Opinion by Judge CLIFTON; Partial Concurrence and Partial Dissent by Judge W. FLETCHER; Partial Dissent by Judge O’SCANNLAIN.
OPINION
CLIFTON, Circuit Judge:Jesse Gonzales1 was convicted in a California state court of first degree murder, with a finding of the special circumstance of killing a law enforcement officer engaged in the lawful pursuit of his duties, and was sentenced to death. The California Supreme Court affirmed the conviction and sentence and denied Gonzales’s petition for post-conviction relief. People v. Gonzalez, 51 Cal.3d 1179, 275 Cal.Rptr. 729, 800 P.2d 1159 (1990). The district court denied his petition for habeas corpus under 28 U.S.C. § 2254, and he appeals that denial to us.
Gonzales’s appeal requires us to consider and apply the decision of the United States Supreme Court earlier this year in Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011). In that decision, the Court held that in reviewing the petition of a state prisoner for habeas relief under the Antiterrorism and Effective Death Penalty Act (“AEDPA”) *972when the prisoner petitions for review of a claim adjudicated in the state courts on the merits under 28 U.S.C. § 2254(d)(1), a federal court may consider only the record that was before the state court when it adjudicated the claim.
One of the arguments made by Gonzales to the California Supreme Court and rejected by that court was that the prosecutor failed to turn over exculpatory material as required under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and related cases. The argument specifically referred to information concerning one prosecution witness, a jailhouse informant named William Acker. Acker testified during the guilt and penalty phases of Gonzales’s trial that Gonzales had admitted that he intentionally killed the deputy sheriff, in effect confessing to Acker that he was guilty of the crime and special circumstance alleged. Some material regarding Acker was turned over by the prosecutor to Gonzales’s defense counsel prior to trial, but other material, concerning Acker’s mental state and credibility, was not. Despite diligent effort by Gonzales, some of the documents that were not turned over did not become known to Gonzales until they were obtained during the federal habeas proceeding in district court, after the state court had rendered its decision. Those materials were not, therefore, part of the state court record.
Under Pinholster, we may not consider those later-discovered materials in reviewing Gonzales’s federal habeas claim. Because it appears to us that those materials strengthen Gonzales’s Brady claim to the point that his argument would be potentially meritorious — that is, that a reasonable state court might be persuaded to grant relief on that claim — it is not appropriate for us to ignore those materials. We remand that portion of the case2 to district court with instructions to stay the proceeding in order to give Gonzales an opportunity to return to state court and present his claim with the benefit of the materials that were not available and not part of the record at the time of the California Supreme Court decision. By that process, we seek to satisfy the intent of AEDPA, as discussed in Pinholster, 131 S.Ct. at 1398, that habeas claims of state prisoners be channeled in the first instance to state court.
We are not persuaded by the other arguments presented by Gonzales. Thus, we affirm the judgment of the district court as to most issues, but vacate the part of the judgment that denied the Brady claim (and related ineffective assistance of counsel claim, see note 2) and remand that claim to the district court with instructions to stay proceedings to permit Gonzales to present the claim to the California Supreme Court.
I. Background
Eleven plain-clothed sheriff deputies arrived in three unmarked vehicles at the home of Gonzales’s parents in La Puente to execute a search warrant on the evening of May 29, 1979. The search warrant was based on an undercover narcotics purchase made several days earlier from Gonzales’s *973cousin at the residence. Four of the deputies approached the front door and one of them knocked and stated “Los Angeles Sheriffs Department. We have a search warrant. Open the door.” Several seconds later the knock and announce was repeated.
The deputies heard what sounded like running and, fearing that narcotic evidence was being destroyed, they attempted to enter the house forcefully. Deputy Robert Esquivel eventually kicked in the door and his momentum carried him into the entryway. Esquivel saw Gonzales standing at the end of the hallway with a shotgun pointed at the front door. The shotgun blast missed Esquivel but hit Deputy Jack Williams who entered the house behind him. Williams died as a result of the shotgun wound. Gonzales was shot and apprehended by the deputies.
Gonzales was charged with first degree murder with the special circumstance of killing a peace officer who was engaged in the lawful pursuit of his duties. His trial was bifurcated into two phases, a guilt phase and a penalty phase. Each phase was tried before a different jury.
During the guilt phase, the facts of the shooting, as described above, were not disputed by the defense. Gonzales’s defense was that he had not heard the officers’ announcements and instead believed the officers were members of a rival gang, known as the Bassetts, coming to kill him and his cousin. The central question at trial was Gonzales’s understanding and intent at the time of the shooting.
The prosecution presented significant evidence showing that Gonzales could not have believed that the officers were gang members. All of the surviving deputies who were by the front door testified as to the manner of the entry and the shooting. In particular, they testified that while they were dressed in casual clothing, all of them, including the officer who was killed, had their badges either affixed to then-jackets or in their hands. They also testified that they twice announced that they were police before entering the home. Additionally, an officer with expertise in gang-related crime testified that La Puente was no longer an area of high gang activity. He testified that almost all gang violence consisted of drive-by shootings, conduct very different from the actions of the officers serving the warrant. He also described the typical gang warrior as a Latino teenager and gave reasons why the officers, all of whom were in their 30’s and, with the exception of Esquivel, were white, could not have been mistaken for gang warriors. Thus, the prosecution argued, Gonzales must have known that he was shooting at law enforcement officers, not rival gang members.
In addition, the prosecution presented evidence to support the contention that Gonzales not only knew he was shooting at officers but that he knew in advance that the police were coming and planned on using the raid as an opportunity to kill a police officer. This theory was based almost entirely on the testimony of William Acker, another prisoner held in the same jail as Gonzales. Acker testified that while in jail, Gonzales admitted to knowing that the men were officers because he had received a phone call informing him of the raid, and further that he planned to “bag a cop” when the officers served the warrant. Acker also testified that Gonzales had planned in advance to say that he believed the officers were Bassett members.
Gonzales sought to counter the prosecution’s evidence. He attempted to show that he reasonably could have believed the officers were gang members. He presented evidence of other gang-related violence in La Puente. He relied on the testimony of two officers with whom he spoke shortly *974after the shooting. Both officers testified that Gonzales told them he had believed the officers were Bassetts.3 To explain why it was reasonable for Gonzales to believe that the Bassetts would storm his house to kill him, Gonzales sought to establish that he had been a former leader of the La Puente gang, rivals of the Bassetts.
Gonzales testified in his own defense. His testimony was that he was inside the house when he heard the cars pull into the driveway. He went to the window but did not recognize the men. He testified that he focused on a Latino male who he said was the front seat passenger in one of the cars. He stated that he believed that the men were Bassetts. He denied seeing badges or hearing the announcements.
While Gonzales denied knowingly killing a police officer, his testimony about the shooting was inconsistent with the facts as described by all of the officers who testified. Among the many inconsistencies was that he insisted that Esquivel, the only Latino officer, was sitting in the front passenger seat. All of the officers stated that Esquivel was driving one of the cars. Gonzales also denied that the cars he saw were the ones the officers had identified as their vehicles.
The defense also sought to counter Acker’s testimony. Gonzales testified that he had never admitted to Acker that he knew the men were police officers. James Nobel, a prisoner who was housed in the cell between Acker and Gonzales, testified that he never saw Gonzales speak with Acker. Nobel also testified that Gonzales had asked him to read aloud the police reports of the incidents because Gonzales was illiterate. Both Gonzales and Nobel said that Acker could have overheard Nobel reading the police reports, which the defense argued explained how Acker knew specific facts about the shooting.
The defense also sought to impeach Acker. During cross examination, Acker admitted that he had previously pled guilty to a charge of murder and that he had provided evidence against his own wife concerning that murder. He denied being a police informant or giving information in other cases. He testified that he hoped giving the information would help him get transferred to an out-of-state prison because he believed he would be killed by gangs if he remained in California. He insisted, though, that he was testifying because “it was a step in the right direction” and would help him get balance in his life. Acker admitted that he could lie if he *975wanted to, but insisted that he was not lying about Gonzales’s statements.
Gonzales was convicted of first degree murder and the special circumstance of killing a police officer engaged in the lawful pursuit of his duties. The case then moved to the penalty phase. The state sought the death penalty. The first penalty phase trial resulted in a hung jury. The penalty phase was retried before a different jury.
The state’s penalty phase case was aimed at establishing aggravating factors that would outweigh any mitigating factors offered by Gonzales.4 The primary aggravating factor offered by the state was the aggravated nature of the killing, which the state sought to establish by proving that Gonzales was aware of the police raid and had planned out the killing of the officer, including his Bassett excuse. The focal point of the state’s case during the penalty phase was Acker’s testimony that Gonzales had confessed to Acker all the key facts that the state argued made Gonzales’s crime worthy of the death penalty.
During the penalty phase, the defense continued to maintain that Gonzales had believed the officers were gang members. However, faced with an existing guilty verdict on the charge of premeditated murder, the defense argued in the alternative that Gonzales did not know about the raid in advance and that therefore the crime was not so heinous and did not warrant the death penalty. For example, evidence was presented that Gonzales had gone to work that day and had not been waiting around for the officers. Gonzales did not testify again during the penalty phase, and no character evidence was presented on his behalf. The second penalty phase jury imposed the death penalty. The trial judge denied a motion for a retrial and a motion to modify the sentence.
Gonzales appealed his conviction and brought a petition for post-conviction relief to the California Supreme Court. The court considered both the appeal and the habeas petition at the same time. Gonzales’s habeas petition claimed, among other things, ineffective assistance of counsel based on his trial counsel’s failure to investigate and present positive character evidence. The California Supreme Court appointed a referee, a Superior Court judge, to review evidence and make factual findings as to what character evidence could have been uncovered by Gonzales’s counsel and what evidence the prosecution may have presented in rebuttal.
At the referee hearing, Gonzales’s trial counsel, Ralph Bencangey, testified about his investigation. He testified that he conducted it on his own and that he interviewed people from the neighborhood. He did not conduct an investigation into Gonzales’s health or school records and did not have Gonzales tested for mental health impairments.
