witness, Dr. Hobeich, a pediatrician with expertise in child abuse. Dr. Hobeich testified about the pain Anthony likely experienced from his injuries, which he compared to “surgery without anaesthesia.” He also described symptoms of a child with Anthony’s injuries, including being “hot to the touch” and “lethargic” and lacking the power or energy for a full cry, making more of a “cat cry” instead to communicate pain before eventually losing consciousness. Dr. Hob-eich testified that Anthony was probably conscious and in pain for at least an hour, and that there was at least a possibility he could have survived his injuries if he had received treatment for them sooner. In closing arguments to the court, defense counsel relied on the mitigating evidence presented at the aggravation/mitigation hearing, but also made a substantial argument that the record did not demonstrate that Lopez ever intended to kill his son. The trial court found the state had proved two aggravating factors: that the defendant committed the offense in an especially heinous, cruel and depraved manner, and that the defendant was an adult and the victim was under the age of fifteen. The court found no statutory mitigating circumstances and indicated it had considered “all evidence presented by the defendant by way of mitigation.”

The court concluded:

The court then imposed the death penalty.

On direct appeal, a majority of the Arizona Supreme Court affirmed the conviction and sentence. Lopez, 847 P.2d at 1092 . The majority indicated it was undertaking an independent review of the record to determine whether the death sentence was appropriate, and concluded that the evidence supported the finding on the two aggravating factors, and that the trial court could properly find that the record refuted the proffered mitigation evidence. Id. at 1090-92. Two justices dissented from the imposition of the death sentence, faulting the trial court for failure to comply with an Arizona statute requiring specific findings regarding mitigating circumstances. Id. at 1092-93 (citing Ariz. Rev.Stat. § 13-703(D)).

Lopez then sought state collateral relief, raising, among other things, a number of claims regarding ineffective assistance of trial and appellate counsel. Following an evidentiary hearing, the superior court denied Lopez’s petition in its entirety. Lopez then filed a petition for review with the Arizona Supreme Court, again raising *1036 a number of ineffective assistance of counsel claims, including allegations that his counsel had “abandoned” him at the sentencing stage. The Arizona Supreme Court issued a postcard denial of this petition. Lopez’s petition for writ of certiorari to the United States Supreme Court was also denied.

Lopez then initiated this habeas action in federal district court. The district court found several claims to be unexhausted and dismissed those claims. Lopez subsequently returned to the state superior court, which denied some claims on procedural grounds and others on their merits. Petitions to the Arizona Supreme Court and United States Supreme Court were also denied. Lopez then returned to the district court and moved to amend his petition to add these now-exhausted claims, but the district court denied the motion, holding that amendment would be futile and would cause undue delay and prejudice to the government. The district court denied relief on the remaining claims on their merits. The district court then sua sponte issued a COA on the issue of whether Lopez’s constitutional rights were violated by the sentencing court’s failure to consider and give effect to mitigation evidence presented at trial. 1

STANDARD OF REVIEW

The district court’s denial of habeas relief is reviewed de novo. Barker v. Fleming, 423 F.3d 1085, 1091 (9th Cir.2005), ce rt. denied sub nom., Barker v. Spalding, — U.S. -, 126 S.Ct. 2041 , 164 L.Ed.2d 796 (2006).

Lopez’s appeal is governed by AEDPA. Under AEDPA, this court may not grant a writ of habeas corpus on behalf of a person in state custody unless the state’s adjudication of his claim “(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; 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).

In assessing whether a state court’s application of law or determination of fact is “unreasonable,” the court cannot simply consider whether it would have reached a different outcome on the same record. Rice v. Collins, 546 U.S. 333 , 126 S.Ct. 969, 976 , 163 L.Ed.2d 824 (2006) (stating that “Reasonable minds reviewing the record might disagree about” the ultimate issue is insufficient for habeas relief). Rather, “[t]he ‘unreasonable application’ clause requires the state court decision to be more than incorrect or erroneous.” Lockyer v. Andrade, 538 U.S. 63, 75 , 123 S.Ct. 1166 , 155 L.Ed.2d 144 (2003) (citing Williams v. Taylor, 529 U.S. 362, 410, 412 , 120 S.Ct. 1495 , 146 L.Ed.2d 389 (2000)). It requires the decision to be “objectively unreasonable.” Id. (citing Williams, 529 U.S. at 410 , 120 S.Ct. 1495 ).

