
623 F.3d 1258 (2010)
Aryon WILLIAMS, Petitioner-Appellant,
v.
Charles L. RYAN, Respondent-Appellee.
No. 07-99013.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted November 5, 2009.
Filed October 26, 2010.
*1260 Julie Hall, Oracle, AZ, for petitioner-appellant, Aryon Williams.
Jeffrey A. Zick, Phoenix, AZ, for respondent-appellee, Charles L. Ryan.
Before: MARY M. SCHROEDER, MARSHA S. BERZON and SANDRA S. IKUTA, Circuit Judges.
Opinion by Judge SCHROEDER, Partial Concurrence and Partial Dissent by Judge IKUTA.

OPINION
SCHROEDER, Circuit Judge:
Aryon Williams was convicted in Arizona state court in 1992 and sentenced to death for the first degree murder of his former girlfriend Rita DeLao, and for the later robbery and attempted murder of Norma Soto. The Arizona appellate courts upheld his convictions and sentence. See State v. Williams, 183 Ariz. 368, 904 P.2d 437 (1995). In this habeas proceeding, the most significant issues concern a claim of concealment of partially exculpatory evidence in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and the failure of the state court to consider mitigating evidence at sentencing in violation of Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978) and Eddings v. Oklahoma, 455 U.S. 104, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982).
The evidence at trial included the testimony of Michelle Deloney, Williams' then girlfriend, that Williams had confessed to her he murdered DeLao. The murder occurred in a relatively remote area of Pinal County, Arizona and there were no eyewitnesses and little physical evidence. On the robbery/attempted murder charge, the victim, Norma Soto, testified at trial and identified Williams as her attacker.
Two years after the convictions were affirmed on appeal, an Assistant Attorney General for Arizona turned over to Williams' attorney a packet of jailhouse letters written before trial that suggested that Williams was not the actual murderer. These letters suggested that Williams had paid another man, Patrick Fields, to do the job. The jailhouse letters led Williams to two witnesses who said they had seen Fields disposing bloody clothing in a park a morning around the time of the murder. Fields turned out to have a history of assaulting women.
By the time Williams became aware of this evidence, these federal habeas proceedings had been instituted. The district court stayed the proceedings so that Williams could, in state court, exhaust a Brady claim arising from the jailhouse letters. The state court, however, refused to grant a request for a first extension of time to prepare a postconviction petition. Williams was, therefore, unable to exhaust state remedies. When he returned to federal court, the district court rejected the State's position that the Brady claim was procedurally barred, but denied the claim on the merits. Like the district court we consider this claim without regard to the *1261 deferential strictures of the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"). We agree with the district court that it is not appropriate to view the claim as procedurally barred because Williams did not have an opportunity to raise it in state court. The district court granted a certificate of appealability ("COA") and we have determined that this claim warrants an evidentiary hearing.
The district court also granted a COA for the claim that the trial court violated Williams' due process rights by failing to provide funds for a mental health expert at sentencing to establish drug dependence as a mitigating factor. Like the district court, we agree that the state court's rejection of this claim was not contrary to or an unreasonable application of Supreme Court precedent.
Of the numerous claims that had not been certified, but that have been briefed pursuant to our rules, we find one to be meritorious. Williams offered his addiction to crack cocaine as a mitigating factor at sentencing. The Arizona Supreme Court refused to consider this as a mitigating factor under applicable Arizona law because Williams did not show he was under the influence of drugs at the time of the murder. Because Williams' challenge to this determination raises a substantial constitutional issue, 28 U.S.C. § 2253(c)(2), we certify the issue and decide it. As we have done in other cases emanating from Arizona courts in the same period, we find that the state court erred by its refusal to consider all mitigating evidence. See Eddings, 455 U.S. at 114-15, 102 S.Ct. 869; Lockett, 438 U.S. at 604-05, 98 S.Ct. 2954; Lambright v. Schriro, 490 F.3d 1103, 1114-15 (9th Cir.2007).

FACTUAL AND PROCEDURAL BACKGROUND
The underlying facts of this case are set out in detail in the Arizona Supreme Court's opinion on direct appeal. State v. Williams, 183 Ariz. 368, 904 P.2d 437 (1995). We summarize them here.
On Saturday, January 27, 1990, Williams and DeLao made plans to spend the night together at Williams' apartment in Casa Grande. When DeLao called, though, Williams told her not to come over since his girlfriend Deloney was still at his apartment. DeLao came over nonetheless and had an argument with Williams outside the building. DeLao pulled a gun on Williams, but Williams was able to disarm her. Williams briefly returned to his apartment, then left it, and did not return until the following morning.
On Sunday morning, a hunter discovered DeLao's body on a dirt road about twenty minutes from Williams' apartment. DeLao had been shot three times and her body had suffered a number of gruesome injuries. She had been beaten, and tire tracks across her stomach indicated that she had been run over by an automobile. Bullets recovered at the scene were consistent with the gun Williams had taken from DeLao shortly before her death.
Deloney testified that Williams confessed to her on Monday that he was with several friends who killed DeLao. According to Deloney, Williams said he had only kicked DeLao, and that his friends had killed her. Williams denied ever confessing involvement in DeLao's death. Also on Monday, Williams drove Deloney to the place where DeLao's car had been abandoned, less than a mile from his apartment in Casa Grande. As Williams approached the car, a police officer processing the car stopped them, and Williams told the officer he thought it was DeLao's car.
Deloney testified that, two weeks after the murder, Williams told her that he had *1262 killed DeLao, admitting that he shot her, hit her with an iron, and ran over her repeatedly with his car. Williams told Deloney that if she ever told anyone, he would kill her.
Five weeks after the murder, Norma Soto, a Circle-K convenience store clerk, was shot several times during a robbery of the store. Soto survived and identified Williams as her attacker, testifying that he shot her after telling her to stop spreading the story that he had killed DeLao. Police soon arrested Williams for both the murder of DeLao and the robbery/attempted murder of Soto.
An Arizona jury, in a consolidated trial, convicted Williams in 1992 of the murder of DeLao, armed robbery, and the attempted murder of Soto. At trial, Deloney was the State's principal witness on the murder charge. She testified about Williams' confessions. The State also presented evidence that, prior to the murder, Williams had burned DeLao's car, shot at her apartment, and slashed her tires. Soto testified and identified Williams as the man who robbed the store and shot her. Williams testified in his own defense and denied any involvement in either criminal episode. Williams did not have a criminal record, although the State introduced evidence that he had abused crack cocaine and become physically abusive to Deloney. On the stand, Williams denied using drugs on the day of the murder.
At sentencing, Williams sought to have the state provide a mental health expert to explore whether his drug usage had affected his mental state when he killed DeLao. The trial court denied this motion, and the Arizona Supreme Court upheld the decision without discussion. See 904 P.2d at 450 ("Defendant also asserts ... that the trial court's denial of funds for an expert violated his right to due process and equal protection under the law. Under the facts of this case, we reject these claims as well.").
Williams also offered his addiction to crack as a mitigating circumstance at sentencing. The trial court refused to consider Williams' drug use in mitigation. The Arizona Supreme Court agreed, holding that "[w]ithout a showing of some impairment at the time of the offense, drug use cannot be a mitigating circumstance of any kind." Id. at 453.
After filing two unsuccessful state postconviction petitions in which he raised the sentencing claims of erroneous denial of a mental health expert and the refusal to consider his addiction as a mitigating factor, Williams instituted federal habeas proceedings. In 1997, while his federal petition was pending, an Assistant Attorney General for Arizona turned over to defense counsel a series of letters, and stated they were discovered "by a secretary during an annual house cleaning at the [Pinal] County Attorney's Office." The State said the letters had "no evidentiary value."
The letters purported to have been written from jail in 1991, prior to Williams' trial, by a woman named Beverly Sweat, to Detective Tom Solis, the lead investigator in the DeLao murder. In the letters, Sweat expressed the desire to provide information she had about a murder, in return for an early release from jail. Solis has denied ever having seen these letters, but has not testified or given a statement under oath to this effect.
The letters contained information Sweat allegedly obtained from a fellow inmate, Yolanda McKaney, that Williams had paid Patrick Fields to kill Rita DeLao and that McKaney had seen a bloodied Fields on one morning around the time of the murder. One letter stated that Sweat was going to have Yolanda McKaney "tell [her] the story about Rita and Patrick Fields." *1263 The letter also noted that "Aaron" (apparently a reference to petitioner Aryon Williams) was "going to get" two people: Fields and Milton Barnett. According to this letter, McKaney told Sweat that the day of the DeLao murder, in Casa Grande, she saw Fields who was "all bloody" and who stated that "Aaron" had paid him a thousand dollars to kill DeLao. According to Sweat, Fields told McKaney that he had cut DeLao's eyes out and run over her with a moped. Sweat also stated that she knew "Aaron is guilty of some part of it," and in the subsequent letters, promised that she could obtain additional information, if she obtained an early release.
Counsel for Williams conducted an investigation on the basis of the Sweat letters and in 1999 obtained declarations from three people mentioned in the letters: McKaney, Barnett, and Fields. McKaney's declaration stated that around the time of the DeLao murder, she saw Fields in a park in the small town of Casa Grande, Arizona, less than a mile from where police discovered DeLao's abandoned car the morning after the murder. She saw a bloodied Fields throw a bloody shirt into a dumpster and burn it. Barnett stated that about this same time, and a few blocks from where McKaney saw Fields, he saw a shirtless Fields throw something into a dumpster. Barnett said that, while sharing a cigarette with Fields, he noticed blood on Fields' clothing. Barnett asked Fields about this blood, and Fields fled. Barnett said he learned of DeLao's murder the next day. Fields' declaration stated he was in county jail at the time of the DeLao murder, but the State later conceded that Fields was not in custody at that time. In the district court Williams produced evidence that Fields had a history of sexual assaults against women. Williams has admitted that he knows Sweat, McKaney, Barnett, and Fields.
In 2002, the district court placed the federal proceedings in abeyance to allow Williams to exhaust a Brady claim based upon the Sweat letters and the subsequent investigation. The Arizona courts never considered the merits of this claim, however, because the Superior Court denied Williams an extension of time to file his state petition, finding that Williams had failed to show good cause under Arizona Rule of Criminal Procedure 32.4(c). The Arizona Supreme Court then summarily denied review.
Back in federal court, Williams moved for "Discovery, Expansion of the Record and [an] Evidentiary Hearing" on the Brady claim. The State opposed on the ground that this claim was procedurally barred.
The district court refused to treat the Brady claim as procedurally barred, holding in effect that the state courts had prevented exhaustion without following any well established rule that would have rendered the petition untimely. The district court noted that the State had failed to cite any case denying a first request for an extension of time in a capital case. To the contrary, Williams cited a number of examples where the state courts had granted such requests. Thus, the district court found that Rule 32.4(c) was not "firmly established and regularly followed." See Ford v. Georgia, 498 U.S. 411, 423-24, 111 S.Ct. 850, 112 L.Ed.2d 935 (1991).
The district court also granted Williams additional discovery related to the investigation of the Sweat letters. The court declined to order an in-court hearing, finding it appropriate to consider documentation and review written evidence, rather than hear witnesses. The court said that it did so because of what it determined to be the "narrow focus" of the Brady claim.
*1264 After completion of discovery and briefing, the district court denied the Brady claim on the merits, holding that Williams was not prejudiced because the letters did not contain any material information. The court noted that none of Williams' new information directly impeached or undercut the evidence presented at trialevidence the jury found sufficient to convict. Rather, the district court found the letters provided further evidence that Williams was culpable by suggesting he had paid Fields to kill DeLao. The court also pointed to inconsistencies in the various declarations, noting that the fact the information originated in a jailhouse undermined its credibility.
The district court issued a COA on the Brady claim and the claim that Williams was entitled to a mental health expert at sentencing. We additionally certify the claim that addiction should have been considered a mitigating factor at sentencing.