Gonzales also presented character witnesses at the referee hearing who testified that Gonzales was a kind individual who had a loving and caring relationship with his children as well as other children. Some also testified that he was a “slow” child and had never learned to read. However, several of these witnesses had limited interactions with Gonzales, and none were aware of his involvement with *976gangs. Two of the witnesses also described the tragic death of Gonzales’s twin sisters in a train accident and the subsequent impact the tragedy had on Gonzales and his family. The referee made factual findings and filed a report with the California Supreme Court.
While Gonzales’s case was pending before the California Supreme Court, a scandal erupted regarding false testimony by jailhouse informants in Los Angeles. Leslie White, a jailhouse informant, revealed that he and other informants in the Los Angeles County jail had fabricated confessions during the period from 1979 through 1988.5 An investigation into the use of jailhouse informants by prosecutors found significant problems. While Acker was never officially identified as a jailhouse informant during the investigation, the revelations of how jailhouse informants had fabricated confessions led Gonzales’s lawyers to seek additional discovery regarding Acker. Gonzales filed discovery motions which were heard by the judge who had presided over his trial. The trial court granted the request for further discovery, but the State sought a writ of mandamus from the California Supreme Court to overturn the discovery order. That issue was consolidated with Gonzales’s habeas petition and direct appeal.
The California Supreme Court upheld Gonzales’s conviction and death sentence and rejected his claims for habeas relief. Gonzalez, 275 Cal.Rptr. 729, 800 P.2d 1159. On the discovery issue, the court held that the trial court could not authorize the discovery sought by Gonzales because it no longer had jurisdiction over the case. It also declined to grant the discovery requests under its direct appeal or habeas jurisdiction. Id., 275 Cal.Rptr. 729, 800 P.2d at 1203-07. The court stated, though, that “we expect and assume that if the People’s lawyers have such information in this or any other case, they will disclose it promptly and fully.” Id., 275 Cal.Rptr. 729, 800 P.2d at 1206. No such information was voluntarily disclosed to Gonzales.
Gonzales filed a petition for habeas corpus in federal court. The district court denied Gonzales’s request for an evidentiary hearing on most of the claims, but it granted discovery on the claim that Gonzales’s trial counsel failed to investigate and the state failed to disclose evidence that Acker was a government agent. This discovery did not unearth evidence that Acker was a government agent, but it did uncover impeachment evidence about Acker that had not been provided to the defense prior to the trial. Specifically, the state turned over six psychological reports prepared by prison psychologists on Acker while he had been incarcerated in California prisons between 1972 and 1979. These reports, discussed in more detail below, indicated that Acker had a severe personality disorder, was mentally unstable, possibly schizophrenic, and had repeatedly lied and faked attempting suicide in order to obtain transfers to other facilities.
Based on this new evidence Gonzales moved for reconsideration of the denial of an evidentiary hearing on his ineffective assistance of counsel and Brady claims. The district court denied the request, holding that while the newly discovered evidence “strengthened some of the elements” of these claims, it did not establish *977materiality. The court subsequently denied Gonzales’s other claims.
Gonzales sought and received a certificate of appealability from the district court under 28 U.S.C. § 22536 and brought this appeal.
II. Discussion
The provisions of AEDPA apply to Gonzales’s petition because it was filed on September 20, 1996, after AEDPA’s effective date. Under AEDPA, a federal court may not grant the writ based on any claim that was adjudicated on the merits by a state court unless the state court decision “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 ... resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d). The district court’s denial of a petition for a writ of habeas corpus is reviewed de novo. Lambert v. Blodgett, 393 F.3d 943, 964 (9th Cir.2004).
Gonzales has raised numerous claims in his habeas petition, some of which relate to the guilt phase, some to the penalty phase, and some to both. We begin by addressing his Brady claim, which he asserts as to both phases. It is the only claim on which we remand this case to the district court. We then address his other claims, which we conclude are not meritorious.
A. Brady Claim7
1. Procedural History
Gonzales’s state habeas petition raised a Brady claim based on allegations that the state failed to turn over evidence about Acker’s criminal history. His argument was based on an inaccurate criminal history printout given to Gonzales’s counsel. It showed Acker was serving a sen*978tence of life without parole, when in fact he was sentenced to life with the possibility of parole. The criminal history also omitted several burglary convictions. Gonzales argued that the state’s failure to correct these errors constituted a Brady violation. In addition, Gonzales argued that the state failed to inform him that Acker was providing information to the police in other criminal cases. The California Supreme Court rejected this claim, concluding that there was no prejudice because “these additional details do not paint a significantly different picture of Acker’s character and motives than appears on the record.” Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1193.
As noted above, Gonzales sought additional discovery about Acker from the state during the pendency of his state appeal. The state trial court granted Gonzales this discovery, but the California Supreme Court overturned the discovery order. This effectively ended Gonzales’s ability to pursue additional Brady claims in state court.
Gonzales’s initial federal habeas petition raised a Brady claim based on the same withheld evidence that was the subject of his state petition. The district court held that Gonzales suffered no prejudice from the withholding of the material and denied the request for an evidentiary hearing. When additional suppressed evidence was uncovered, Gonzales twice moved for reconsideration of his Brady claim. The district court twice denied the request, con-eluding that while the newly discovered evidence “strengthened some of the elements” of these claims, it did not establish materiality. The court based its conclusion on its belief that Acker was adequately impeached and his testimony was corroborated by other evidence. Notably, the district court concluded that “[a]t the guilt phase, and to a lesser degree at the penalty phase, this was not a case where it is likely the jury had to believe Acker’s testimony in order to believe the prosecution’s theory.”
2. Cullen v. Pinholster
After we heard oral arguments in this case, the Supreme Court filed its decision in Cullen v. Pinholster, — U.S.-, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011).8 We ordered and received supplemental briefs from the parties regarding the impact of that decision. Two elements of Pinholster are of particular importance for the case before us.
First, Pinholster specifically held that “review under § 2254(d)(1) is limited to the record that was before the state court that adjudicated the claim on the merits.” Pinholster, 131 S.Ct. at 1398.
Second, in announcing that holding, Pinholster emphasized that, under AED-PA, the state courts are to bear primary responsibility for adjudicating habeas claims brought by state prisoners. In the Court’s words, AEDPA “demonstrate^ Congress’ intent to channel prisoners’ *979claims first to the state courts.... ‘The federal habeas scheme leaves primary responsibility with the state courts.’ ” Id. at 1398-99, (quoting Woodford v. Visciotti, 537 U.S. 19, 27, 123 S.Ct. 357, 154 L.Ed.2d 279 (2002) (per curiam)).
The Acker psychological reports were not part of the record when the California Supreme Court rendered its decision because they were not obtained by Gonzales until later, while he was pursing his federal habeas petition in district court. A Brady claim was made before the state court, but it was narrower because Gonzales was not aware at the time of the psychological reports that had been withheld. As we discuss in detail below, we have concluded that the Acker psychological reports might have been helpful to Gonzales’s defense. Before discussing those reports, however, it is necessary to determine what consideration, if any, we can properly give to them in light of Pin-holster.
Gonzales argues that Pinholster*s limitation of our review to the record before the state court does not apply to his Brady claim based on the psychological reports because it is a “new claim,” not decided on the merits by the California Supreme Court. In Pinholster the Court referenced but declined to draw the dividing line between a “new claim” and a claim decided on the merits by the state court and subject to review under § 2254(d). Justice Sotomayor’s dissent in Pinholster questioned how the Court’s holding would apply to a hypothetical situation somewhat similar to the one before us: a petitioner who diligently pursued a Brady claim in state court is denied relief on the grounds that the withheld evidence presented in the Brady claim was not material, but subsequently is able to force production of additional undisclosed exculpatory evidence. Pinholster, 131 S.Ct. at 1417-18 (Sotomayor, J., dissenting). The majority opinion written by Justice Thomas responded to Justice Sotomayor’s concern by noting that “Justice Sotomayor’s hypothetical involving new evidence of withheld exculpatory witness statements may well present a new claim,” but stated that it did “not decide where to draw the line between new claims and claims adjudicated on the merits.” Id. at 1401 n. 10 (internal citation omitted).
Under the circumstances, we conclude that Pinholster applies here and prevents us from considering the new evidence in reviewing Gonzales’s Brady claim under § 2254(d). Gonzales raised and the state court explicitly rejected a Brady claim regarding information about Acker. Moreover, the suggestion that Gonzales has presented a “new claim” inherently invites questions regarding exhaustion. In light of Pinholster*s emphasis on the primary responsibility of the state court, we conclude that the new evidence needs to be presented to the state court before it can be considered by us on habeas review of the state court’s decision.
That does not mean that we can or should disregard the new evidence, however. We cannot fault Gonzales for a lack of diligence with respect to the withheld reports. Responsibility for the late appearance of those documents lies with the state. Despite discovery requests by Gonzales’s trial counsel and the inherent obligation of the prosecutor to turn over exculpatory material, these reports were withheld. Gonzales made further discovery requests while pursuing post-conviction relief in state court, but the California Supreme Court granted the State’s request to set aside the trial court’s order permitting the discovery. That court did so while expressing its expectation that prosecutors would voluntarily and promptly turn over any such evidence, but that *980expectation was not fulfilled. For us simply to ignore the materials that did not emerge until the federal habeas proceedings would be to reward the prosecutor for withholding them.
As discussed below, we conclude that if the new evidence were considered, Gonzales could make a colorable or potentially meritorious Brady claim, meaning that a reasonable state court could conclude that the withholding of the psychological reports constituted a Brady violation at the guilt phase, the penalty phase, or both. Because the claim is not clearly meritless, we do not believe dismissal of Gonzales’s Brady claim is the appropriate result.
We conclude that the appropriate course for us at this point is to remand to the district court with instructions that it stay and abey the habeas proceedings to allow Gonzales to present to state court his Brady claim including the subsequently-disclosed materials. In effect, we follow the suggestion offered by Justice Breyer in his concurring opinion in Pinholster that a petitioner “can always return to state court presenting new evidence not previously presented. If the state court again denies relief, he might be able to return to federal court to make claims related to the latest rejection.” See Pinholster, 131 S.Ct. at 1412 (Breyer, J., concurring).9
The stay and abey process is the same process that may be employed when a petitioner files a petition containing unexhausted claims. In Rhines v. Weber, 544 U.S. 269, 278, 125 S.Ct. 1528, 161 L.Ed.2d 440 (2005), the Court instructed that “if the petitioner had good cause for his failure to exhaust, his unexhausted claims are potentially meritorious, and there is no indication that the petitioner engaged in intentionally dilatory litigation tactics ... the district court should stay, rather than dismiss” the petition. Here, Gonzales had good cause for not presenting the new evidence to the state court, has not engaged in intentional dilatory litigation tactics, and, as is explained below, has a potentially meritorious claim.