DISCUSSION

I. The Sentencing Court’s Alleged Failure to Consider hand Give Effect to Mitigating Evidence Presented at Trial

Lopez’s one certified claim alleges that the state sentencing court failed to consider and give effect to all the mitigating evidence he presented. Lopez relies principally on Eddings v. Oklahoma, 455 *1037 U.S. 104 , 102 S.Ct. 869 , 71 L.Ed.2d 1 (1982), which held that a sentencing court could not refuse to consider a petitioner’s unhappy upbringing and emotional disturbance as mitigating evidence.

Here, however, the sentencing court did not prevent Lopez from presenting any evidence in mitigation, nor did it affirmatively indicate that there was any evidence it would not consider. Indeed, the sentencing court expressly stated that it “ha[d] considered all evidence presented by the defendant by way of mitigation.” Lopez acknowledges this statement, and also admits that a court is usually deemed to have considered all mitigating evidence where the court so states. See Clark v. Ricketts, 958 F.2d 851, 859 (9th Cir.1992); Parker v. Dugger, 498 U.S. 308, 314 , 111 S.Ct. 731 , 112 L.Ed.2d 812 (1991) (“We must assume that the trial judge considered all this evidence before passing sentence. For one thing, he said he did.”).

Lopez argues that the court’s statement is insufficient in this case because the judge made contradictory statements earlier during the aggravation/mitigation hearing which suggested she was excluding a “whole category of mitigation evidence”— evidence which was offered at trial but not reintroduced at the sentencing hearing. The genesis of Lopez’s argument is the court’s statement early in the proceedings that “[a]s to [the murder count] the Court is considering only those factors presented at the aggravation/mitigation hearing.” However, when the statement is placed in context, it does not carry the meaning Lopez would assign to it.

At the beginning of the sentencing hearing, the court ruled on various motions by Lopez to exclude statements by himself and the victim’s family which appeared in the presentence report. The court granted Lopez’s motion to strike these statements, “consistent with the Court’s decision to rely upon evidence received in trial and the presentence hearing.” (emphasis added). Shortly thereafter, the court stated:

(emphasis added). Having referenced the presentence report, the Court then went on to clarify, consistent with its earlier ruling:

When the court’s statement is put in this context, it is apparent that the judge was not announcing she was confining her consideration to only evidence that was introduced at the aggravation/mitigation hearing, but rather attempting to restate her ruling that she would not consider the statements in the presentence report.

Lopez argues that the statement is at least ambiguous and that we should not speculate as to whether all the mitigating factors were actually considered. As discussed above, however, the sentencing court’s statement is susceptible of Lopez’s interpretation only if read in isolation, and is certainly not enough to overcome the presumption that the state court knew and followed the law. See Woodford v. Visciotti, 537 U.S. 19, 24 , 123 S.Ct. 357 , 154 L.Ed.2d 279 (2002). Under AEDPA, we *1038 must do more than find the statement ambiguous — we would have to conclude that the Arizona Supreme Court was objectively unreasonable in concluding the sentencing court did, in fact, review all the proffered mitigating evidence. See Lockyer, 538 U.S. at 75 , 123 S.Ct. 1166 . Relying on the sentencing court’s express statements that it had read the presen-tence reports, heard the trial and the aggravation/mitigation hearing, and considered all evidence presented by Lopez, the Arizona Supreme Court concluded that “[t]he record before us clearly indicates that the trial judge considered all the mitigating factors presented by Lopez.” Lopez, 847 P.2d at 1091 . This is not an unreasonable determination of the facts in light of the record before it. See Parker, 498 U.S. at 314-15 , 111 S.Ct. 731 (assuming trial judge considered all mitigating evidence before passing sentence because he said he did and state law required him to). 2

Moreover, the sentencing judge clearly made findings that were based on trial evidence, thus negating the argument that the court only considered evidence from the aggravation/ mitigation proceeding. For example, the court found that Lopez “willfully and intentionally” abused the child, that the baby was entrusted to Lopez’s care, and that Lopez denied the child medical treatment to protect himself, although the actual circumstances of the crime and aftermath were not discussed by witnesses at the penalty phase hearing. In fact, it appears that at one point Lopez similarly viewed the record, as in one of his state post-conviction petitions, he asserted: “At sentencing, this court imposed the death penalty; it appears this court reached its decision to impose death in part from testimony at the guilt phase of the trial.” (emphasis added).