ANALYSIS

I. The Brady Claim
First, we address as a threshold matter the State's renewed contention that Williams' Brady claim is procedurally barred, even though Williams was prevented from raising it because the state trial court denied him a first extension of time. In this court, as in the district court, the State has not cited to a single other instance of an Arizona court denying a first extension of time to file a habeas petition in a capital case. The State, therefore, has not shown the denial was pursuant to a well established rule against first extensions in capital cases. Procedural default must be based on the application of a well established rule. See Ford, 498 U.S. at 423-24, 111 S.Ct. 850.
Because this claim was denied in state court on an inadequate procedural ground, there was thus no failure on the part of Williams. We agree with the district court that Rule 32.4(c) was arbitrarily applied in this case. As the district court concluded "every first request for an extension of time in a capital case" had been granted previously in Arizona courts.
As a result of the state court's arbitrary application of its rules, there is no state court decision to which this court can defer. The deference AEDPA requires for state court determinations, therefore, does not apply and our review of this claim is de novo. See Pirtle v. Morgan, 313 F.3d 1160, 1167 (9th Cir.2002).
A state commits a Brady violation where 1) the evidence in question is favorable to the accused, 2) the state "wilfully or inadvertently" suppressed the information, and 3) the suppression prejudiced the defendant. See Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). Prejudice exists where the state suppresses "material" information; evidence is material if had it been disclosed "there is a reasonable probability ... the result of the proceeding would have been different." Kyles v. Whitley, 514 U.S. 419, 433, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (citation omitted).
The Brady materials here consist of the packet of Sweat letters that turned up in the District Attorney's office years after trial, and led counsel to obtain the declarations of McKaney, Barnett, and Fields. See Paradis v. Arave, 240 F.3d 1169, 1178-79 (9th Cir.2001) (noting that Brady material consists of admissible evidence or inadmissible evidence that could have been used to impeach a government witness). The Sweat letters thus suggested there were witnesses who, around the time of DeLao's murder, saw a bloodied Patrick Fields disposing of bloody clothing into dumpsters about a half a mile from where police found DeLao's abandoned *1265 car. When defense counsel followed up on these leads after the letters were disclosed, she obtained declarations from the witnesses identified in the letters substantially reiterating this information. The Sweat letters further suggested that there might be a witness who could testify that Williams did not commit the murder himself, but paid Fields to do it.
Williams contends that this information is sufficient to justify habeas relief. The State contends, however, with some validity, that the new evidence does not undermine Deloney's testimony that Williams confessed his involvement in the murder to her. Nor does it, according to the State, have any impact on the evidence that Williams was the last known person to be with DeLao, and that they had an argument when DeLao threatened Williams with the firearm that was used in her murder. The Sweat letters are also consistent with Williams' first confession to Deloney that he had only kicked DeLao, and that someone else killed her. See 904 P.2d at 441. The State also points out that prior to the murder, Williams had burned DeLao's car and shot at her house; the Sweat letters do not conflict with that evidence either.
Insofar as the letters suggest Williams was involved in the murder in a different capacity than as the actual killer, the State contends the letters suggest only an alternate theory of equal culpability, and we have held such evidence undermines a Brady claim where the new evidence fails to show the defendant was "less guilty." See Morris v. Ylst, 447 F.3d 735, 740-41 (9th Cir.2006) (finding no Brady violation where new information "did not say Petitioner was not guilty, or that he was any less guilty" and did not suggest another party "struck" the victim).
Here, we must part company with the State's position, because new evidence suggesting an alternate perpetrator is "classic Brady material." Boyette v. Lefevre, 246 F.3d 76, 91 (2d Cir.2001); see United States v. Jernigan, 492 F.3d 1050, 1056-57 (9th Cir.2007) (en banc) ("Withholding knowledge of a second suspect conflicts with the Supreme Court's directive that the criminal trial, as distinct from the prosecutor's private deliberations, be preserved as the chosen forum for ascertaining the truth about criminal accusations.") (internal quotation marks, citation, and brackets omitted). Not only are the Sweat letters inconsistent with the State's theory at trialthat Williams was the only individual responsible for DeLao's murder but they also point to an alternative suspect who may himself have been responsible for the brutal crime.
The two witnesses mentioned in the letters, McKaney and Barnett, provided declarations that pointed only to Fields. There is also reason to believe the declarations from Barnett and McKaney are more reliable than the Sweat letters. Sweat prepared the letters in hopes of obtaining an early release from jail, and thus had every motivation to tell the police what she thought they wanted to hear. Barnett and McKaney, in contrast, had no apparent motivation to sign a false declaration implicating Fields. Williams has also provided a plausible explanation that the statement in the Sweat letters that he was "going to get" Fields was unrelated to the murder. Williams believed Fields was responsible for the violent assault of one of his longtime friends.
Fields is at least a plausible alternative suspect: he had a history of violence against women and lied about being in jail at the time of the murder. McKaney and Barnett both saw Fields disposing of bloody clothing around the time of the murder and a short walk away from where police discovered DeLao's abandoned car. *1266 Williams, Fields, Barnett, and McKaney all knew one another and lived in the same small town. Juror affidavits suggest that at least one juror reluctantly voted to convict on the basis on the evidentiary record. There was also little physical evidence connecting Williams to the crime. This lends materiality to new evidence that someone else was involvedand possibly solely responsible. See Jernigan, 492 F.3d at 1054 (considering the strength of the prosecutor's case in weighing the materiality of suppressed evidence); Gantt v. Roe, 389 F.3d 908, 913 (9th Cir.2004) (holding that newly discovered information is material when it undermines a conviction based upon little physical evidence).
The Sweat letters thus provided the government with information concerning a possible alternative suspect that, if disclosed to the defense, would have allowed Williams to decide whether to put McKaney and Barnett on the stand to testify. We have recognized the principle that the government may not, consistent with Brady, suppress information that another person committed the crime for which the defendant is on trial. See Jernigan, 492 F.3d at 1056-57.