This course provides the state court with the first opportunity to resolve this claim. It also protects Gonzales’s interest in obtaining federal review of his claim. As in the case of unexhausted claims that meet the Rhines requirements, Gonzales’s “interest in obtaining federal review of his claims outweighs the competing interests in finality and speedy resolution of federal petitions.” Id. Once the state court has spoken on this claim, Gonzales may, if necessary, return to district court and reactivate the federal proceedings.
We now turn to a discussion of the new materials. Our discussion below is only to demonstrate why we conclude that Gonzales has a colorable or potentially meritorious Brady claim such that a reasonable state court could find a Brady violation. We do not decide whether there was a Brady violation. That determination is for the California Supreme Court to make in the first instance.
3. A Potentially Meritorious Brady Claim
“The prosecution’s affirmative duty to disclose evidence favorable to a defendant can trace its origins to early 20th-century strictures against misrepresentation” by prosecutors. Kyles v. Whitley, 514 U.S. 419, 432, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). As the Supreme Court recognized in 1935, a prosecutor is “the representative not of an ordinary party to a controversy, but of a sovereignty *981... whose interest, therefore, in a criminal prosecution is not that it shall win a case, but that justice shall be done.” Berger v. United States, 295 U.S. 78, 88, 55 S.Ct. 629, 79 L.Ed. 1314 (1935). In subsequent decisions, most notably Brady, the Court has consistently “under-scored the ‘special role played by the American prosecutor in the search for truth in criminal trials.’ ” Banks v. Dretke, 540 U.S. 668, 696, 124 S.Ct. 1256, 157 L.Ed.2d 1166 (2004) (quoting Strickler v. Greene, 527 U.S. 263, 281, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)).
The Supreme Court has also repeatedly reaffirmed that Brady is one of the central bulwarks against injustice in our criminal justice system. The Court has stressed the central premise of Brady; even though an individual prosecutor may win a conviction, society as a whole loses when that conviction is wrong. Our system, therefore, places a “duty [on prosecutors] to refrain from improper methods calculated to produce a wrongful conviction.” Cone v. Bell, 556 U.S. 449,129 S.Ct. 1769, 1782, 173 L.Ed.2d 701 (2009) (quoting Berger, 295 U.S. at 88, 55 S.Ct. 629). Principal among a prosecutor’s duties is to provide a defendant with all material exculpatory and impeachment evidence prior to trial. This obligation recognizes the significant advantage the state has over an individual defendant in regards to gathering information and seeks to level the playing field. We expect our government to fight fair and not deny a defendant evidence that could exculpate him or ameliorate the penalty he faces. Only by giving a defendant this evidence can the government ensure that “justice is done its citizens in the courts.” Brady, 373 U.S. at 87, 83 S.Ct. 1194.
The elements of a claim for a Brady violation are that “[t]he 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, 527 U.S. at 281-82, 119 S.Ct. 1936. The state does not appear to contest the first two elements, so we discuss these only briefly before turning to the issue of materiality, which the state does contest.
a. Favorable to the Accused
In United States v. Bagley, the Supreme Court recognized that “[i]mpeachment evidence ... as well as exculpatory evidence, falls within the Brady rule,” because it is “favorable to an accused.” 473 U.S. 667, 676, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). There is a color-able argument that the psychological reports could have been used to impeach Acker. Impeaching Acker was important for Gonzales’s defense in both phases. Gonzales can, therefore, make a colorable argument that the withheld evidence was favorable to him.
b. Evidence was Suppressed
Gonzales can also make a colorable argument that the evidence was suppressed. Brady does not require a showing that the state willfully or intentionally suppressed the evidence; even inadvertent suppression will satisfy this prong of the test. See Brady, 373 U.S. at 87, 83 S.Ct. 1194 (suppression of evidence by prosecution violates due process “irrespective of the good faith or bad faith of the prosecution”). The psychological reports were in the possession of the prosecutor’s office prior to the trial. Even if they had not been, a prosecutor has a duty under Brady to “learn of any exculpatory evidence known to others acting on the government’s behalf.” Carriger v. Stewart, 132 F.3d 463, 479-80 (9th Cir.1997) (en banc) (prosecutor violated Brady when he *982did not turn over witness’s prison records); see also Strickler, 527 U.S. at 275 n. 12, 119 S.Ct. 1936.
c. Materiality
Suppressed evidence is material if “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, 514 U.S. at 435, 115 S.Ct. 1555. In other words, the petitioner does not need to prove that a different result would have occurred, just that there is “a reasonable probability of a different result.” Id. at 434, 115 S.Ct. 1555 (internal quotation marks omitted). “The question is not whether the defendant would more likely than not have received a different verdict with the evidence, but whether in its absence he received a fair trial, understood as a trial resulting in a verdict worthy of confidence.” Id. We conclude that a reasonable state court could conclude that there was a reasonable probability of a different result if the information contained in the psychological reports had been available to the defense and presented to the juries.
We reach this conclusion by undertaking a two-step inquiry. First, we ask whether a reasonable state court could conclude that there was a reasonable probability that the new evidence would have changed the way in which the jurors viewed Acker’s testimony. We determine that a state court could so conclude. We then ask whether a reasonable state court could conclude that there was a reasonable probability that this change would have resulted in a different verdict during either or both phases. We conclude that given Acker’s role in both phases, there is a pótentially meritorious claim that there was a reasonable probability of a different verdict at one or both phases.10
i. Jurors’ view of Acker
Our inquiry into how the jurors viewed Acker is primarily focused on how the withheld evidence could have provided additional or alternative means of impeachment. There is a colorable argument that a factfinder would have found the information about Acker contained in these reports disturbing, and that it would have been difficult for anyone, let alone a reasonable factfinder, to trust the witness described in these reports. The reports were prepared by psychologists employed by the State. They characterized Acker as predatory, manipulative, and unscrupulous, and they detailed his past lies and manipulations. See Bern v. Lambert, 283 F.3d 1040, 1055 (9th Cir.2002) (evidence that witness “had regularly lied” and “was untrustworthy and deceptive” would have “severely undermined his credibility.”).
Perhaps the most severe examples of Acker’s manipulative and deceptive behavior were the three occasions when he faked committing suicide in order to obtain prison transfers or otherwise influence his placement within the prison system. A 1972 Psychiatric Evaluation reported that Acker admitted that he had faked suicide at the Norwalk Receiving Center in order to be placed in the hospital, from which it would be easier to escape. A 1973 Psychiatric Evaluation reported an attempted hanging, which Acker stated “was only a gesture designed to prevent his egress from CMC East,” the hospital in which he had been placed. Finally, a 1974 report described another fake suicide attempt in *983April or May of 1974, which Acker said he faked because “he wanted out” of the facility.
Beyond the fake suicide attempts, the reports specifically described Acker’s other manipulative behavior. One of the psychiatrists reported that Acker asked, “how much money would it take to give me a good report.” Another psychiatrist described Acker as “the type of an individual who was constantly testing me.” The 1979 diagnostic study prepared for Acker’s sentencing for his murder conviction concluded that he was “intelligent, manipulative, unscrupulous” and “capable of any measure of brutality in the service of achieving what he wants to do.”
In addition to showing Acker to have a history of lying and manipulative behavior, the reports could be viewed to cast significant doubt on what Acker stated was his primary motivation for testifying against Gonzales. Acker repeatedly said that he was testifying because of a desire to turn his life around and do the right thing. The psychological reports showed that Acker had previously lied about reforming his life. The psychological report from 1972 stated that Acker told the psychologist he had turned his life around because he had “undergone a religious experience.” After making these statements and being released from prison, he committed first degree murder and numerous robberies.11 A subsequent social evaluation of Acker noted that he had been “offered therapy in the past and has used it as a tool to get out of prison early and has not attempted to use it as a tool to change his own behavior.”
A reasonable state court could conclude that these prior statements would have enabled Gonzales to show that Acker’s professed reason for testifying was false. A court could also conclude that Gonzales would have then been able to focus the jurors on Acker’s “continuing interest in obtaining [the state’s] favor” and that as a result “they might well have distrusted [Acker’s] testimony, and insofar as it was uncorroborated, disregarded it.” Banks, 540 U.S. at 701, 124 S.Ct. 1256; see also On Lee v. United States, 343 U.S. 747, 757, 72 S.Ct. 967, 96 L.Ed. 1270 (1952) (noting that testimony from witness receiving benefits from government “may raise serious questions of credibility”).
The reports also indicated that Acker had schizophrenia, which a reasonable state court could determine would have raised serious questions in the factfinder’s mind about Acker’s competency to perceive accurately and testify truthfully. As early as 1974, Acker was diagnosed with “[s]chizophrenia, chronic, undifferentiated type.” In 1975, he was diagnosed with “[schizophrenia, residual type.” A 1977 report noted that Acker was “mentally unstable” and had “a severe personality disorder, and he has previously been diagnosed as schizophrenic.” Courts have long recognized the impeachment value of evidence that a government witness has a “severe illness, such as schizophrenia, that dramatically impaired [his] ability to perceive and tell the truth.” United States v. Butt, 955 F.2d 77, 82-83 (1st Cir.1992) (“For over forty years, federal courts have permitted the impeachment of government witnesses based on their mental condition at the time of the events testified to.”). A reasonable state court could conclude that an assessment that Acker had not only lied in the past but had a mental condition that *984made him prone to lying could have affected the jury’s evaluation of his credibility.
Finally, a state court could conclude that the psychiatric reports would have provided an opportunity to impeach Acker by showing that the state’s own expert employees had repeatedly expressed doubts about Acker’s credibility, truthfulness, and competency. See Silva v. Brown, 416 F.3d 980, 988 (9th Cir.2005) (requirement witness not have psychological evaluation was evidence of “potentially devastating fact that the state itself doubted [the witness’s] mental competency”); Benn, 283 F.3d at 1055 (evidence that police doubted veracity of informant because of past lies was material Brady evidence).