Lopez contends that the trial court must have failed to consider the trial record because it did not find the lack of intent to kill as a mitigating factor. Of course, the trial court did not specifically discuss any of the mitigating evidence that Lopez presented, so a failure to discuss this factor does not necessarily indicate it was not considered. In addition, on the date the court pronounced sentence, Lopez’s counsel made an argument before the court that was primarily based on the lack of intent to kill. 3

In light of the foregoing, we agree with the district court that the Arizona Supreme Court was not objectively unreasonable in determining that the sentencing court had considered all of Lopez’s proffered mitigating evidence, including the evidence presented at trial. 4

II. Meaningful Appellate Review

After the district court sua sponte issued the COA as to Issue I, Lopez asked this court to expand the COA. A motions panel denied this request, but in *1039 dicated Lopez could re-raise these issues in his opening brief, which he has done. We construe this additional briefing as a further motion to expand the COA. See Circuit Rule 22 — 1(e). To receive a COA, Lopez must demonstrate that “reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.” Slack v. McDaniel, 529 U.S. 473, 484 , 120 S.Ct. 1595 , 146 L.Ed.2d 542 (2000).

Lopez argues that the Arizona Supreme Court failed to provide meaningful independent review of his sentence. This issue is not, as Lopez argues, somehow encompassed by the certified issue discussed above. To the contrary, the district court expressly limited its COA to alleged errors committed by “the sentencing court[ ].” Rather, Lopez raises an entirely independent constitutional claim 5 regarding the Arizona Supreme Court’s review process, alleging that the Court mistakenly determined that the trial court found “no mitigation,” when the trial court in fact weighed the mitigating factors against the aggravators. This claim is not only unexhausted, it is actually raised for the first time on this appeal. 6 We therefore deny a COA on this issue.

Lopez also attempts to sweep this claim within one he did raise below in the district court: that the state trial court made constitutionally inadequate findings. Lopez argued below that the trial court’s failure to list the factors it considered and its conclusions surrounding them violated due process and made it impossible for the Arizona Supreme Court to perform its independent duty of review. However, Lopez does not point to any “clearly established” Supreme Court precedent setting forth the record the sentencing court must make in order to permit sufficient appellate review. See 28 U.S.C. § 2254 (d)(1). The district court thus denied Lopez’s claim, noting that there was no clearly established Supreme Court law or constitutional requirement “that a particular sentencing record be produced by the trial court.” We agree, and have expressly held that “[w]hile it is important that the record on appeal disclose to the reviewing court the considerations which motivated the death sentence ... due process does not require that the sentencer exhaustively document its analysis of each mitigating factor as long as a reviewing federal court can discern from the record that the state court did indeed consider all mitigating evidence offered by the defendant.” Jeffers v. Lewis, 38 F.3d 411, 418 (9th Cir.1994) (en banc) (citing Gardner v. Florida, 430 U.S. 349, 361 , 97 S.Ct. 1197 , 51 L.Ed.2d 393 (1977) (plurality opinion)); see also Williams v. Stewart, 441 F.3d 1030, 1057 (9th Cir.2006) (“[T]he trial court is not required to ‘itemize and discuss every piece of evidence offered in mitigation’ ... [so long as it makes] clear to the reviewing court that the sentencing court considered all relevant mitigating evidence that was *1040 offered.”); Clark, 958 F.2d at 858 n. 5 (noting that after Parker , it is clear the “due process clause does not require the sentencing court to conduct an on-record discussion of each mitigating factor”). Because the district court’s determination on the merits of this claim is not debatable among jurists of reason, we deny the COA on this uncertified claim.