The Sweat letters also provided the names of two potential witnesses that could have testified to events that undercut the prosecution's theory that Williams was the lone assailant. Rather than focusing on the information in the letters, and the potential materiality of the witnesses' testimony that might implicate another perpetrator, the district court prematurely deemed these two witnesses presumptively not credible on the basis of inconsistencies in their declarations. Yet, the two declarations were executed in 1999, nine years after the murder. Given this fact, some inconsistencies do not necessarily make their stories wholly incredible. More important, "[w]hen analyzing a Brady claim, we do not reweigh evidence [or] assess the credibility of witnesses [to] decide whether the suppressed evidence establishes the guilt of a third party beyond a reasonable doubt or exonerates petitioner." Scott v. Mullin, 303 F.3d 1222, 1232 (10th Cir. 2002) (internal quotation marks, citation, and brackets omitted). The critical question is whether the suppressed Brady material could have provided material evidence that may have changed the result. The district court concluded on the basis of written statements alone that Barnett and McKaney were inherently unbelievable witnesses. The court did so without holding an in-court evidentiary hearing in order to determine whether they would have been able to provide material evidence that may have changed the result of Williams' trial. This was error. We follow our opinion in Earp v. Ornoski, 431 F.3d 1158, 1169-70 (9th Cir.2005).
In Earp, also a death penalty case, we stressed that credibility should be assessed on the basis of an in-court hearing where the judge can see and hear the witnesses. See id. There, as here, the district court had resolved a habeas claim on the basis of written declarations and we held that to be error. See id. We stated that "[b]ecause the veracity of the witnesses who signed the affidavits on which Earp based his claim was at issue, the claim could not be adjudicated without an evidentiary hearing on this disputed issue of material fact." Id. at 1170.
We are similarly unable to determine on this limited record, whether there is a "reasonable probability" of a different result at trial had this information been available. See Kyles, 514 U.S. at 433, 115 S.Ct. 1555. Although there are many questionable aspects in the statements and their sources, this is a capital case in which courts' responsibility to ensure that due process was afforded the defendant is critical *1267 in order to prevent the execution of an individual in the face of evidence that might show him innocent of the crime of conviction. See Burger v. Kemp, 483 U.S. 776, 785, 107 S.Ct. 3114, 97 L.Ed.2d 638 (1987) ("Our duty to search for constitutional error with painstaking care is never more exacting than it is in a capital case."). The district court abused its discretion in determining these issues on the basis of the documentary evidence alone. This case is not one of the "rare instances" where "credibility may be determined without an evidentiary hearing." See Earp, 431 F.3d at 1169-70.
The dissent states that Williams is not entitled to an in-court evidentiary hearing on his Brady claim because he "actively opposed one" in the district court. (Dissenting Op. at 1278.) This is not an accurate description of the record. Williams expressly moved for an evidentiary hearing on his Brady claim, and the district court found he had satisfied AEDPA's strict requirements for obtaining one. See 28 U.S.C. § 2254(e)(2). The State then argued that the district court should summarily deny the claim without holding an evidentiary hearing because Williams had not shown that he was unaware of the information about Fields in the Sweat letters and the letters were not credible. Alternatively, the State requested an evidentiary hearing so that it could conduct discovery and develop evidence related to Williams' and Williams' counsel's knowledge of Field's alleged participation in the murder, and cross-examine Sweat, McKaney, and Barnett to investigate the inconsistencies between the letters and the declarations. At that point, Williams opposed the State's attempt to use an evidentiary hearing to conduct investigatory discovery when the court had previously granted the State a five-month extension to investigate these matters, and it had failed to do so. We do not view this course of events as active opposition to an in-court evidentiary hearing, and disagree with the dissent's conclusion that Williams invited error by "express[ly] disavow[ing]" an in-court hearing.
We also disagree with the dissent's conclusion that the Sweat letters could not have been material to the guilt phase of Williams' trial because the letters were not exculpatory. (Dissenting Op. at 1275-76.) As the dissent recognizes, the standard for materiality is whether "there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Kyles, 514 U.S. at 433, 115 S.Ct. 1555 (citation omitted). The dissent contends that because Sweat claimed in her letters that Williams had paid Fields to kill DeLao, and under Arizona law a person could be convicted of first-degree murder if he hired someone else to commit a homicide, the Sweat letters could not have provided evidence that would have exculpated Williams from culpability for DeLao's murder. But if the account of events provided by McKaney and Barnett in their declarations is accurate, it is not altogether clear that Williams was involved in DeLao's murder at all. For that reason, an in-court evidentiary hearing was needed so that the district court could assess the credibility of these witnesses and determine whether there was a reasonable probability the result at the guilt phase of Williams' trial would have been different had the State disclosed the Sweat letters in a timely fashion.
The dissent faults us for considering the McKaney and Barnett declarations in our analysis of whether the Sweat letters are material. (Dissenting Op. at 1279.) This contention, however, is premised on the faulty assumption that the prosecution could not have known that the information in the Sweat letters was material. Clearly, *1268 a reasonable prosecutor would have known that the Sweat letters, which identified two new witnesses and an alternative suspect, could lead to evidence material to Williams' culpability for the murder of DeLao. The declarations confirm that is so, by indicating that the witnesses were available and possessed material information which may have exculpated Williams. The Supreme Court has explained that a prosecutor who has any doubt about the materiality of a piece of evidence favorable to the defendant should disclose the evidence. Kyles, 514 U.S. at 439, 115 S.Ct. 1555 ("[A] prosecutor anxious about tacking too close to the wind will disclose a favorable piece of evidence."); United States v. Agurs, 427 U.S. 97, 108, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976) ("[T]he prudent prosecutor will resolve doubtful questions in favor of disclosure."). It is therefore appropriate to consider the declarations of McKaney and Barnett, and any testimony they may provide at an evidentiary hearing on remand, to determine whether the State's suppression of the Sweat letters violated Williams' due process rights under Brady.
We hold the district court erred by not further developing the factual record of the Brady claim. It would be improper to dismiss the possibility that Williams was denied access to information tending to implicate the guilt of another in the perpetration of this heinous crime. We thus remand this Brady claim in order for the district court to decide, on the basis of an appropriate record, whether there were witnesses who could have provided material evidence favorable to Williams at trial. After hearing any available testimony from McKaney, Barnett, Fields, Solis, and Sweat, the district court will be in a better position to assess whether this newly discovered evidence undermines the jury's verdict, and whether the government violated the Brady principle in failing to inform Williams about it before trial.