The state argues, and the district court concluded, that regardless of the impeachment value of this evidence, it was nevertheless not material because Acker was already sufficiently impeached. Defense counsel did present some impeachment evidence, but courts have repeatedly held that withheld impeachment evidence does not become immaterial merely because there is some other impeachment of the witness at trial. Where the withheld evidence opens up new avenues for impeachment, it can be argued that it is still material. See Banks, 540 U.S. at 702, 124 S.Ct. 1256 (rejecting argument that since witness was otherwise impeached withheld impeachment evidence was immaterial); United States v. Kohring, 637 F.3d 895, 905-06 (9th Cir.2011) (even though witness was impeached on memory problems, evidence of alleged sexual misconduct and suborning perjury was not cumulative because it “would have added an entirely new dimension to the jury’s assessment of [the witness]” such that “ ‘there is a reasonable probability that the withheld evidence would have altered at least one juror’s assessment [of the evidence]’ ” (quoting United States v. Price, 566 F.3d 900, 914 (9th Cir.2009))); Horton v. Mayle, 408 F.3d 570, 580 (9th Cir.2005) (“[T]hat the jury had other reasons to disbelieve [the witness] does not render the suppressed [impeachment evidence] immaterial.”); Benn, 283 F.3d at 1055 (“The mere fact that a prosecution witness has a prior record, even when combined with other impeachment evidence that a defendant introduces, does not render otherwise critical impeachment evidence cumulative.”).
While cumulative impeachment evidence might have been immaterial, a reasonable state court could determine that the psychology reports “ ‘provided the defense with a new and different ground of impeachment’ ” and as such were not cumulative. Silva, 416 F.3d at 989 (quoting Benn, 283 F.3d at 1056.) In Silva, the court recognized that even though the witness was impeached on his forthrightness, the withheld evidence, in that case a plea deal which prohibited the witness from undergoing a psychiatric evaluation prior to trial, was not cumulative because it related to his reliability. In Carriger, the district court had ruled that an informant’s prison records, which described him as repeatedly lying, having a sociopathic personality, and being manipulative were immaterial for Brady purposes because the jury was made aware of his burglary conviction and plea deal. 132 F.3d at 480-82. Recognizing that the withheld evidence opened a new avenue of impeachment, we reversed because “the government cannot satisfy its Brady obligation to disclose exculpatory evidence by making some evidence available and claiming the rest would be cumulative.” Id. at 481.
During both phases defense counsel did attempt to impeach Acker by his conviction for murder, his desire to be transferred to an out-of-state prison, previous cases where Acker had testified about *985jailhouse confessions, and his statement that he could lie when he wanted to, although he denied doing so in this case. None of the evidence presented at trial actually demonstrated Acker had lied in the past or that he was known to be manipulative and deceptive. See Bern, 283 F.3d at 1055 (evidence that informant had lied in the past was noncumulative impeachment evidence). It is one thing for a witness to admit that he could lie; everyone can lie. Evidence of Acker’s past lies, deception, and manipulation would have provided hard evidence, different from that already presented, to support Gonzales’s argument that Acker was lying.
In addition, Gonzales has a colorable argument that the new evidence would have opened up other unexplored opportunities for impeachment. A reasonable state court could determine that none of the impeachment at trial touched on Acker’s competency to perceive and tell the truth, which reasonably could have been put at issue by evidence that Acker was schizophrenic. Similarly, there is a color-able argument that none of the impeachment evidence available to Gonzales at trial allowed him to cast doubt on Acker’s purported desire to turn his life around or demonstrate that the state had previously expressed doubts about Acker’s veracity and competency.
Finally, Gonzales has a color-able argument that the jury believed Acker despite the impeachment evidence presented to them. This argument could rest in part on the fact that Acker was an important witness for the government, especially during the penalty phase, and that “[i]n cases in which the witness is central to the prosecution’s case, the defendant’s conviction indicates that in all likelihood the impeachment evidence introduced at trial was insufficient to persuade a jury that the witness lacked credibility.” Bern, 283 F.3d at 1055.
There is also documentary evidence that a reasonable state court could conclude supports the argument that the jury believed Acker. In a memo written after the first penalty phase trial resulted in a hung jury, the prosecutor stated that he spoke with the first penalty phase jurors and that most of them, including all of the women, found Acker’s testimony convincing. Acker’s testimony and defense counsel’s cross examination were essentially the same in all three trials. Given that the cited jurors in the first penalty trial found Acker credible, this memo could be viewed to provide some evidence that the jurors in the other trials did as well.
In light of the manner in which Acker was described in these reports and the potential new avenues of impeachment opened by these descriptions, we conclude that a reasonable state court could determine that a jury would have doubted Acker’s veracity, motive for testifying, and competency if presented with the evidence in the psychological reports.
ii. A Different Outcome
We next consider whether there is a colorable argument that there is a reasonable probability that the additional impeachment of Acker through the psychological reports would have led to a different outcome at either the guilt or penalty phase. We conclude that a reasonable state court could decide that Acker’s importance to the prosecution’s cases was significant enough that additional impeachment of him reasonably could have changed the outcome.
Acker’s testimony amounted to a confession by Gonzales to first degree premeditated murder of a police officer, both the crime he was charged with and the facts the state argued warranted sentencing him *986to death. As the Supreme Court has noted “[a] confession is like no other evidence. Indeed, ‘the defendant’s own confession is probably the most probative and damaging evidence that can be admitted against him.’” Arizona v. Fulminante, 499 U.S. 279, 296, 111 S.Ct. 1246, 113 L.Ed.2d 302 (1991) (quoting Bruton v. United States, 391 U.S. 123, 139-40, 88 S.Ct. 1620, 20 L.Ed.2d 476 (1968) (White, J., dissenting)); see also Maxwell, 628 F.3d at 507-08 (informant was “the ‘make-or-break witness’ ” and his testimony about defendant’s jailhouse confession was the “centerpiece of the prosecution’s case”). While there was other circumstantial evidence, Acker’s testimony was the only direct evidence establishing that Gonzales had a premeditated plan to kill a police officer.
In addition, a state court could conclude that the damage the suppressed impeachment evidence could cause was “best understood by taking the word of the prosecutor.” Kyles, 514 U.S. at 444, 115 S.Ct. 1555. The prosecutor spent time during his summations discussing Acker’s testimony and countering the attempted impeachment of him, and a court could view this as further support for the proposition that Acker was central to the prosecution’s cases. See Horton, 408 F.3d at 580 (“The prosecutor’s emphasis on the importance of [the witness’s] testimony bolsters the conclusion that disclosure of the [impeachment evidence] may have significantly damaged the prosecution’s case.”). There is also the memo written by the prosecutor after the hung jury in the first penalty trial, in which the prosecutor stated that his ability to retry the penalty phase depended on whether “Acker is available and is willing to testify.” A reasonable state court could view the prosecutor’s arguments and memo as evidence that Acker was important to the prosecution’s case, especially in the context of the penalty phase.
We do not decide here that the new evidence would have resulted in a different outcome in either phase. It is possible that even without this new evidence the jury did not believe Acker. It is also conceivable that, based on the other evidence presented to it, the jury could have concluded that Gonzales was guilty and deserved the death penalty. However, in order to establish a Brady violation, Gonzales would only have to show a “reasonable probability” that the outcome would have been different. Given the nature of Acker’s testimony, a reasonable state court could conclude that Acker’s testimony “was the glue that held the prosecution’s case together,” Horton, 408 F.3d at 579, and that there is a reasonable probability that further impeachment of Acker could have resulted in a different outcome.
4. Remand to District Court
Based on the above analysis, we conclude that Gonzales could make a potentially meritorious or colorable Brady claim based on the psychological reports. In order to allow the state court to consider this Brady claim and to ensure Gonzales can seek federal review of the claim if necessary, we remand the case as to this claim to the district court with instructions to stay and abey the case pending review of this claim by the California Supreme Court.12
*987 B. Ineffective Assistance of Counsel: Character Evidence
As stated above, we are not persuaded by any of the other arguments presented by Gonzales. We start with several claims seeking relief based on ineffective assistance of counsel.
Gonzales contends that he received ineffective assistance of counsel during both the guilt and penalty phase because his attorney failed to investigate or present any character evidence during either phase. In order to establish ineffective assistance of counsel, a petitioner must prove both deficient performance by his counsel and prejudice caused by the deficiency. To demonstrate deficient performance Gonzales must show that counsel’s performance “fell below an objective standard of reasonableness” based on “the facts of the particular case [and] viewed as of the time of counsel’s conduct.” Strickland v. Washington, 466 U.S. 668, 688-90, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). In order to establish prejudice Gonzales “must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. at 694, 104 S.Ct. 2052. Because failure to meet either prong is fatal to Gonzales’s claim, there is no requirement that we “address both components of the inquiry if the defendant makes an insufficient showing on one.” Id. at 697, 104 S.Ct. 2052.
The California Supreme Court rejected Gonzales’s claims of ineffective assistance of counsel for failure to present character evidence. See Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1198-99.13 Under AEDPA this conclusion is reviewed only to ensure it is not contrary to or an unreasonable application of federal law. In reviewing the California Supreme Court’s ruling we are guided by the Supreme Court’s instruction that when a petitioner raises a Strickland claim through a habeas petition governed by the AED-PA, he must surmount two highly deferential standards. Harrington v. Richter, — U.S.-, 131 S.Ct. 770, 778, 178 L.Ed.2d 624 (2011) (“Federal habeas courts must guard against the danger of equating unreasonableness under Strickland with unreasonableness under § 2254(d).”). “[T]he question is not whether counsel’s actions were reasonable. The question is whether there is any reasonable argument that counsel satisfied Strickland’s deferential standard.” Id.