III. Exhaustion of Ineffective Assistance of Counsel Claim Regarding Failure to Investigate and Present Reasonably Available Mitigating Evidence

In his federal habeas petition, Lopez asserts that his counsel rendered ineffective assistance by failing to investigate and present all relevant mitigating evidence at sentencing, including evidence of organic brain damage, dysfunctional childhood, childhood sexual assault, a good employment record and remorse. The district court did not reach the merits of this claim, however, because it found this issue had not been exhausted to the Arizona Supreme Court.

Because the district court dismissed Lopez’s claim on a procedural ground, we apply Slack to both the procedural ground and the underlying constitutional claim to determine if they are debatable among jurists of reason. Valerio v. Crawford, 306 F.3d 742, 774 (9th Cir.2002). With respect to the substantive prong, however, we take only a “quick look” to determine whether the petition facially alleges the denial of a constitutional right. Id. at 775 (internal quotation marks omitted).

In order to fulfill exhaustion requirements, a petitioner must present to the state courts the “substantial equivalent” of the claim presented in federal court. Picard v. Connor, 404 U.S. 270, 278 , 92 S.Ct. 509 , 30 L.Ed.2d 438 (1971). “[S]tate courts have been given a sufficient opportunity to hear an issue when the petitioner has presented the state court with the issue’s factual and legal basis.” Weaver v. Thompson, 197 F.3d 359, 364 (9th Cir.1999). However, a petitioner may provide further facts to support a claim in federal district court, so long as those facts do not “fundamentally alter the legal claim already considered by the state courts.” Vasquez v. Hillery, 474 U.S. 254, 260 , 106 S.Ct. 617 , 88 L.Ed.2d 598 (1986).

Lopez did seek post-conviction relief in Arizona Superior Court pursuant to Arizona Rule of Criminal Procedure 32. He alleged, among other things, that he had received ineffective assistance of counsel in violation of Strickland v. Washington, 466 U.S. 668 , 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984). Although the state correctly notes that Lopez’s initial bifurcated petition did not specifically challenge counsel’s lack of preparation for the penalty phase, the issue was eventually briefed in memoranda to the state trial court, and that court did issue a ruling on the merits.

The state court also permitted an evi-dentiary hearing on Lopez’s claim. At the evidentiary hearing,. Lopez presented evidence about his trial counsel’s failure to investigate and present mitigation for the capital sentencing, as well as expert testimony about an allegedly competent defense attorney’s duties of investigation and presentation of mitigating evidence. An expert testified that competent defense counsel had a duty to investigate Lopez’s background and social history, and as a result of counsel’s failure to do so, the sentencing judge did not discover that Lopez grew up in a dysfunctional household with alcoholic parents and also began drinking at an early age. The expert also testified that trial defense counsel failed to provide the examining psychologist with any evidence of family, medical or social history.

*1041 The state court rejected this claim on the merits, concluding that evidence of Lopez’s alcohol abuse was not sufficiently substantial to call for leniency. Lopez then appealed the denial to the Arizona Supreme Court. In his statement of issues, Lopez indicated he was prejudiced by his trial counsel’s “abandonment [of] his client at the trial and/or sentencing.” He identified Strickland as the governing federal constitutional standard. His petition for review elaborated on the claim as follows:

The Arizona Supreme Court denied Lopez’s petition.

We conclude that the district court erred by determining that Lopez’s ineffective assistance of counsel claim for failure to investigate and present mitigating evidence was unexhausted. Lopez did at least make the general allegations of his counsel’s lack of penalty phase preparation to the Arizona Supreme Court (including improper delegation to an inexperienced subordinate and failure to prepare mental health experts), and the state court record contains some evidence of a dysfunctional childhood and alcoholism. 7 A “quick look” at the merits of his federal claim also reveals that Lopez has sufficiently alleged the deprivation of a constitutional right. Valerio, 306 F.3d at 775 . We therefore grant the COA on Lopez’s penalty phase ineffective assistance claim for failure to investigate and present mitigating evidence and remand to the district court for further proceedings. 8