II. Williams' Request for a Mental Health Expert to Present Mitigating Evidence
Williams next contends the state court unreasonably applied Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), when it denied him psychiatric assistance at sentencing to present mitigating evidence related to his crack cocaine usage. Because Williams failed to make our required threshold showing that his mental state was in issue, we reject this claim.
The Supreme Court in Ake held that due process requires the state to provide an indigent defendant funds for psychiatric assistance when he makes a preliminary showing that his mental state was a significant factor at the time of the offense. 470 U.S. at 83, 105 S.Ct. 1087. The Arizona Supreme Court did not explain its reasoning in rejecting Williams' Ake claim. We therefore independently review the record, but only, as required by AEDPA, may grant relief if the state court unreasonably applied controlling federal law as determined by the Supreme Court. See Pirtle, 313 F.3d at 1167.
The district court denied the Ake claim in this case on two bases. First, the district court noted that other circuits have interpreted Ake to require a state to provide a defendant expert psychiatric assistance at sentencing only where the state also planned to rely on psychiatric testimony. See Mason v. Mitchell, 320 F.3d 604, 616 (6th Cir.2003). Yet, we have never read Ake so narrowly. See Hoffman v. Arave, 455 F.3d 926, 934 (9th Cir.2006) ("[In Ake], the Supreme Court held that where an indigent defendant can demonstrate that his mental capacity is likely to be a `significant issue' at trial or capital sentencing, he has an absolute right to be *1269 provided with psychiatric and psychological expert assistance."), vacated in part on other grounds, 552 U.S. 117, 128 S.Ct. 749, 169 L.Ed.2d 580 (2008); Ronald Williams v. Stewart, 441 F.3d 1030, 1049 (9th Cir. 2006) (per curiam); Smith v. McCormick, 914 F.2d 1153, 1157 (9th Cir.1990).
The district court also ruled that Williams had himself failed to make a sufficient threshold showing that his mental state was at issue at the time of the murder, because there was so little in the record to indicate, that due to drug use, Williams' mental state was impaired. The district court granted a COA. We affirm on the latter ground.
Before triggering Ake's due process right to psychiatric assistance, a defendant must "demonstrate[ ] to the trial judge that his sanity at the time of the offense is to be a significant factor." Ake, 470 U.S. at 83, 105 S.Ct. 1087. The defendant in Ake made this threshold showing for the trial phase by relying on an insanity defense. Id. at 86, 105 S.Ct. 1087. In addition, he had exhibited "bizarre" behavior at arraignment, and established that he required heavy medication to control his illness. Id. A competency examination revealed his illness had begun years earlier. Id. At sentencing the prosecution sought to prove, as an aggravating factor, that the defendant posed a future danger. Id. The defendant then placed his mental state at issue at sentencing by relying upon the trial testimony of a psychiatrist that because of mental illness he posed a future danger. Id. He requested the court to appoint an expert to assist at the capital sentencing phase and the Supreme Court ultimately agreed he was entitled to one. Id. at 86-87, 105 S.Ct. 1087.
Williams' initial showing, in contrast, was weak. His defense at trial was not insanity or diminished capacity, but that he did not do it. He contends he put his mental state at issue at sentencing through Michelle Deloney's trial testimony that he used crack the day before the murder, and through other testimony that a violent change in character coincided with his starting to use drugs. Applying the required level of deference, we find that it was not "objectively unreasonable" for the state courts to determine this was an insufficient threshold showing. Lockyer v. Andrade, 538 U.S. 63, 75, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003); 28 U.S.C. § 2254(d)(1), (2). Even with Deloney's testimony, there was little evidence that Williams' drug use had in fact affected the crime. For example, there was no evidence of bizarre behavior exhibited by Williams at the time of the offense. See Ronald Williams, 441 F.3d at 1048-50 (holding that a defendant who did not rely on an insanity defense, had been found competent, and failed to exhibit "bizarre" or "psychotic" behavior failed to put his mental state at issue); see also James v. Gibson, 211 F.3d 543, 554 & n. 5 (10th Cir.2000) (holding that the defendant had not made a sufficient showing that his mental state was at issue at the time of a murder even though there was evidence that at one point he had suffered from a mental disorder). Petitioner thus made no showing that drugs impaired his mental state "at the time of the offense." See Ake, 470 U.S. at 83, 105 S.Ct. 1087.
The dissent incorrectly suggests that whether a defendant has placed his mental state at issue is irrelevant at sentencing. (Dissenting Op. at 1279-80.) The Court in Ake made clear that a defendant must show that his mental state was a "significant factor" at both the guilt and penalty phases. See id. at 83-84, 105 S.Ct. 1087.
We thus affirm the district court's denial of Williams' Ake claim. The trial court was not required to appoint a mental *1270 health expert at sentencing because the defendant did not make any showing that his mental state at the time of the murder was at issue by virtue of drug use.

III. Drug Use as a Mitigating Circumstance
Williams also asked the sentencing court to treat his drug use as a mitigating factor. The trial court refused and he contends the Arizona Supreme Court improperly required a direct causal nexus between his drug use and the murder before it would afford the drug use any mitigating weight at sentencing. This claim has merit, because the Supreme Court has repeatedly held no such nexus is required in capital cases. See, e.g., Tennard v. Dretke, 542 U.S. 274, 284-87, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004).
Although Williams had denied drug use during the guilt phase of the trial, he presented drug use as a mitigating factor at sentencing through the testimony of Deloney and a friend, Raymundo Mendez. Deloney testified that Williams was a nonviolent person up until the time he started to abuse crack. She stated that once he started to abuse drugs he became progressively more violent. Mendez testified that he had known Williams most of his life. He said Williams initially had a reputation as a quiet and peaceful person. He also testified that about the time Williams became known as a drug user, that he became violent and started carrying guns with him. Williams did not testify at his sentencing hearing.
The state trial court ruled that Williams failed to establish his drug use as a mitigating factor because it found "there was no evidence, including considering [Williams'] own testimony, to indicate that cocaine usage by [Williams] was a factor in the perpetration of the murder." The Arizona Supreme Court affirmed this ruling on direct appeal. The court stated that, under Arizona law, "[w]ithout a showing of some impairment at the time of the offense, drug use cannot be a mitigating circumstance of any kind." 904 P.2d at 453. The court thus refused to consider this mitigating circumstance because Williams "offered no evidence showing that he was intoxicated when he murdered [DeLao]." Id.
The district court considered and rejected this claim on the merits, holding the state court was not required to consider Williams' drug use as a mitigating circumstance. The district court declined to issue a COA, but the issue, at the very least, is one upon which reasonable jurists could disagree. See Miller-El v. Cockrell, 537 U.S. 322, 327, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). We therefore certify this issue and consider its merits.
We may reverse only if the Arizona Supreme Court's decision was contrary to clearly established federal law. See 28 U.S.C. § 2254(d)(1). The federal law is clear that a sentencing court must consider all mitigating evidence. The decision of the Arizona Supreme Court that drug use could not be considered as a mitigating factor "of any kind," is contrary to the Supreme Court's consistent decisions in capital cases beginning more than a decade before Williams' trial. See Smith v. Texas, 543 U.S. 37, 45, 125 S.Ct. 400, 160 L.Ed.2d 303 (2004); Tennard, 542 U.S. at 284-87, 124 S.Ct. 2562; Eddings, 455 U.S. at 114-15, 102 S.Ct. 869; Lockett, 438 U.S. at 604-06, 98 S.Ct. 2954.
The Lockett plurality in 1978 struck down an Ohio statute that allowed courts to consider only specified mitigating factors. 438 U.S. at 597, 609-11, 98 S.Ct. 2954. The Court held that "in all but the rarest kind of capital case, [the sentencer should] not be precluded from considering, *1271 as a mitigating factor, any aspect of a defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death." Id. at 604, 98 S.Ct. 2954.
A court majority in Eddings extended Lockett and held that an Oklahoma court violated the Constitution when it refused to consider evidence of a defendant's abusive childhood. 455 U.S. at 113, 102 S.Ct. 869. The Court stated that a trial court "may determine the weight to be given relevant mitigating evidence [but that it] may not give it no weight by excluding such evidence from [its] consideration." 455 U.S. at 114-15, 102 S.Ct. 869.
In Tennard, the Court rejected a Fifth Circuit test that barred the consideration of mitigating evidence unless "the criminal act was attributable to this severe permanent condition." 542 U.S. at 283, 124 S.Ct. 2562. The Court held that "a State cannot bar the consideration of . . . evidence if the sentencer could reasonably find that it warrants a sentence less than death." Id. at 285, 124 S.Ct. 2562 (internal quotation marks and citation omitted).
In Smith the Court explicitly rejected a Texas court's refusal to consider mitigating evidence unless there was a "nexus" between the mitigating circumstance and the murder. 543 U.S. at 45, 125 S.Ct. 400. The Court found that such a "nexus test" was a "a test [it had] never countenanced and now ... unequivocally rejected." Id. Tennard and Smith are retroactively applicable. See Schad v. Ryan, 606 F.3d 1022, 1045 (9th Cir.2010) (per curiam) ("Tennard and Smith are retroactively applicable to the Arizona Supreme Court's... decision in this case."); see also Styers v. Schriro, 547 F.3d 1026, 1035-36 (9th Cir.2008) (applying Smith retroactively).
At the time of Williams' trial, Arizona courts recognized a nexus test similar to those rejected in Tennard and Smith. See, e.g., State v. Djerf, 191 Ariz. 583, 959 P.2d 1274, 1289 (1998) ("The trial court considered the evidence but found it irrelevant and declined to give it weight because proof was lacking that [the defendant's] family background had any effect on the crimes."). This court has repeatedly ordered habeas petitioners resentenced when the death penalty rested upon Arizona courts' use of this unconstitutional test. See, e.g., Lambright, 490 F.3d at 1114-15; Styers, 547 F.3d at 1035-36.
The Arizona Supreme Court made the same error in this case and we must reach the same result. By holding that "drug use cannot be a mitigating circumstance of any kind" unless Williams demonstrated "some impairment at the time of the offense," the Arizona Supreme Court imposed a "nexus" requirement contrary to Eddings, Lockett, Tennard, and Smith. The Arizona courts had discretion as to the weight to be given Williams' drug addiction, but erred by refusing to consider it at all unless he proved it was a factor in the crime. We thus vacate the death sentence, reverse, and remand for issuance of a writ of habeas corpus. "Further sentencing by the state court shall be conducted in conformance with applicable law." Lambright, 490 F.3d at 1128.