1. Guilt Phase
To support his claim of ineffective assistance of counsel during the guilt phase Gonzales points to evidence present*988ed during the referee hearing conducted at the request of the California Supreme Court. At the hearing, witnesses testified that Gonzales was a loving father who cared about his children, was attentive to them, and was also caring towards other children. He argues that this evidence was relevant because the parties stipulated that Gonzales’s infant son and another child were in the house when the shooting occurred. Gonzales argues that the character evidence would have strengthened his defense that he was not aware of the raid and was not planning to kill an officer, because if he had been, he would have made sure the children were out of the house.
It was reasonable for the California Supreme Court to conclude that this claim was meritless because the failure to present this character evidence was not prejudicial. First, it is unlikely the witnesses Gonzales might have called would have been persuasive. Two of the witnesses, Dr. Furth and Mr. Clancy, had very limited contact with Gonzales. Dr. Furth admitted to basing her opinion on the few times that Gonzales had brought his children to her office for medical appointments. Mr. Clancy was Gonzales’s middle school teacher and had seen him only a few times since then. The other witnesses, George Gonzales, Raymond de Jesus, Patricia Espinoza, and Maria Blanco, were either family or close friends, making their testimony suspect based on their close relationship with Gonzales and their admitted desire to help him avoid the death penalty.
Most importantly, none of these witnesses were aware of Gonzales’s gang involvement. Gonzales’s professed fear of a raid by the Bassetts necessarily highlighted his significant gang involvement, which would have cast doubt on how well the proposed witnesses knew him and on their ability to adequately judge his character. Furthermore, the fact that all of these witnesses would testify that they were unaware of Gonzales’s role as a gang leader could have undermined the defense argument that Gonzales feared attack by the Bassetts, giving defense counsel a strategic reason for not introducing this evidence.
Second, even if the jury were to afford some credibility to these witnesses, there was evidence which was inconsistent with these witnesses’ descriptions of Gonzales. Gonzales had left an unsecured shotgun and shells in the same room as his infant son. Drug paraphernalia including syringes were also found lying around the house. The jury could have seen these facts and Gonzales’s self-described gang history as inconsistent with someone who was purportedly so concerned for the welfare of the children.
Third, this character evidence would have provided limited support for the conclusion that Gonzales did not know about the raid in advance. According to Gonzales, this evidence demonstrated that if he knew about the raid in advance and was planning on killing a police officer, he would have ensured that the children were not in the home at all. But that assumed that Gonzales was aware of exactly when the police officers would arrive and knew when the children needed to be out of the house. The jury also could have thought that Gonzales merely did not think through his plan, or could have concluded that having the children in the house was part of Gonzales’s plan to make the shooting look like an accident.
Finally, even if the jury did draw Gonzales’s desired inference from this evidence and concluded based on the presence of the children that Gonzales did not have advance notice of the raid, the guilt phase jury could have convicted him even *989if they believed he did not have advance notice. The jury could also have found Gonzales guilty of first degree murder if they did not believe that Gonzales had advance notice, but did believe that he knew at the time of the shooting that the men were officers. If the jury convicted on this basis, the children being in the home would have been irrelevant.
2. Penalty Phase
Gonzales raises a similar claim in the context of the penalty phase, arguing that the failure of his lawyer to investigate and present character and background evidence during the penalty phase constituted ineffective assistance of counsel. The California Supreme Court rejected the claim because it found there was a valid strategic reason for not presenting character evidence. Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1197-1201. Once again, Gonzales must show that the California Supreme Court was unreasonable in reaching this conclusion. Gonzales cannot meet this requirement because he cannot show prejudice arising from the failure to present this evidence. See Wong v. Belmontes, — U.S. -, 130 S.Ct. 383, 386, 175 L.Ed.2d 328 (2009) (prejudice requires a showing of “a reasonable probability that a competent attorney, aware of the available mitigating evidence, would have introduced it at sentencing, and that had the jury been confronted with this mitigating evidence, there is a reasonable probability that it would have returned with a different sentence”) (internal quotation marks and alterations omitted).
Gonzales points to two types of character evidence that he claims his attorney should have discovered and presented. The first type, already discussed in the context of the guilt phase, consisted of testimony by family, friends, neighbors, and a former teacher, all of whom described Gonzales as a kind person who was respectful of adults and caring towards children. However, as discussed above, this testimony was suspect because none of these witnesses were aware of Gonzales’s drug and gang history. It is improbable that this evidence would have caused the jury to reach a different sentence.
More importantly, introduction of this evidence would have opened the door to evidence about allegations that Gonzales was involved in a gang rape in 1972. Gonzales had been accused of being involved in a gang rape but ultimately only pled guilty to a charge of misdemeanor battery on the victim’s friend. Defense counsel was able to limit evidence of this incident during the penalty phase to a stipulation as to this conviction. Gonzales’s attorney testified at the referee hearing that he did not develop or introduce character evidence because he was worried about the prosecution introducing additional details about the incident. The referee and the California Supreme Court found that had Gonzales raised the issue of his character, the prosecution would have been able to present the facts underlying the battery conviction.
While there was some evidence presented at the referee hearing that the rape victim would have denied that Gonzales had raped her, Gonzales still pled guilty to battery on the victim’s friend. Therefore, the best Gonzales could have hoped for was a showing that he was not one of the rapists but did batter the victim’s friend, and at worst the jury could have believed that Gonzales was involved in or assisted in allowing the rape. Given how weak the mitigating character evidence was, it was not unreasonable for the California Supreme Court to conclude that Gonzales’s counsel had a valid strategic reason for not introducing the character evidence so as to avoid the details of this incident. See Burger v. Kemp, 483 U.S. 776, 791, 107 *990S.Ct. 3114, 97 L.Ed.2d 638 (1987) (concern about prior convictions was valid reason not to introduce character evidence); Siripongs v. Calderon, 133 F.3d 732, 736-37 (9th Cir.1998) (same).
The second type of evidence was information about Gonzales’s life history. The bulk of this testimony portrayed Gonzales’s family as a stable lower-class family. The only potentially helpful information was that two of Gonzales’s sisters died in a train accident when he was younger and that after this accident Gonzales’s parents neglected the remaining children. This testimony came from Gonzales’s aunt. Additionally, the defendant’s brother testified that there was a change in the family after the death of his sisters. While it is unclear what these witnesses meant, it is conceivable that this evidence could have been presented to the jury to induce sympathy for Gonzales, and its introduction would not have opened the door to the gang rape evidence.
While this evidence could have been introduced, it was not the kind of evidence that would have made a sentencer “conclude[] that the balance of aggravating and mitigating circumstances did not warrant death.” Strickland, 466 U.S. at 695, 104 S.Ct. 2052. Generally Gonzales appears to have come from a stable family. While Gonzales’s aunt used the word “neglect,” it does not appear that she means that the children were abandoned or abused. Furthermore, Gonzales was already sixteen when the accident occurred so it is questionable how much any neglect would have affected him. Additionally, there was no evidence of the kinds of abuse which other courts have found sufficiently material to warrant relief. See, e.g., Wiggins v. Smith, 539 U.S. 510, 535, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (evidence of abuse at hands of alcoholic absentee mother and “physical torment, sexual molestation, and repeated rape” while in foster care); Boyde v. Brown, 404 F.3d 1159,1180 (9th Cir.2005) (counsel was deficient for failing to investigate and present evidence of physical and sexual abuse by parents). While the death of his sisters was undoubtedly tragic and the shock may have caused Gonzales’s parents to be inattentive to him, this evidence was not sufficient to engender enough sympathy to overcome the aggravating circumstances of the murder.
We conclude that the state court did not unreasonably determine that there was not a reasonable probability that had this evidence been presented to the jury the result would have been different. Since Gonzales failed to establish that the alleged deficiency by his counsel caused him prejudice, these ineffective assistance of counsel claims fail.
C. Ineffective Assistance of Counsel: Mental Impairment Evidence
Gonzales also alleges that his counsel was deficient because he failed to investigate and present evidence at the guilt and penalty phases that Gonzales had a mental impairment that would have affected his judgment at the time of the shooting. Gonzales points to a medical opinion by Dr. Stein, a doctor retained by Gonzales’s habeas counsel, which stated that Gonzales has a mental impairment which “would make it extremely difficult for him to choose between alternatives within a short period or to size up options available to him.” Dr. Stein also opined that “[e]ven if Gonzales had heard the police officers announce themselves, it is highly likely he would have still tended to distort or misperceive the events and have been unable to grasp the correct response.” Id. Gonzales asserts that this mental impairment evidence would have explained why, once he believed the men *991were Bassetts, he was unable to process the evidence that they were in fact officers.
The California Supreme Court rejected this claim because Gonzales had not shown that his counsel was deficient. In doing so it first determined that federal law contained “no blanket obligation to investigate possible ‘mental’ defenses.” Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1195. Rather, an attorney only needs to investigate mental health defenses if there are “facts known to counsel from which he reasonably should have suspected that a meritorious defense was available.” Id. It then made a factual determination that counsel was not aware of any evidence that would have made “the possibility of convincing ‘mental’ evidence ... reasonably apparent to a competent attorney.” Id. In reviewing this conclusion we once again ask only “whether there is any reasonable argument that counsel satisfied Strickland’s deferential standard.” Richter, 131 S.Ct. at 778. Here, there are reasonable arguments that counsel was not deficient. Because Gonzales has failed to satisfy his burden under the deficiency prong, there is no need to address the prejudice prong.
First, the California Supreme Court’s determination that there is “no blanket obligation to investigate possible ‘mental’ defenses, even in a capital ease” was not an unreasonable application of federal law. Strickland explicitly addresses counsel’s duty to investigate, instructing that “counsel has a duty to make reasonable investigations or to make a reasonable decision that makes particular investigations unnecessary.” 466 U.S. at 691, 104 S.Ct. 2052 (emphasis added); see also Wiggins, 539 U.S. at 527, 123 S.Ct. 2527 (“[A] court must consider not only the quantum of evidence already known to counsel, but also whether the known evidence would lead a reasonable attorney to investigate further.”); Douglas v. Wood-ford, 316 F.3d 1079, 1085 (9th Cir.2003) (“Trial counsel has a duty to investigate a defendant’s mental state if there is evidence to suggest that the defendant is impaired.”). There is no clear Supreme Court case law always requiring a mental health investigation at the guilt or penalty phase. See Pinholster, 131 S.Ct. at 1406-07 (“Strickland itself rejected the notion that the same investigation will be required in every case.”). The Court has generally eschewed blanket rules in the context of ineffective counsel. Strickland, 466 U.S. at 696, 104 S.Ct. 2052 (“Most important, in adjudicating a claim of actual ineffectiveness of counsel, a court should keep in mind that the principles we have stated do not establish mechanical rules.”).