IV. Procedural Bar Regarding Defense Counsel’s Failure to Rebut Testimony by Dr. Hobeich

In his federal petition, Lopez claims that his trial counsel was also ineffective for failing to rebut the testimony of the state’s aggravation witness, Dr. Hobeich, who presented testimony about the pain Lopez’s son likely suffered before death. The district court first found this claim to be unexhausted, and then, procedurally barred on an adequate and independent *1042 state law ground. As with the previous claim, we analyze whether to grant a COA by applying the Slack standard to the district court’s procedural ruling and to the underlying constitutional claim. Valerio, 306 F.3d at 774 .

In December 2000, Arizona amended its Rule 32 state post>-conviction procedures, adding a new avenue of relief from a death sentence if “[t]he defendant demonstrates by clear and convincing evidence that the facts underlying the claim would be sufficient to establish ... that the court would not have imposed the death penalty.” Ariz. R.Crim. P. 32.1(h). After the district court dismissed Lopez’s claim as unex-hausted, in 1999 Lopez returned to state court, seeking relief under this provision by arguing that his counsel’s deficient performance deprived the state court of evidence that would have changed his sentence. The state trial court, however, held the claim precluded under Rule 32.2(a)(3), 9 concluding the claim could have been presented in Lopez’s first post-conviction proceeding. See Ariz. R.Crim. P. 32.2(a)(3) (providing for dismissal of a claim that “has been waived at trial, on appeal, or in any previous collateral proceeding.”). Lopez sought review with the Arizona Supreme Court, but it refused to consider the claim.

Lopez then returned to the district court and sought to amend his habeas petition to add this claim. The district court rejected the proposed amendment, citing the state court’s procedural default of the claim. Lopez, however, argues that the state court’s reliance on Rule 32.2(a)(3) was in error, because he had brought his claim under Rule 32.1(h), and Rule 32.2(b) prohibits the state court from applying Rule 32.2(a)(3) to 32.1(h) claims. Rule 32.2(b) provides:

The district court reasoned that, although the state court did not cite Rule 32.2(b) or 32.1(h) in its ruling, the court’s dismissal of the claim under Rule 32.2(a)(3) meant it “must have necessarily concluded that the claim failed to constitute an exception to Rule 32.2(a) preclusion as set forth in Rule 32.2(b).” 10 In other words, in the district court’s view, the state court had interpreted Rule 32 to require dismissal under 32.2(a) if the showing required under 32.2(b) was not satisfied.

The district court’s interpretation is entirely plausible. Although the first sentence of Rule 32.2(b) states that “Rule 32.2(a) shall not apply” to claims for relief based on certain subsections, including 32.1(h), the rule goes on to state various requirements and concludes that, “[i]f the *1043 specific exception and meritorious reasons do not appear substantiating the claim and indicating why the claim was not stated in the previous petition or in a timely manner,” the claim is to be dismissed. As the district court noted, state courts are presumed to know and correctly apply state law. See Walton v. Arizona, 497 U.S. 639, 653, 110 S.Ct. 3047 , 111 L.Ed.2d 511 (1990), overruled on other grounds by Ring v. Arizona, 536 U.S. 584 , 122 S.Ct. 2428 , 153 L.Ed.2d 556 (2002); Beaty v. Stewart, 303 F.3d 975, 986 (9th Cir.2002). Moreover, Lopez specifically argued to the Arizona Supreme Court that the trial court had erred in finding the claim precluded, and the Court did not reverse the ruling.

We grant the COA because the district court’s procedural determination is debatable among reasonable jurists and Lopez has facially alleged a deprivation of a constitutional right, but we nonetheless affirm the district court’s ruling. This court, when sitting as a habeas court, generally respects state court determinations of state law. See Powell v. Lambert, 357 F.3d 871, 874 (9th Cir.2004); see also Estelle v.McGuire, 502 U.S. 62, 67-68 , 112 S.Ct. 475 , 116 L.Ed.2d 385 (1991) (a federal habeas court cannot reexamine a state court’s interpretation and application of state law). We have previously recognized an exception to this deference if the state court’s interpretation is “clearly untenable and amounts to a subterfuge to avoid federal review of a deprivation by the state of rights guaranteed by the Constitution.” Knapp v. Cardwell, 667 F.2d 1253, 1260 (9th Cir.1982). As discussed above, there are ways to construe the state court’s ruling that would not make it “clearly untenable,” and we are therefore bound by the state court’s interpretation and application of its own procedural rules. 11 The district court properly declined to permit Lopez to amend his petition in light of the state court’s ruling.