IV. Williams' Remaining Claims
Williams' brief to this court raised a number of issues the district court declined to certify. The district court found these issues procedurally barred and did not consider them on the merits. We have reviewed the district court's decision and reviewed the record and decline to certify any additional issues.

CONCLUSION
We vacate the judgment of the district court denying the petition and remand for *1272 an in-court evidentiary hearing on the petitioner's Brady claim challenging the conviction. We also remand with instructions to grant the petition on petitioner's claim of denial of due process at sentencing for failure to consider all mitigating circumstances. We otherwise affirm the denial of relief.
AFFIRMED in part, VACATED in part, and REMANDED.
IKUTA, Circuit Judge, dissenting in part and concurring in part:
I respectfully dissent from the majority's disposition of petitioner Aryon Williams's claim based on Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). While I concur in the result reached by the majority on Williams's other two claims, I write separately to express my disagreement with the majority's reasoning.

I
I agree with the majority that Williams's Brady claim is not procedurally barred and that we may consider its merits. I disagree, however, with the majority's decision to remand to the district court for an in-court evidentiary hearing. Instead, I would hold that the prosecution's suppression of the letters written by Beverly Sweat rose to the level of a Brady violation with respect to the penalty phase of Williams's capital case, but not with respect to the guilt phase. Accordingly, I would uphold the district court's denial of the habeas writ as to Williams's conviction, but grant the writ as to his sentence.

A
Five years after Williams was convicted and sentenced to death for the murder of Rita DeLao, the prosecution turned over to the defense a series of jailhouse letters offering to provide information about the DeLao murder in exchange for early release from jail. The letters had been received by the government six years earlier, before Williams's trial had begun, and were written by a woman named Beverly Sweat. They were addressed to Detective Tom Solis, the lead investigator in DeLao's murder.
In the letters, Sweat identified two individuals with information about DeLao's murder, Yolanda McKaney, a fellow jailmate of Sweat, and Milton Barnett. The letters also identified an additional perpetrator in the commission of the murder, Patrick Fields, and an alternate theory of the crime, namely that Williams had paid Fields to commit the murder on his behalf. Relevant here, the letters stated:
Try questioning Milton Barnett Jr. [Yolanda McKaney] mention his name too so may he knows something last WED, we went to the yard and me and Yolanda [McKaney] was talking to [Williams] an he said there was two people he was going to get one from Eloy → Patrick Fields one from Casa Grande Milton Barnette [Williams] kept asking question about Milton so check it out.
...
I went ahead an talk to Yolanda [McKaney] an she told me the what happen the night Rita [DeLao] good killed, she said she was walking down trekelle Road in Casa Grande an ran into Patrick [Fields] he was all bloody an she ask him why was he all bloody an he told her he had just killed Rita [DeLao] an [Williams] had paid him 1000 for doing it he had a knife on him, an said he used it to cut her eyes out also used a mopad to run over her an her an Patrick burned up the cloths he had on an the went an spent the money which took about two or three days. I think you should talk to her about this I know [Williams] is *1273 guilty of some part of it but I wish you would get me out of here before you bring it to surface....
Patrick Fields was a mentally unstable person who, at the time of DeLao's murder, had an extensive criminal history with charges including burglary, aggravated assault, and sexual assault. Fields was also responsible for a series of attacks against women in the months after DeLao's murder, in the same area where DeLao was killed.
Based on the government's withholding of these letters, Williams attempted to raise a Brady claim in a state postconviction petition. The state post-conviction court did not reach the merits of this claim, however, because it held that the claim was procedurally barred. Williams had asked for an extension of time to file the petition under Arizona Rule of Criminal Procedure 32.4(c)(1), which permits the state court to grant a defendant a sixty-day extension in which to file a successive post-conviction petition "[o]n a showing of good cause." The state court determined that there was no good cause for the extension and, as such, denied Williams's request.
Presenting the Brady issue to the district court, Williams moved for an evidentiary hearing to explore the scope of the prosecutor's potential wrongdoing. The district court granted the request, but determined that, "[i]n light of the narrow focus" of the Brady claim and "because [Williams's] motion d[id] not ... indicate why particular evidence requires oral presentation," it would conduct the hearing "through receipt of written evidence" rather than through live testimony. The government contested this ruling, arguing that an in-court hearing was necessary to permit cross-examination of Williams's witnesses. Williams responded that an in-court hearing was not warranted because the government had been given sufficient time to investigate the claim through discovery. The district court ultimately declined the government's request to conduct the hearing in person.
Reviewing the Brady issue on the merits, the district court focused its analysis on the declarations of McKaney and Barnett, which Williams's counsel had collected in the course of an investigation into the Brady issue after the government's disclosure of the Sweat letters, years after Williams's conviction and sentencing. McKaney's declaration reported that she had witnessed Fields burning a bloody shirt in an alley dumpster around the time of DeLao's death. Similarly, Barnett's declaration reported that he had seen Fields, covered in blood, dispose of something in an alley dumpster the day before he heard DeLao had been killed.
Ultimately, the district court concluded that the information regarding Patrick Fields was not material under Brady because it neither impeached Michelle Deloney's testimony that Williams had confessed to the crime nor "exculpate[d] [Williams]; rather it affirm[ed Williams's] involvement in the murder." The district court noted that McKaney and Barnett would be subject to "adversarial testing" in the event of a new trial because their declarations were inconsistent, both with each other and with the Sweat letters. In addition, the district court observed that the Sweat letters erroneously described the manner in which DeLao was killed, and that the credibility of Sweat and McKaney was subject to question because of the nature of their jailhouse discussions. Based on its holding that Williams had failed to satisfy Brady's materiality prong, the district court denied habeas relief.