Second, the California Supreme Court’s determination that counsel would not have been aware that a mental health investigation would lead to “materially favorable evidence,” Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1195, was a reasonable factual determination. The only facts that Gonzales suggested should have put his counsel on notice was the fact that Gonzales was illiterate and that he had been sick as a child. The California Supreme Court requested a response from defense counsel as to why he failed to conduct a mental health investigation, and he explained that Gonzales “seemed normal and alert, and he participated knowledgeably in strategy discussions.” Id., 275 CaLRptr. 729, 800 P.2d at 1194. In regards to Gonzales’s illiteracy, counsel stated “he attached little significance to defendant’s illiteracy, because poor reading skills are common in low-income communities for reasons unrelated to mental ability.” Id. The California Supreme Court found counsel’s responses uncontroverted and dispositive.
As Strickland requires, the California Supreme Court “evaluate[d] the conduct from the counsel’s perspective at the time” and then “judge[d] the reason*992ableness of counsel’s challenged conduct on the facts of the particular case, viewed as of the time of counsel’s conduct.” 466 U.S. at 689-90, 104 S.Ct. 2052. Given that “counsel is strongly presumed to have rendered adequate assistance,” id. at 690, 104 S.Ct. 2052, the California Supreme Court was not unreasonable in accepting counsel’s statement that from his perspective there was nothing unusual about Gonzales’s illiteracy, in combination with other facts he knew about Gonzales, that would have required him to seek a mental health evaluation.
Nor has Gonzales adequately explained why his illiteracy would have necessarily put his counsel on notice that a mental impairment defense would be fruitful. The fact that Gonzales appeared normal and alert and was able to participate in strategy discussions would have been much more relevant in considering whether to pursue a mental impairment investigation. We find nothing unreasonable with the state court’s conclusion that defense counsel did not have reason to believe that a mental health investigation would have been fruitful.14
D. Ineffective Assistance of Counsel: Evidence that Acker was a Government Agent
Gonzales also argues that his counsel was ineffective for failing to investigate and present evidence that William Acker was a government agent. Inherent in this claim is the assumption that Acker was a government agent. However, despite having pursued this claim for close to thirty years, Gonzales has never been able to provide evidence to support his assertion that Acker was acting as a government agent. As the California Supreme Court correctly noted, “[a]bsent evidence of direct motivation by the police or a prior “working relationship’ between Acker and the authorities,” there is no basis for concluding Acker was a government agent. Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1193.
Even after the discovery authorized by the district court, nothing in the record suggested that Acker had an established relationship with the police prior to his conversations with Gonzales. Gonzales points to the fact that Acker also testified about jailhouse confessions in other murder cases and argues that it cannot be mere coincidence that Acker was placed next to several murder suspects who all purportedly confessed to him. He also suggests that there was something unusual going on because Acker was referred for a probation evaluation even though he should not have been eligible for probation on his murder conviction.
*993Conjecture and coincidences cannot stand in the stead of actual evidence that Acker was a government agent, however, particularly given the high standard of deference given to the state court’s conclusion. We agree with the district court that “petitioner has not presented, and cannot come up with, clear and convincing evidence to controvert, or rebut the presumption of correctness applicable to, the state court’s finding that Acker did not act as law enforcement’s agent in petitioner’s case.” Because there is no evidence that Acker was a government agent, there is no basis to find that the conclusion reached by the California Supreme Court on this claim was factually or legally unreasonable.
E. Ineffective Assistance of Counsel: Lingering Doubt
Gonzales next argues that his counsel provided ineffective assistance during the penalty phase because his counsel failed to understand and explain to the jury the one mitigating factor he presented to the jury, “lingering doubt.”15 Lingering doubt was a valid mitigating factor recognized by the California Supreme Court in People v. Terry, 61 Cal.2d 137, 37 Cal.Rptr. 605, 390 P.2d 381, 387 (1964). Lingering doubt is some doubt regarding the defendant’s guilt for the crime of conviction, less than reasonable doubt but preventing absolute certainty, which mitigates against imposing the death penalty.
Defense counsel did try to create lingering doubt by presenting evidence during the penalty phase to support the theory that Gonzales had mistakenly believed the police were gang members. However, in his opening and closing statements, defense counsel made confusing statements that suggested that the jury could not consider whether they had doubt about Gonzales’s guilt. While counsel’s performance might have been less than stellar, his statements about lingering doubt did not have a material adverse effect on the penalty phase.
The prosecutor focused his case for aggravation almost exclusively on one aggravating factor, “the aggravated nature of the crime.” The state sought to establish this factor by proving that Gonzales knew about the raid in advance and planned to use the raid as an opportunity to “bag a cop.” In his opening statement during the penalty phase trial that produced the death sentence verdict, the prosecutor told the jury that “the evidence will show that the defendant planned to kill a cop. Not that it was thought of lightly, that it was just a split-second situation, spontaneous, but he planned to kill a cop. Something to the effect he was going to bag a cop.” During his summation the prosecutor reiterated that the murder deserved the death *994penalty because Gonzales “planned to kill a cop during a raid,” had “a detailed Bassett story to show how he was going to cover it up,” and was “standing there with a shotgun, lying in wait.” The prosecution’s penalty phase case rested on proving the “bag a cop” theory.
Having reached the conclusion that Gonzales’s crime warranted the death penalty, the jury necessarily found that the aggravating circumstances outweighed the mitigating ones. Given the prosecutor’s arguments, it is highly likely that they concluded there was a premeditated plan to “bag a cop.” Having reached this conclusion, they also necessarily rejected the argument that would have created lingering doubt, that Gonzales mistakenly believed the officers were gang members. Therefore, it was not unreasonable for the California Supreme Court to conclude that any deficiency in defense counsel’s lingering doubt argument was immaterial.
F. Prosecutorial Misconduct: False Testimony by Acker
Gonzales also claims that the prosecution used false testimony by Acker. Gonzales alleges that Acker lied about his reasons for testifying against Gonzales. It is clearly established law that “a State may not knowingly use false evidence, including false testimony, to obtain a tainted conviction. ...” Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959). The California Supreme Court applied this law and rejected this claim. It concluded that while there may have been inconsistencies in Acker’s testimony, “one cannot state a prima facie case of perjury or concealment simply by showing inconsistencies in the witness’s testimony.” Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1194. The California Supreme Court also rejected Gonzales’s contention that Acker perjured himself at the guilt trial by not mentioning that the state had paid for him to have one of his tattoos removed. The court noted that “any inference that Acker had received benefits for his cooperation in this and other cases by the time of the second penalty trial does not establish that his contrary guilt phase testimony was false when given.” Id., 275 CaLRptr. 729, 800 P.2d at 1174. Given the evidence before the court, this conclusion was reasonable.
The exact nature of Gonzales’s claim before this court is not entirely clear, but it appears to be that the California Supreme Court denied this claim without allowing him the opportunity to engage in the discovery necessary to support it. However, Gonzales was given the opportunity to conduct discovery into this claim by the district court and failed to uncover any evidence demonstrating the prosecutors knowingly allowed Acker to he during his testimony. Once again, conjecture and coincidence cannot win the day, particularly given the deference due the state court’s conclusions. Absent such evidence, there is no reason to question the California Supreme Court’s conclusion that the claim is meritless.
G. Hicks Claims
Gonzales next claims that his federal due process rights were violated by statements made by the prosecutor during his closing argument for the penalty phase. Gonzales points to three types of statements: instructing the jurors that they should not consider sympathy, discussing the jury’s discretion to impose the death penalty if it found the aggravating circumstances outweighed the mitigating circumstances, and suggesting the absence of a mitigating circumstance be treated as an aggravating circumstance.
Gonzales is unable to point to any clearly established federal law from the Su*995preme Court that establishes any of these statements as a deprivation of due process under federal law, as required by the AEDPA. Instead, Gonzales has argued that the prosecutor’s statements were in violation of state law and that in making these statements the prosecutor violated his constitutional right to have the jury exercise its discretion in the manner authorized by state law. He derives this principle from Hicks v. Oklahoma, 447 U.S. 343, 100 S.Ct. 2227, 65 L.Ed.2d 175 (1980), which held that if a state guaranteed a defendant the right to have a jury decide his sentence, it was unconstitutional to deny him resentencing by a jury after the statute under which he was sentenced was deemed unconstitutional. The Court stated that:
Where, however, a State has provided for the imposition of criminal punishment in the discretion of the trial jury, it is not correct to say that the defendant’s interest in the exercise of that discretion is merely a matter of state procedural law. The defendant in such a case has a substantial and legitimate expectation that he will be deprived of his liberty only to the extent determined by the jury in the exercise of its statutory discretion.
Id. at 346,100 S.Ct. 2227.
Gonzales reads Hicks too broadly. See Chambers v. Bowersox, 157 F.3d 560, 565 (8th Cir.1998) (distinguishing Hicks and “rejecting] the notion that every trial error, even every trial error occurring during the sentencing phase of a capital case, gives rise to a claim under the Due Process Clause”). In Hicks the defendant was denied his state law right to have a jury decide his punishment, which implicated issues of fundamental fairness. Hicks was not concerned with how a jury exercised its discretion. Here, regardless of the prosecutor’s statements, the decision to impose death was still made, as required by state law, by a jury in the “exercise of its statutory discretion.”
Moreover, Gonzales’s argument also fails because it relies on the erroneous conclusion that he was denied a right guaranteed to him by state law. See Ross v. Oklahoma, 487 U.S. 81, 91, 108 S.Ct. 2273, 101 L.Ed.2d 80 (1988) (rejecting Hicks challenge because defendant “received all that was due under [state] law”). Gonzales raised each of these claims as independent state law claims before the California Supreme Court. That court found no violation of state law in any of the prosecutor’s statements. See McSherry v. Block, 880 F.2d 1049, 1052 (9th Cir.1989) (“We are bound by th[e] state court’s construction of its own penal statute.”).