V. Defense Counsel’s Failure to Object to Evidence of Prior Injuries

During the guilt phase of Lopez’s trial, the medical examiner, Dr. Henry, testified that Anthony suffered from several healing injuries, including rib fractures and bruises about his face and torso. Lopez argues that his counsel should have moved to exclude this evidence under Arizona Rule of Evidence 404(b), as evidence of other crimes, wrongs, or acts not admissible to prove the character of a person, and asks this court to grant a COA on this issue. He argues the evidence was not admissible under any of the exceptions, such as to prove absence of mistake or accident, because the state had not proven by clear and convincing evidence that Lopez caused the other injuries. See State v. Nordstrom, 200 Ariz. 229 , 25 P.3d 717, 736 (2001). Lopez contends that had this evidence been excluded, there is a reasonable probability that the jury would have convicted him of a lesser-included offense — • reckless child abuse — which is a non-capital felony.

This claim was raised in state post-conviction proceedings and denied on the merits. The state court concluded that defense counsel’s decision not to object to the admission of the evidence did not fall below an objective standard of reasonableness, and that even if the evidence was not admissible, there was no reasonable probability of a different outcome. The district court concluded that the state court’s ruling was neither contrary to nor an unrea *1044 sonable application of clearly established federal law. We grant the COA because the issue is debatable among jurists of reason, but we affirm the district court’s decision.

The first prong of Strickland considers whether Lopez’s counsel fell below an objective standard of reasonableness by failing to object to the evidence of prior injuries as Rule 404(b) evidence. 466 U.S. at 687-88 , 104 S.Ct. 2052 . Even if we assume that the state court unreasonably determined that Lopez’s counsel was not deficient for failing to at least object to this evidence, to satisfy the second prong of Strickland , Lopez must also demonstrate a “reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 694 , 104 S.Ct. 2052 .

Dr. Henry’s testimony clearly focused on the three major injuries that ultimately resulted in Anthony’s death — injuries to his head, chest and abdomen. Occasional references to older bruises or healing rib fractures were made when describing the condition of the body at the time of the autopsy. Dr. Henry also testified that the abdominal injuries might have occurred more than a day earlier, but that it was also possible they had been inflicted around the same time as the head injuries. But the truly damaging portion of Dr. Henry’s testimony was not descriptions of other minor bruises or injuries — it was his consistent testimony that Anthony’s three serious injuries were not consistent with accidental injuries, were highly unlikely to have been caused by a falling nightstand as described by Lopez, and were not inflicted by a single blow, but by separate and very forceful blows to the head, chest and abdomen.

Perhaps more importantly, the prosecution did not use any of Dr. Henry’s testimony about prior injuries to argue Lopez’s state of mind. The only reference to the prior bruises in the closing argument was to point out that the victim’s mother was either not particularly observant or not credible. Instead, the focus of the closing argument mirrored the crux of Dr. Henry’s testimony: the injuries Anthony suffered were not accidental, they required a great deal of force, and they likely required repetitive blows, which, the prosecution argued, required effort and thought. The prosecution argued that the severity of Anthony’s injuries simply did not permit a finding of recklessness — that Lopez had either intentionally and willfully inflicted these injuries on the child, or that it was some freak accident, but that there was no in between. The prosecution also pointed out the inconsistencies in Lopez’s statements to police, his reluctance to take the child to the hospital, and that Lopez’s explanation of what happened was inconsistent with the medical evidence.