B
As explained by the majority, the state court's denial of Williams's request for an *1274 extension under Arizona Rule of Criminal Procedure 32.4(c)(1), which had the effect of barring consideration of Williams's claim on procedural grounds, was not a "firmly established and regularly followed state practice" in the capital context, Ford v. Georgia, 498 U.S. 411, 423-24, 111 S.Ct. 850, 112 L.Ed.2d 935 (1991) (internal quotation marks omitted), and therefore the state court's ruling was inadequate to bar habeas relief. Because Williams's claim was not "adjudicated on the merits," 28 U.S.C. § 2254(d)(1), there is "no state court decision on this issue to which to accord deference," and I agree with the majority that our review of this claim is de novo. See Pirtle v. Morgan, 313 F.3d 1160, 1167 (9th Cir.2002) ("[W]hen it is clear that a state court has not reached the merits of a properly raised issue, we must review it de novo.").
"[W]hen the State withholds from a criminal defendant evidence that is material to his guilt or punishment, it violates his right to due process of law in violation of the Fourteenth Amendment." Cone v. Bell, ___ U.S. ___, 129 S.Ct. 1769, 1782, 173 L.Ed.2d 701 (2009). As the majority states, "[t]here are three components of a true Brady violation: The evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching; that evidence must have been suppressed by the State, either willfully or inadvertently; and prejudice must have ensued." Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). Stated otherwise, a Brady violation results when the prosecution suppresses evidence that is "material," that is, when "there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Id. at 280, 119 S.Ct. 1936. Under this standard, reversal of a conviction or sentence is required upon a "showing that the favorable evidence could reasonably be taken to put the whole case in such a different light as to undermine confidence in the verdict." Kyles v. Whitley, 514 U.S. 419, 435, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). Here, there is no dispute that the government suppressed the Sweat letters; therefore, the court's inquiry is confined to whether the suppressed letters are favorable to Williams and whether their suppression was prejudicial to the result of his proceeding.
Williams articulates a number of reasons why the Sweat letters are material. The letters identify by name an additional suspect in DeLao's murder and two individuals with information about the crime. The perpetrator identified in the letters, Fields, was mentally ill and had an extensive criminal history. According to the letters, Fields confessed to McKaney that he committed the murder, and this confession occurred on the night the murder occurred, while Fields was still covered in blood.
Williams argues that, because he was convicted and sentenced on the basis of circumstantial evidence, there is a reasonable probability that the result of the proceeding would have been different had the letters been disclosed. First, Williams contends that disclosure of the letters would have enabled him to point to another person who committed the crime, thereby supporting his claim of innocence. Williams asserts that, had he known about Barnett and McKaney, he would have been able to call them to the stand and they would have testified regarding their knowledge of Fields's participation in the crime. Williams claims he also could have introduced evidence that Fields was a likely suspect, based on his mental instability and history of committing criminal acts in the area.
*1275 Second, Williams theorizes that disclosure of the letters and the police's failure to follow up with Sweat, McKaney, and Barnett would have furthered his trial theory that the police were negligent in their investigation of the crime. Like the defendant in Kyles, Williams argues that the information in the letters would have permitted "the defense [to] examine[ ] the police to good effect on their knowledge of [Fields's] statements and so have attacked the reliability of the investigation in failing even to consider [Fields's] possible guilt." 514 U.S. at 446, 115 S.Ct. 1555.
Last, Williams contends that he could have used the information in the letters to impeach Michelle Deloney's testimony that Williams confessed to committing the crime, because the version of events described by Deloney differed from that depicted in the letters.
Our recent en banc decision United States v. Jernigan supports Williams's argument that the information regarding Patrick Fields as an additional perpetrator was material to Williams's defense. 492 F.3d 1050 (9th Cir.2007) (en banc). Jernigan also dealt with a situation where the prosecutor withheld information regarding another possible perpetrator of the crime for which the defendant was on trial. See id. at 1051. There, the defendant was charged with bank robbery based primarily on her physical likeness to eyewitnesses' descriptions of the robber. Id. The prosecutor withheld evidence of an alternative suspect fitting the same physical description who had been arrested for robbing nearby banks after the defendant was already in custody. Id. at 1054-55. In reviewing whether the suppression of the existence of the alternative suspect constituted a Brady violation, we determined that the information was material and therefore that the defendant's habeas writ should be granted. Id. at 1057.
Our holding in Jernigan was based on the principle that "[w]ithholding knowledge of a second suspect conflicts with the Supreme Court's directive that `the criminal trial, as distinct from the prosecutor's private deliberations, be preserved as the chosen forum for ascertaining the truth about criminal accusations.'" Id. at 1056-57 (brackets omitted) (quoting Kyles, 514 U.S. at 440, 115 S.Ct. 1555). Jernigan indicates that credible information about a second suspect to a crime is generally material and therefore should be disclosed to the defendant.
Like the suppressed evidence in Jernigan, the Sweat letters provide information that credibly indicates the existence of a second suspect. The letters give a detailed description of specific, named individuals, at least one of whom was known to the informant, all of whom were part of the same community in a small town. At least one of the individuals identified in the letters, Yolanda McKaney, allegedly interacted with Patrick Fields near the time of the murder and reported that he was covered in blood and confessed to the crime. Moreover, the prosecutor would have known at the time of receiving these letters that Fields was a plausible suspect, based on then-recent incidents in which Fields had attacked other women in the area. Under Jernigan, these circumstances weigh in favor of the letters' materiality.
For Williams to prevail on this claim, however, he must also prove that the letters are "favorable" to him, Strickler, 527 U.S. at 281, 119 S.Ct. 1936, either because they are exculpatory or because they have impeachment value. See id. at 281-82, 119 S.Ct. 1936. On this point, Williams's case and Jernigan diverge. Unlike the suppressed evidence in Jernigan, the Sweat letters do not exculpate Williams by proposing an alternative suspect to the DeLao *1276 murder; rather, they identify Fields as an additional suspect or accomplice to the crime. At most, the letters state that Williams paid Fields to commit the act, and they expressly maintain that "[Williams] is guilty of some part of it."
That the letters identify an accomplice rather than an alternative suspect is dispositive of Williams's claim that the letters are material as to his conviction. Our case law advises that suppressed evidence is not exculpatory (and a Brady claim will fail) if the evidence merely suggests that another person is "equally guilty" as the defendant, or if it fails to show that "the [defendant is] not guilty, or that he [is] any less guilty." Morris v. Ylst, 447 F.3d 735, 740 (9th Cir.2006). In Arizona, a person may be guilty of first degree murder whether he hires someone to commit the act or commits it himself, see Ariz.Rev.Stat. § 13-1105 (1989); e.g., State v. Carlson, 202 Ariz. 570, 48 P.3d 1180 (2002). Thus, while the information in the Sweat letters might have changed the prosecutor's theory of the case at trial, it would not have made Williams any "less guilty" of first degree murder. Accordingly, the non-disclosure of the letters cannot constitute a Brady violation with respect to the jury's finding of guilt on the murder charge.[1]
The majority points out that the Sweat letters could be exculpatory as to Williams's guilt "if the account of events provided by McKaney and Barnett in their declarations is accurate." Maj. Op. at 1267. I disagree. As discussed below, information that comes to light years after trial and sentencing cannot alter the materiality of potential Brady information because the Brady analysis must be made from the perspective of the prosecutor at the time of non-disclosure. The Sweat letters, not the McKaney and Barnett declarations (which were never in the prosecutor's files), are the potential Brady material. The Sweat letters are not exculpatory as to Williams's culpability for the crime, and McKaney and Barnett's post hoc declarations cannot retroactively make them so.
This does not end the inquiry, however. The Supreme Court has made clear that suppressed evidence which is not material to the defendant's guilt may still be material to the defendant's sentence. See Cone, 129 S.Ct. at 1786. Indeed, such was the case in Brady, in which the prosecutor suppressed an accomplice's confession to the crime for which the defendant was convicted and sentenced to death. Brady v. State, 226 Md. 422, 174 A.2d 167, 168 (1961). The state court determined that nothing in the accomplice's confession would have reduced the defendant's offense to a lesser crime than murder in the first degree, and hence the suppression was not material to the defendant's guilt. Id. at 172. However, the suppression was material to the defendant's sentence, and therefore the state court ordered a new trial on the question of punishment only. Id.; see also Cone, 129 S.Ct. at 1786 (holding that suppressed evidence was not material to the defendant's guilt but was material to his sentence). The Supreme Court affirmed. Brady, 373 U.S. at 91, 83 S.Ct. 1194.
In this case, as in Brady, the distinction between the value of suppressed evidence as to guilt and as to punishment is significant. While the Sweat letters are not *1277 exculpatory with respect to Williams's culpability for the crime, they are exculpatory with respect to his role in the physical act of murder, and thus raise a "reasonable probability" that, had they been disclosed, Williams would not have been sentenced to death. See Cone, 129 S.Ct. at 1783.
The state court sentenced Williams to death based on the presence of two statutory aggravating factors: (1) Williams was previously convicted of a felony involving the use or threat of violence (the armed robbery and attempted murder of Norma Soto), see Ariz.Rev.Stat. § 13-703(F)(2) (1989); and (2) Williams murdered DeLao in an especially heinous and depraved manner, see Ariz.Rev.Stat. § 13-703(F)(6) (1989).[2]State v. Williams, 183 Ariz. 368, 904 P.2d 437, 452 (1995). The state supreme court upheld application of this latter factor because the murder involved gratuitous violence "in excess of that necessary to kill," and because DeLao was helpless during the attack. Id.
In Arizona, the "heinous and depraved portion of the (F)(6) aggravator focuses on the defendant's state of mind at the time of the crime[ ] ... as evidenced through [the defendant's] actions." State v. Carlson, 202 Ariz. 570, 48 P.3d 1180, 1193 (2002) (internal citation omitted); see also State v. Gretzler, 135 Ariz. 42, 659 P.2d 1, 10 (1983) (holding that "heinous and depraved go to the mental state and attitude of the perpetrator as reflected in his words and actions"). The state court's ruling that "[Williams] committed the murder in an especially heinous or depraved manner," Williams, 904 P.2d at 452, was based on the assumption that Williams physically committed the crime (and hence the gratuitous violence of the slaying and helplessness of the victim could be attributed to his actions). The Sweat letters suggest, however, that Fields, and not Williams, committed the actual killing. There is nothing in the letters to indicate that Williams was even present when the murder occurred.
If the Sweat letters had been disclosed, Williams could have argued that he did not commit the crime in a heinous and depraved manner, because he did not physically murder DeLao and was not even a witness to the act. Thus, as pertains to sentencing, the letters contain exculpatory information that could have reduced the likelihood that Williams would be sentenced to death. The government's failure to disclose the letters was also prejudicial: without the aggravating factor of heinousness and depravity, the only basis for sentencing Williams to death would have been his prior violent felony conviction, and there is a reasonable probability that the trial court would not have applied the death penalty on that basis alone. Thus, by suggesting that Fields and not Williams committed the physical act of murder, the letters "could reasonably be taken to put the whole [sentencing proceeding] in such a different light as to undermine confidence in the [penalty applied]." Kyles, 514 U.S. at 435, 115 S.Ct. 1555. As such, it was a violation of Brady for the prosecutor to withhold the letters from Williams for sentencing purposes.