Finally, even if there was error, it was not enough to establish a denial of due process. That requires a showing of a denial of “that fundamental fairness essential to the very concept of justice.” Lisenba v. California, 314 U.S. 219, 236, 62 S.Ct. 280, 86 L.Ed. 166 (1941). This is not a case where “the prosecutor[’s] comments ‘so infected the trial with unfairness as to make the resulting conviction a denial of due process.’ ” Darden v. Wainwright, 477 U.S. 168, 181, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986) (quoting Donnelly v. DeChristoforo, 416 U.S. 637, 643, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974)).
H. Bouie Claim
Gonzales next claims a violation of his due process rights under Bouie v. City of Columbia, 378 U.S. 347, 353, 84 S.Ct. 1697, 12 L.Ed.2d 894 (1964). In Bouie the Court applied the underlying concept of the ex post facto clause of the Constitution, which on its face only applies to legislative acts, to the judiciary. It held that just as the ex post facto clause prohibits punishing an individual under a law *996that was not in effect at the time of the person’s actions, the due process clause protects against “unforeseeable judicial enlargement of a criminal statute.” Id. In other words, a court cannot reinterpret a criminal statute in an unforeseeable manner so that it criminalizes additional conduct and then apply that novel interpretation retroactively. We have considered Gonzales’s Bouie claim and conclude that there was no due process violation.
Gonzales’s claim arises out of the manner in which the jury was instructed on the special circumstance of which he was convicted: killing a peace officer engaged in the lawful performance of his duties. The trial court modified the instruction on the special circumstance so that the jury was instructed that a police officer serving a search warrant was engaged in the performance of his duties.16 Gonzales did not object to this instruction during trial, but in his direct appeal to the California Supreme Court he argued that the modification violated established California law. He contended that under California law an officer serving a facially valid, but actually invalid warrant was not engaged in the lawful performance of his duties and that the validity of the warrant was a question for the jury to decide. He argued the court erred by telling the jury that an officer serving a search warrant was automatically engaged in the performance of his duties, because in doing so it prevented the jury from making its own determination about the warrant’s validity.
Gonzales’s argument relied on the California Supreme Court’s holding in People v. Curtis, 70 Cal.2d 347, 74 Cal.Rptr. 713, 450 P.2d 33 (1969), that in order to be convicted of a crime with an element involving physical force against an officer the jury had to find that the officer was lawfully engaged in his duties. A footnote in Curtis suggested that an officer serving an invalid warrant was not lawfully performing his duties. Id., 74 Cal.Rptr. 713, 450 P.2d at 37 n. 4. However, the court had never explicitly held that an officer was not engaged in the performance of his duties if he was serving a facial valid but actually invalid warrant.
The California Supreme Court rejected Gonzales’s argument, and held for the first time, over a dissent, that “if a warrant is valid on its face, an officer carrying out its command to search or arrest is lawfully engaged in duty ... even if the facts disclosed to the magistrate in support of the warrant were not legally sufficient to establish probable cause.” Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1177. Because federal courts will not consider issues of state law as part of habeas review, Gonzales attempted to repackage this claim as a violation of federal due process. He argued that Curtis was the law at the time of his crime and that the California Supreme Court’s decision in his appeal was an unforeseeable enlargement of a criminal statute that was retroactively applied to him in violation of due process as established in Bouie.
There are several problems with Gonzales’s Bouie argument. First, the California Supreme Court’s decision in Gonzalez was not unforeseeable. In fact, we think it unlikely that the court would have reached any other conclusion. To do so would have sanctioned violence against law enforcement officers who believed they were lawfully performing their jobs. Curtis, which dealt with an officer making an *997unlawful arrest and using excessive force, was clearly directed at denying officers who were knowingly engaging in unlawful exercises of police power the extra protection of criminal statutes like the special circumstance at issue here. The dicta in the footnote, while suggesting that a warrant must be actually valid, is a broad, general statement which was not controlling law.
Even if we thought the California Supreme Court’s decision was unforeseeable, we do not believe that Bouie is applicable here. Bouie dealt with the reinterpretation of a criminal statute such that conduct that at the time would not be criminal was later held, after the fact, to be criminal under the statute. In Bouie, the South Carolina Supreme Court reinterpreted a trespassing statute that had previously been interpreted to only criminalize unlawful entry to, in addition, also criminalize remaining on property after being asked to leave. It then retroactively applied that new interpretation to civil rights demonstrators who had been charged with trespassing because they had refused to leave a restaurant where they were holding a sit-in. The Supreme Court held this interpretation to violate the due process clause because at the time the defendants acted their conduct was not criminal and they had no notice that their actions were illegal. Bouie, 378 U.S. at 362, 84 S.Ct. 1697.
Applying Bouie here would not further the principle underlying that decision. The theory behind Bouie was that judicial enlargement of a criminal statute, like an ex post facto law, fails to give a defendant adequate notice that his conduct is criminal. Id. at 350, 84 S.Ct. 1697 (discussing principle that “a criminal statute must give fair warning of the conduct that it makes a crime”). Here the court’s ruling had nothing to do with the defendant’s actions, but instead had to do with the victim’s status. An individual who sees an officer serving a warrant would not ordinarily know at the time that the warrant, was not valid. There is no suggestion that Gonzales knew that the search warrant was invalid or was justified in resisting it on that basis by shooting the officer attempting to serve it. Prior to Gonzalez, someone who shot an officer in the process of serving a warrant had notice that he may be subject to the death penalty. Bouie’s concern with fair notice to the defendant is inapplicable here.
Finally, even if we found Bouie applicable here, the alleged error was harmless. On habeas review the “substantial and injurious effect” standard applies to determine whether a constitutional error was harmless. Fry v. Pliler, 551 U.S. 112, 121, 127 S.Ct. 2321, 168 L.Ed.2d 16 (2007). Gonzales challenged the validity of the warrant on appeal and the California Supreme Court held that “[b]y any applicable standard, the warrant was valid.” Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1169. During the trial Gonzales never contended that the warrant was invalid and never introduced any evidence that would have cast doubt on its validity.17 *998Based on the evidence presented at trial, there was no basis for the jury to conclude the officers were not acting pursuant to their official duties. Therefore, there is no reason to believe the changed language affected the outcome of the trial. Since any error would have been harmless, Gonzales’s Bouie argument would fail regardless of its legal merit.
III. Response to Partial Dissent
The partial dissent disagrees with the portion of our decision that remands the Brady claim based on the psychological reports to the district court with instructions to stay the habeas proceedings until Gonzales has had an opportunity to present this new evidence to the California Supreme Court. Disagreement is expressed on both factual and legal grounds.
Factually, the partial dissent disputes our assessment of the impact of the psychiatric reports withheld from defense counsel, concluding that “[a]t most, these reports suggest that Acker has an antisocial personality and that he tries to manipulate the prison system to obtain transfers to his preferred place of detention.” Partial Dissent, at 20770. That characterization appears to us to be a substantial understatement, as demonstrated by the description of those reports set out above, at 20706-09. We also disagree with the partial dissent’s view that the withheld documents were not material because Acker had already been sufficiently impeached, as discussed at 20709-12. For the reasons discussed in more detail at 20712-14, we conclude there was a reasonable possibility that the verdict might have been different if the evidence had not been withheld.
The disagreement as to law is more significant. The partial dissent describes our decision as “an end run around PinholstePs holding from (1) a hypothetical problem cited in its dissent, (2) a hypothetical solution posed in a concurrence, (3) a footnote in the majority opinion responding to both, and (4) an incredibly broad definition of the word ‘claim.’ ” Partial Dissent, at 998.
The last comment is especially puzzling, because we do not adopt a “broad” definition of the word “claim.” We conclude that Gonzales had not presented a new “claim” distinct from claim already presented and rejected by the California Supreme Court, see above at 20701-02, though at a time when that court was not aware of the psychiatric reports withheld from the defense. Judge Fletcher’s separate concurring opinion raises the suggestion that this argument could be identified as a “new claim,” but that is not a conclusion of the majority opinion.
More broadly, the partial dissent reads Pinholster to say something which the majority of the Court explicitly declined to say. The discussion which the partial dissent describes as “hypothetical” appears to us to concern precisely the situation presented to us in this case: “new evidence of withheld exculpatory witness statements.” Pinholster; 131 S.Ct. at 1401 n. 10. If there were compelling evidence of that nature, the partial dissent would apparently have us disregard it, nonetheless.
The partial dissent does not fault petitioner for failing to discover the withheld information or for failing to include it in his previous petition to the California Supreme Court, and properly so. Gonzales can’t be blamed for not knowing or pre*999senting to the state court what was withheld from him.
The only fault found by the partial dissent is that, in its view, by not immediately requesting a stay and seeking to return to state court after learning of the psychological reports in 2003, Gonzales “engaged in intentionally dilatory litigation tactics.” Partial Dissent at 1021. But prior to the announcement of the Court’s decision in Pinholster earlier this year, there did not appear to be any barrier to Gonzales pursuing his argument in federal court. Pin-holster reversed a decision of this court, and the law in this circuit prior to that reversal did not require or even suggest that Gonzales should have done what the partial dissent castigates him for not doing. By the time of the Court’s decision in Pinholster was announced, Gonzales’s appeal had already been submitted to our panel for decision, so at that point there was nothing else for him to do.
Staying the proceeding in federal court to give Gonzales an opportunity to present the previously withheld material to the California Supreme Court is a sensible solution to the problem posed by this case. Indeed, we note that even the State, in supplemental briefing after oral argument of this case, suggested that we should return the case to state court to let it decide on the significance of the withheld information. That suggestion appears reasonable to us.
We doubt that the stay and abey process will have to be employed very often, because Pinholster is now the recognized law, and because there should not be many such instances of withheld exculpatory witness statements not discovered until years later, after state court proceedings have concluded. But to disregard that evidence in the situation presented by this case would be to reward the prosecution for successfully withholding the evidence in the first place. We cannot accept such an unjust and illogical result, and we do not believe that is what the law requires.