Although Lopez argues that the jury could have found recklessness but for the allegedly improper testimony about the prior bruises, we agree with the district court that the state court was not objectively unreasonable in determining that there was no reasonable probability of a different guilt phase outcome based on this record. We therefore affirm the district court’s denial of Lopez’s petition on this claim.

AFFIRMED IN PART, REVERSED IN PART, AND REMANDED.

. The court also issued a COA as to whether Lopez's claim that his rights were violated when the sentencing court improperly limited the scope of mitigation evidence was procedurally barred. However, Lopez concedes that this second issue is either moot or immaterial since the district court reached the claim on its merits.

. This court reviews the Arizona Supreme Court's decision because it is the last reasoned decision on this issue. Barker, 423 F.3d at 1091-92 . The determination of what the trial judge found is an issue of historical fact. Parker, 498 U.S. at 320 , 111 S.Ct. 731 .

. The sentencing court found that Lopez had “willfully and intentionally physically abused the child entrusted to his care and caused his death.” Lopez argues that this statement simply underscores that the court did not find an "intent to kill,” just intent to abuse, but the state argues that the “willfully and intentionally” language also modifies "caused his death.” Because either interpretation is plausible, the statement is at best ambiguous, and does not cut strongly one way or the other.

.Because we agree with this conclusion, we need not address the district court’s alternate holding that even if the trial court had erred and failed to consider all the mitigating evidence presented at trial and sentencing, any such error was cured by the Arizona Supreme Court's independent review of the record.

. The Eighth and Fourteenth Amendments prohibit the government from imposing the death penalty in an arbitrary or irrational fashion, and the Supreme Court has held that "meaningful appellate review” is necessary to ensure that the death penalty is not imposed in such a manner. Pulley v. Harris, 465 U.S. 37, 45 , 104 S.Ct. 871 , 79 L.Ed.2d 29 (1984) (citing Gregg v. Georgia, 428 U.S. 153, 198, 204-06 , 96 S.Ct. 2909 , 49 L.Ed.2d 859 (1976) (joint opinion of Stewart, Powell, and Stevens, JJ.)); Parker, 498 U.S. at 321 , 111 S.Ct. 731 .

. The only error in the Arizona Supreme Court's review that Lopez alleged in his federal habeas petition was the Court's failure to conduct proportionality review of his death sentence. In addition, in Lopez’s state and federal filings, he consistently asserted — contrary to his assertion now — that the trial court had made an (erroneous) finding of “no mitigation."

. We recognize that Lopez’s habeas counsel conceded to the federal district court that some sub-parts of this claim were not exhausted by post-conviction counsel. However, this court can independently review the state court record to determine whether the issue has actually been exhausted. See Aiken v. Spalding, 841 F.2d 881, 883 (9th Cir.1988) (per curiam).

. We note that Lopez apparently wishes to supplement the record in federal court with additional evidence of prejudice — information that could have been presented in the penalty phase mitigation proceeding, but was not presented due to defense counsel’s allegedly deficient performance — that was not presented to the state courts. On remand, the district court will therefore need to determine whether Lopez, who received an evidentiary hearing in state court, is entitled to supplement the record or receive an additional evidentia-ry hearing in federal court. See 28 U.S.C. § 2254 (e)(2); 28 U.S.C. foil. § 2254, R.7 (setting forth the rule for expanding the record on federal habeas review).

. The state court actually cited "32.1(a)(3),” which does not exist; the citation is apparently a typographical error, as Lopez acknowledges.

. Lopez now argues that the district court erred by relying on a theoretical but unstated procedural bar; however, this is not quite what the district court did. Rather, the district court concluded that the state court must have found the Rule 32.2(b) exception did not apply to save Lopez’s new petition, and that this was why the state court had dismissed under the ordinarily applicable Rule 32.2(a).

. Lopez does not otherwise challenge the application of Rule 32.2(a) as an “independent and adequate" state law ground, see Stewart v. Smith, 536 U.S. 856, 861 , 122 S.Ct. 2578 , 153 L.Ed.2d 762 (2002), and Ortiz v. Stewart, 149 F.3d 923, 931-32 (9th Cir.1998), nor does he attempt to demonstrate cause and prejudice for the procedural default.