C
I respectfully dissent from the majority's decision to remand this case for an in-court evidentiary hearing. The majority *1278 errs in its decision to remand, both because Williams has waived any right to such a hearing, and because Brady does not allow a court to evaluate the materiality of suppressed evidence through the lens of information and testimony gathered years after trial.
First, the majority fails to acknowledge that Williams has waived his right to an in-court evidentiary hearing on this claim. Williams's appellate brief makes only passing mention of the in-court hearing issue without any analysis or legal authority. The rule in this circuit is that "we review only issues which are argued specifically and distinctly in a party's opening brief." Greenwood v. F.A.A., 28 F.3d 971, 977 (9th Cir.1994). "We will not manufacture arguments for an appellant." Id. Williams's single observation that the district court should have conducted an in-person evidentiary hearing, without supporting reasoning, is insufficient to raise this issue on appeal. See Hilao v. Estate of Marcos, 103 F.3d 767, 778 n. 4 (9th Cir.1996).
To the extent this issue is even before us, Williams is barred from arguing for an in-person evidentiary hearing. Not only did Williams fail to move the district court for an in-person hearing, he actively opposed one. Indeed, the reason given by the district court for holding a paper hearing rather than an in-court one was that Williams's motion for a hearing did "not identify specific evidence to be developed at an evidentiary hearing, or indicate why particular evidence requires oral presentation." Later, when the government requested that the hearing be conducted in-person, Williams objected, arguing that an in-person hearing was unwarranted because "[t]he State of Arizona has had over fifteen years since they received the letters to investigate these issues, and ... five additional months provided by [the district court] specifically for" the purpose of exploring inconsistencies in the McKaney and Barnett declarations. Given Williams's express disavowal of an in-court hearing, the district court's decision not to hold the hearing in-person was at most invited error, and certainly not a basis for remand here. See Marx v. Loral Corp., 87 F.3d 1049, 1056 (9th Cir.1996) (stating that appellants "should be barred from asserting [a] theory on appeal" that directly contradicts their position in the district court); Deland v. Old Republic Life Ins. Co., 758 F.2d 1331, 1336 (9th Cir.1985) (stating that a litigant "may not on review complain of issues ... where the objection is inconsistent with the position taken below" (internal quotation marks omitted)).
The majority's reasoning on this point misses the mark. While the majority explains Williams's motivation for opposing the State's motion (because in Williams's view, the State should have already completed its investigation of these matters), the majority does not make clear how this additional information negates the fact that Williams expressly opposed an in-court evidentiary hearing. See Maj. Op. at 1266-67. Rather, the majority acknowledges that the State moved for an in-court evidentiary hearing, and that Williams opposed it. Maj. Op. at 1266-67.
Second, an in-person evidentiary hearing would serve no purpose in this context. A reviewing court's evaluation of whether the suppression of a particular piece of evidence violated the prosecutor's duties under Brady is based on the character of the information known to the prosecutor at the relevant time, that is, before trial, during the course of trial, and during sentencing. See United States v. Agurs, 427 U.S. 97, 107, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976) ("[I]n advance of trial, and perhaps during the course of a trial as well, the prosecutor must decide what, if anything, *1279 he should voluntarily submit to defense counsel."); Villasana v. Wilhoit, 368 F.3d 976, 979 (8th Cir.2004) ("[T]he prosecutor's absolute duty to disclose under Brady is limited to evidence a reasonable prosecutor would perceive at the time as being material and favorable to the defense." (emphasis added)). Information that comes to light after trial and sentencing cannot alter the materiality of potential Brady information from the only perspective that matters: the perspective of the prosecutor at the time of non-disclosure. See Agurs, 427 U.S. at 108, 96 S.Ct. 2392 (stating that, though there is a "significant practical difference between the pretrial decision of the prosecutor and the post-trial decision of the judge" in determining what evidence must be disclosed, "[l]ogically the same standard [for evaluating the evidence] must apply at both times"). While it is true that Brady holds the prosecutor responsible for determining whether some seemingly insignificant piece of information may become material in the course of trial, the prosecutor has never been held responsible for foreseeing that such information could turn out to be material in the context of evidence developed years after trial. See Kyles, 514 U.S. at 437, 115 S.Ct. 1555 (stating that, under Brady, "the prosecution, which alone can know what is undisclosed, must be assigned the consequent responsibility to gauge the likely net effect of all such evidence and make disclosure when the point of `reasonable probability' is reached"). In light of this principle, neither the McKaney and Barnett declarations nor any further testimony at an in-court hearing can shed additional light on the question whether the prosecutor should have known that the Sweat letters were material as to Williams's guilt.
Rather than accepting this point, the majority attempts to smuggle post hoc evidence (such as the McKaney and Barnett declarations and an evidentiary hearing) into the Brady determination for an obvious reason: the Sweat letters themselves are not exculpatory as to Williams's guilt. Nor could a reasonable prosecutor have known that the Sweat letters might lead to exculpatory evidence, because contrary to the majority's suggestion, see Maj. Op. at 1267-68, the declarations contradict the Sweat letters as to the crucial issue of Williams's culpability for the crime. Prosecutors have no obligation under Brady to weigh whether the evidence in their files might somehow lead to future contradictory evidence in determining whether to disclose. To hold otherwise would be tantamount to requiring prosecutors to disclose everything in their case files, which Brady does not do. See United States v. Bagley, 473 U.S. 667, 675, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985) (stating that a prosecutor is not required under Brady to "deliver his entire file to defense counsel"). Because the Sweat letters themselves are not material to the guilt phase, and because post-hoc evidence will not make them so, there is no reason to require the district court to hold an evidentiary hearing.
For the same reason, the majority's reliance on Earp v. Ornoski, 431 F.3d 1158 (9th Cir.2005), for the proposition that credibility must typically be assessed through live testimony, Maj. Op. at 1266-67, is misplaced. It may be that, where credibility is properly at issue, "an in court hearing where the judge can see and hear the witnesses" is appropriate. Maj. Op. at 1266 (citing Earp, 431 F.3d at 1169-70). But because no credibility question arises in Williams's claim, there is no basis to hold such a hearing here.
Accordingly, the majority errs both in providing a form of relief to which Williams is not entitled, and in requiring the district court to consider the materiality of the Sweat letters in the context of *1280 after-acquired evidence that was not known and could not have been known to the government at the time of trial. The majority's new formulation of the prosecutor's Brady obligation represents a dangerous expansion, one which is contrary to the Supreme Court's balanced approach.

II
Although I concur in the result reached by the majority on Williams's other two claims, namely his claim under AEDPA that the state court unreasonably applied Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), and his claim under AEDPA that the state court should not have required a causal nexus between his drug use and crime of conviction at sentencing, I disagree with the majority's analysis, for the reasons described below.