IV. Conclusion
We affirm all of the district court’s rulings on all of the non -Brady claims. However, because we believe that with the new evidence of the psychological reports Gonzales could make a colorable Brady claim, we remand to the district court on this claim (along with the related ineffective assistance claim) with instructions to stay the habeas proceedings until Gonzales has had an opportunity to present this new evidence to the California Supreme Court.
AFFIRMED in PART; REVERSED and REMANDED in PART.
. It appears that Gonzales’s name is spelled wrong in the case caption. This error dates back to his trial and is reflected in the caption of the California Supreme Court's decision as well. People v. Gonzalez, 51 Cal.3d 1179, 275 Cal.Rptr. 729, 800 P.2d 1159 (1990). In order to avoid confusion we have retained the erroneous spelling in the caption, but have correctly spelled Gonzales’s name in the opinion.
. In addition to the Brady claim, we also remand to the district court with similar instructions as to one of several ineffective assistance of counsel claims asserted by Gonzales, that being a claim that his counsel was ineffective for not earlier obtaining the materials that arguably would have impeached Acker. As we explain below, at 20698 note 7, that particular ineffective assistance claim substantially overlaps with the Brady claim. For clarity, we will generally not discuss or refer to that ineffective assistance claim separately, but when we refer to our disposition of the Brady claim we include that ineffective assistance claim as well.
. Deputy Mace testified that while en route to the hospital, Gonzales said that he had believed that the men trying to enter his home were members of the Bassett gang and that he did not know they were police officers until he had been shot. The testimony of Sergeant Verdugo, who investigated the murder with his partner Sergeant Overlease, was somewhat less clear. Verdugo testified about what Gonzales said during an interview at the hospital early the following morning. Gonzales described the incident as a "freak accident.” He initially stated that he was watering the lawn until he saw the “cops coming” and ran into the house. The record is unclear whether Gonzales recognized the men as "cops” when he saw them approaching the house, or whether his description of them as cops to Verdugo was based on his learning by the time of the interview that the men were police. The record is also unclear on what was said next. Verdugo testified at trial that Gonzales stated that he was confused. According to Verdugo's report of the conversation, Gonzales said that the officers were confused. It is undisputed that Gonzales then stated that he had been watering the lawn, but was inside with his infant son when he heard the cars arrive. He heard pounding and yelling at the door, but could not hear what was said. Gonzales reiterated to Verdugo that he believed the men were Bassett members.
. Under the 1978 California death penalty statute, in effect at the time of Gonzales's crime and applied at his trial, the guilt phase jury first had to find the defendant guilty of first degree murder and one of the enumerated special circumstances. If that requirement was met, the penalty phase jury was instructed to consider aggravating and mitigating circumstances and to impose the death penalty if it concluded that the aggravating circumstances outweighed the mitigating circumstances. See Cal.Penal Code § 190.3 (1978).
. Our court recently dealt with a case involving another informant from this period. See Maxwell v. Roe, 628 F.3d 486 (9th Cir.2010). Our colleague, Judge Stephen Trott, who previously served as a Los Angeles Assistant District Attorney, has written and lectured extensively about the problems inherent in prosecutors’ use of jailhouse informants. See Stephen S. Trott, Words of Warning for Prosecutors Using Criminals as Witnesses, 47 Hastings L.J. 1381, 1394 (1996).
. Gonzales failed to request a certificate of appealability on his claim of ineffective assistance of counsel based on the failure to investigate and present character evidence during the penalty phase. Gonzales claims to have inadvertently omitted this claim from his request and has asked this panel to grant one for it. Because the claim substantially overlaps with another claim which was certified, we conclude that the failure to request certification was an inadvertent mistake and grant the request for a certificate of appealability on this claim.
. Gonzales has also raised an ineffective assistance of counsel claim based on his counsel's failure to discover the impeachment evidence. The analysis of materiality for ineffective assistance of counsel is the same as the analysis of prejudice for Brady, see United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985), so our Brady prejudice analysis applies directly to this ineffective assistance of counsel claim. The district court rejected this ineffective assistance claim on the same ground that it rejected the Brady claim: the additional evidence was not material under Brady or prejudicial under Strickland. It is not clear to us that this ineffective assistance claim adds anything to Gonzales’s Brady claim, but out of caution we resolve this ineffective assistance claim in the same way as the Brady claim. It is remanded to the district court with the same instruction to stay and abey, in order to give the state court the first opportunity to resolve the claim in light of the late-disclosed materials. In order to avoid confusion with the other ineffective assistance claims asserted by Gonzales, as to which we affirm the district court’s dismissal, we will not separately discuss this ineffective assistance claim in this decision and will treat it as included within our discussion of the Brady claim.
By this action, we do not suggest any determination by us with regard to whether counsel’s performance was so unprofessional as to satisfy the other prong under Strickland. In order to give the state court a fair opportunity to consider the issue, we will not take it up ourselves now.
. Recently we followed Pinholster in denying a habeas petitioner’s request for an evidentiary hearing relating to an ineffective assistance of counsel claim involving new evidence not presented to the state court. See Stokley v. Ryan, 659 F.3d 802 (9th Cir.2011). We concluded that we did not have to determine whether Pinholster applied in that case, however, because the petitioner’s claim failed either way. Id. at 807. The present case poses a different situation, however, as the only relief sought by the petitioner in Stokley was for an evidentiary hearing. Id. at 808-09. Further, we found that the petitioner in Stokley did not present a colorable ineffective assistance of counsel claim, id. at 808-14, whereas the new evidence of psychological reports presented by Gonzales could make a colorable Brady claim.
. The separate opinion of Judge O'Scannlain, dissenting in part, disagrees with this portion of our decision in this case. The majority’s response to the partial dissent appears below, at 998-99.
. We recognize that it was probably true, as the district court suggested, that Acker’s testimony held greater importance in the penalty phase than in the guilt phase. We need not decide here whether the evidence was actually material in one or both of the trials, as that conclusion should be made in the first instance by the state court.
. The reports would also have shown that Acker was in fact a career criminal who first interacted with the law at age 8, and since the age of 14 had spent all but fourteen months incarcerated.
. While Gonzales’s Brady argument before this court focuses mostly on the Acker psychological reports, he also argues that the California Supreme Court erred by denying relief based solely on the evidence that Gonzales knew about and cited in his argument to that court, such that it is appropriate for us to grant habeas relief to him at this time. We disagree. Applying the AEDPA standard, we conclude that the determination of the California Supreme Court that there was no prejudice, based on the material known to it at *987the time of its decision, was not unreasonable. Gonzales's counsel was able to present evidence that Acker had committed murder and robbery in the past. The fact that he had committed several more robberies would not have painted a significantly different picture. Additionally, even though the criminal history printout indicated that Acker was not eligible for parole, Gonzales’s counsel still questioned Acker on whether he hoped that his testimony would help him with the parole board. We do not resolve whether the cumulative effect of the materials alleged at the time of the state court decision to have been withheld and the later-disclosed materials was prejudicial. The California court may consider that question for itself.
. The California Supreme Court only expressly ruled on this claim in regards to the penalty phase. However, "[wjhere a state court's decision is unaccompanied by an explanation, the habeas petitioner’s burden still must be met by showing there was no reasonable basis for the state court to deny relief.” Harrington v. Richter,-U.S. --, 131 S.Ct. 770, 784, 178 L.Ed.2d 624 (2011).
. We also note that while Gonzales has presented this argument as one about a mental impairment investigation, it is actually an argument that counsel did not think of a potential avenue for supporting the defense’s theory that Gonzales believed the officers were gang members. Just because counsel did not come up with all potential ways to prove the case does not make the counsel's performance ineffective. See Richter, 131 S.Ct. at 789 ("Counsel was entitled to formulate a strategy that was reasonable at the time and to balance limited resources in accord with effective trial tactics and strategies.”); see also Strickland, 466 U.S. at 689, 104 S.Ct. 2052 ("There are countless ways to provide effective assistance in any given case. Even the best criminal defense attorneys would not defend a particular client in the same way.”); Chandler v. United States, 218 F.3d 1305, 1316 n. 16 (11th Cir.2000) (“No lawyer can be expected to have considered all of the ways. If a defense lawyer pursued course A, it is immaterial that some other reasonable courses of defense (that the lawyer did not think of at all) existed and that the lawyer's pursuit of course A was not a deliberate choice between course A, course B, and so on.”).
. The California Supreme Court did not explicitly address this argument as an ineffective assistance of counsel argument. It did reject an argument that the jury was misled to ignore any lingering doubt in the penalty phase through either counsels' arguments or the jury instructions. This is, in essence, a conclusion that either counsel was not deficient or that any deficiency was immaterial. Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1189. It also rejected several unspecified ineffective assistance claims, which the court describes as including "incompetently failing] to ... present mitigating penalty evidence” and making "tactical errors at the penalty phase affect[ing] the balance of aggravation.” Id., 275 Cal.Rptr. 729, 800 P.2d at 1202. Gonzales exhausted the issue because his petition before the California Supreme Court clearly raised this issue as one of ineffective assistance of counsel. California Amended Petition at 65-6. "Where a state court’s decision is unaccompanied by an explanation, the habeas petitioner’s burden still must be met by showing there was no reasonable basis for the state court to deny relief.” Richter, 131 S.Ct. at 784.
. The instruction in question, with the modification in brackets, defined "performance of his duties” as "any lawful act of conduct while engaging in the maintenance of the peace and security of the community or in the investigation or prevention of a crime; [to wit, the serving of a search warrant].”
. Justice Mosk stated in his Gonzalez dissent that Gonzales presented evidence and argument that the police acted unlawfully when they broke into the residence to execute the warrant. Gonzalez, 275 Cal.Rptr. 729, 800 P.2d at 1210 (Mosk, J., dissenting). However Justice Mosk was not discussing the validity of the search warrant, but rather the means of entry, which is not at issue in this appeal. Furthermore Justice Mosk appears to have been mistaken; we can find no evidence that during trial the defense argued the officers’ entry into the house was unlawful. In fact defense counsel stated that he was not going to challenge that the officers knocked and announced themselves. Gonzales also evidently raised some arguments before the district court that the warrant was invalid, such *998"as differing heights and times between the warrant affidavit and the underlying arrest report.” Assuming, arguendo, that these alleged deficiencies could make the warrant invalid, these arguments were not made at trial.