A
Williams argues that the state court unreasonably applied Ake, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53, when it denied him psychiatric assistance at sentencing to present mitigating evidence related to his crack cocaine usage. The state supreme court reached this claim, but did not explain its reasoning in rejecting it. I agree with the majority that when the state court denies relief on the merits but provides no rationale for its decision, we "perform an `independent review of the record' to ascertain whether the state court decision was objectively unreasonable." Himes v. Thompson, 336 F.3d 848, 853 (9th Cir.2003) (quoting Delgado v. Lewis, 223 F.3d 976, 982 (9th Cir.2000)). In this situation, AEDPA deference still applies; "[t]hat is, although we independently review the record, we still defer to the state court's ultimate decision." Pirtle, 313 F.3d at 1167. "Independent review of the record is not de novo review of the constitutional issue, but rather, the only method by which we can determine whether a silent state court decision is objectively unreasonable." Himes, 336 F.3d at 853.
In setting forth the standard for when a criminal defendant is entitled to a psychiatric expert provided by the state, Ake distinguishes between the trial and sentencing phases of the defendant's criminal proceedings. See 470 U.S. at 83, 105 S.Ct. 1087. At trial, "when a defendant demonstrates to the trial judge that his sanity at the time of the offense is to be a significant factor at trial," Ake holds that "the State must, at a minimum, assure the defendant access to a competent psychiatrist who will conduct an appropriate examination and assist in evaluation, preparation, and presentation of the defense." Id. Psychiatric assistance in this context is limited by its terms to the defendant's trial and trial preparation, and does not extend to the defendant's sentencing proceedings. See id.
With respect to the defendant's due process entitlement to a psychiatric expert at sentencing, Ake provides a separate test. Under Ake, entitlement to a psychiatric expert at sentencing is limited to defendants charged with capital crimes. See id. ("We have repeatedly recognized the defendant's compelling interest in fair adjudication at the sentencing phase of a capital case."). "[I]n the context of a capital sentencing proceeding," Ake holds that a defendant is entitled to a mental health expert only "when the State presents psychiatric evidence of the defendant's future dangerousness." Id. at 84, 105 S.Ct. 1087. The defendant may use the psychiatric expert in this situation to "rebut the State's evidence of his future dangerousness." Id.
The majority fails to even acknowledge that Ake provided distinct tests for the trial phase and penalty phase of a defendant's case. Instead, the majority applies *1281 Ake's test for the trial phase to Williams's claim that he was deprived of a psychiatric expert at sentencing. Maj. Op. at 1269 (interpreting Ake as requiring the government to provide a psychiatric expert to a defendant, both at trial and capital sentencing, when the defendant can make the threshold showing that "his sanity at the time of the offense is to be a significant factor" (internal quotation mark omitted)); cf. Tuggle v. Netherland, 516 U.S. 10, 12, 116 S.Ct. 283, 133 L.Ed.2d 251 (1995) ("[W]e held in Ake[ ], that when a prosecutor presents psychiatric evidence of an indigent defendant's future dangerousness in a capital sentencing proceeding, due process requires that the State provide the defendant with the assistance of an independent psychiatrist"); Simmons v. South Carolina, 512 U.S. 154, 165, 114 S.Ct. 2187, 129 L.Ed.2d 133 (1994) (interpreting Ake as holding that a defendant is entitled to a psychiatric expert at capital sentencing proceedings "where the State presents psychiatric evidence of a defendant's future dangerousness"). The majority's interpretation of Ake, in my view, is erroneous.
Because Williams argues that he was denied a psychiatric expert only at sentencing, the state court's rejection of Williams's Ake claim could be contrary to or an unreasonable application of Ake only if the government presented psychiatric evidence of Williams's future dangerousness in his capital sentencing proceedings. 470 U.S. at 86, 105 S.Ct. 1087 (holding that the defendant was entitled to a psychiatric expert at sentencing because his "future dangerousness was a significant factor at the sentencing phase"). Here, the government did not. Applying the required level of AEDPA deference, it was therefore not objectively unreasonable for the state court to deny this claim. See § 2254(d)(1); Lockyer v. Andrade, 538 U.S. 63, 75, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003).

B
The state court refused to treat Williams's drug use as a mitigating factor in deciding his sentence. Williams contends that the state court's refusal was based on a requirement that his drug use have a direct causal nexus to his crime of conviction, and that this causal requirement was contrary to or an unreasonable application of Supreme Court precedent. See, e.g., Eddings v. Oklahoma, 455 U.S. 104, 114-15, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982). Because the state supreme court adjudicated this claim on its merits in a reasoned decision, the deferential AEDPA standard applies. See Himes, 336 F.3d at 852-53. Therefore, under § 2254(d)(1), we can reverse the state court's decision only if it "was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States."
As described in the majority opinion, at the time of Williams's trial, Arizona courts refused to consider mitigating evidence unless that evidence had a nexus to the crime for which the defendant was being sentenced. See, e.g., State v. Djerf, 191 Ariz. 583, 959 P.2d 1274, 1289 (1998). Following this rule, the state sentencing court declined to consider Williams's drug use as a mitigating factor because it determined that, "[w]ithout a showing of some impairment at the time of the offense, drug use cannot be a mitigating circumstance of any kind." Williams, 904 P.2d at 453.
I agree with the majority that this decision by the state court was contrary to the clearly established Supreme Court holdings in Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978) (plurality), and Eddings, 455 U.S. 104, 102 S.Ct. 869, both of which prohibit courts from categorically excluding mitigating evidence *1282 from consideration in capital sentencing proceedings. See Eddings, 455 U.S. at 114-15, 102 S.Ct. 869 ("[The sentencing court] may determine the weight to be given relevant mitigating evidence. But [the court] may not give it no weight by excluding such evidence from [its] consideration."); Lockett, 438 U.S. at 604, 98 S.Ct. 2954 ("[I]n all but the rarest kind of capital case, [the sentencing court should] not be precluded from considering, as a mitigating factor, any aspect of the defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death." (emphasis and footnote omitted)).
I write separately, however, because I disagree with the majority's reliance on Tennard v. Dretke, 542 U.S. 274, 284-87, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004), and Smith v. Texas, 543 U.S. 37, 45, 125 S.Ct. 400, 160 L.Ed.2d 303 (2004), as "clearly established Federal law" relevant to analyzing the state court's decision under AEDPA. The Supreme Court has made clear that "`clearly established Federal law' under [AEDPA] is the governing legal principle or principles set forth by the Supreme Court at the time the state court renders its decision." Lockyer, 538 U.S. at 71-72, 123 S.Ct. 1166 (emphasis added); see also Murdoch v. Castro, 609 F.3d 983, 990 (9th Cir.2010) (en banc) ("The Supreme Court has restricted `clearly established Federal law' under § 2254(d)(1) to `the holdings, as opposed to the dicta, of [the Supreme] Court's decisions as of the time of the relevant state-court decision.'" (internal quotation marks omitted) (emphasis added) (quoting Carey v. Musladin, 549 U.S. 70, 74, 127 S.Ct. 649, 166 L.Ed.2d 482 (2006))). As such, a federal court reviewing a state court's decision under AEDPA must consider only those Supreme Court precedents that were available to the state court at the time it conducted its review. See Williams v. Taylor, 529 U.S. 362, 390, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). We cannot fault the state court for failing to apply a precedent that did not come into existence until after its consideration of a petitioner's case. See id.
Here, the state supreme court rendered its decision on September 26, 1995. Williams, 904 P.2d 437. Therefore, at the time of its decision, the state supreme court had the benefit of the Supreme Court's holdings in Lockett, 438 U.S. 586, 98 S.Ct. 2954, and Eddings, 455 U.S. 104, 102 S.Ct. 869, which were issued in 1978 and 1982, respectively. Those cases constitute "clearly established Federal law" under AEDPA. See § 2254(d)(1); Lockyer, 538 U.S. at 71-72, 123 S.Ct. 1166. By contrast, the state supreme court did not have the benefit of Smith, 543 U.S. 37, 125 S.Ct. 400, and Tennard, 542 U.S. 274, 124 S.Ct. 2562, both of which were decided in 2004, almost a decade after the state court reviewed Williams's claim. Smith and Tennard are therefore not "clearly established Federal law," and the state court's decision cannot be judged against the principles announced in those cases. See Murdoch, 609 F.3d at 990.
The majority's reasoning that "Tennard and Smith are retroactively applicable" to Williams's claim, Maj. Op. at 1271, is beside the point. The issue is whether those cases are "clearly established" Supreme Court precedents under AEDPA, § 2254(d)(1); whether they announced retroactively applicable principles poses an entirely different question, which is not raised here, cf. Schad v. Ryan, 606 F.3d 1022, 1045 (9th Cir.2010). See Williams, 529 U.S. at 412, 120 S.Ct. 1495 (explaining that whether a Supreme Court precedent is retroactively applicable to a defendant's claim poses a different question than whether the precedent is "clearly established" *1283 for AEDPA purposes). Smith and Tennard are relevant, at most, because they reiterate the rule announced in Eddings and Lockett. See Styers v. Schriro, 547 F.3d 1026, 1035 (9th Cir.2008) (per curiam) (citing Smith for the principle articulated in Eddings). But beyond this limited applicability, Smith and Tennard are not and cannot themselves be considered "clearly established Federal law" for purposes of this court's analysis of Williams's claim.

III
The majority erroneously remands to the district court for an in-court evidentiary hearing on matters not relevant to deciding Williams's Brady claim. Not only is an in-court evidentiary hearing not warranted here, but it is a form of relief that Williams did not properly request before this court, and expressly disavowed before the district court. In my view, the government's failure to disclose to the defense credible information concerning an alternative perpetrator to the murder constituted a Brady violation with respect to Williams's sentence, and Williams's writ should be granted as to his punishment. I therefore respectfully dissent from the majority's treatment of Williams's Brady claim. Except for the issues identified above, I join my colleagues' decision as to the remainder of Williams's claims.
NOTES
[1]  Nor could the letters be used to impeach Deloney's credibility. See Strickler, 527 U.S. at 281-82, 119 S.Ct. 1936 (suppressed information is favorable to the accused when it is exculpatory or has impeachment value). Deloney testified that Williams confessed to her that he committed the crime. The letters do not bear any relation to Deloney's statements that Williams confessed, nor do they call into question Deloney's veracity as a witness.
[2]  The state court found no statutory mitigating factors, but found as non-statutory mitigation that Williams had no criminal record prior to the murder and that defendant had in the past displayed good conduct and character. Concluding that the mitigating evidence was insufficient to invoke leniency, the state court sentenced Williams to death. Williams, 904 P.2d at 444.
