Per Curiam Opinion; Concurrence by Judge SILVERMAN.
OPINION
PER CURIAM:Harvey Lee Heishman, III, a California prisoner under sentence of death, appeals from denial of a petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254. Heishman asserts claims of prosecutorial misconduct during the guilt phase of his trial and ineffective assistance of counsel during the penalty phase. We affirm.
I. Background and Standard of Review
Heishman met Nancy Lugassy in July 1979. Lugassy invited Heishman to her home the evening they met, and that night Lugassy ran crying to her neighbor and told him that she had been raped. Lugassy identified Heishman from a photo array, and police arrested him and charged him with rape. Heishman posted bail and then appeared for arraignment on October 24, 1979. The municipal court scheduled a preliminary examination for November 20, 1979.
On November 1, 1979, Nancy Lugassy was shot dead in her front yard, and Heishman was eventually arrested and charged with the murder. At trial, the prosecution presented the testimony of Lugassy’s neighbors, who had heard gunshots or identified the car that had driven away after the shooting, but the only direct evidence of Heishman’s involvement in the killing came from two witnesses: Cheryl Miller and Nancy Gentry. Both testified that they had been involved in Heishman’s plan to kill Lugassy, and both testified only after receiving complete immunity. Gentry was the only witness who placed Heishman at the scene on the night of the murder, and during more than a day of cross-examination Heishman’s attorneys, assistant public defenders William A. Keep and John Costain, conducted a thorough impeachment. Nevertheless, at the conclusion of the guilt phase, the jury found Heishman guilty of first degree murder with special circumstances.
During the penalty phase of Heishman’s trial, the aggravation evidence focused on Lugassy’s murder and Heishman’s history of sexual violence. See People v. Heish*1034man, 45 Cal.3d 147, 246 Cal.Rptr. 673, 753 P.2d 629, 666-67 (1988). Five women testified that they had been sexually assaulted by Heishman, and the prosecution submitted evidence of convictions for sexual assaults of two of the five witnesses and three additional victims. Id. at 650. Overall, the prosecution’s evidence showed that from December 1969 until July 1978, Heishman was either on probation, on parole or in prison for various sexual assaults. Id. at 666.
Heishman’s attorneys also presented a case in mitigation, which “pertained to [Heishman’s] general character and background.” Id. at 650. A chaplain, corrections officers and former employers testified as to Heishman’s good character and work habits, and two ex-girlfriends and his ex-wife testified as to their positive and nonviolent relationships with him. Id. at 650-51. His mother testified that he was an Rh-factor baby, requiring blood transfusions, and she and other family members described Heishman’s discovery of the body of his grandmother after she had committed suicide and his resultant withdrawal. Id. at 651. Heishman’s sister testified that she had participated in therapy sessions with her brother while he was in prison and that, when Heishman had talked about his prior rape cases, he had begun crying and expressed remorse for his earlier acts. Id. Heishman’s counsel did not present any psychiatric evidence. At the conclusion of the penalty phase, the jury sentenced Heishman to death.
Heishman pursued direct appeals culminating in a lengthy decision by the California Supreme Court affirming the conviction. See id. at 712, 246 Cal.Rptr. 673, 753 P.2d 629. He filed his federal habeas petition on June 26, 1990. After returning to state court multiple times to exhaust state remedies, Heishman filed the operative fourth amended federal petition in October 1993. The district court held multiple evidentiary hearings and issued over 200 pages of decisions before denying the last of Heishman’s claims on June 12, 2007, and entering judgment. After Heishman submitted a notice of appeal, the district court issued a certificate of appealability for the claims that we now address.
“We review de novo a district court’s decision to deny a petition for habeas corpus,” Bailey v. Hill, 599 F.3d 976, 978 (9th Cir.2010), although “[t]he district court’s factual findings are reviewed for clear error,” Stanley v. Schriro, 598 F.3d 612, 617 (9th Cir.2010). The decision to grant or deny an indigent habeas petitioner’s request for expert services “will be overturned on appeal only for an abuse of discretion.” Stubbs v. Gomez, 189 F.3d 1099, 1107 (9th Cir.1999). We similarly review “the decision to admit or deny expert testimony for abuse of discretion.” United States v. Reed, 575 F.3d 900, 918 (9th Cir.2009). The Anti-Terrorism and Effective Death Penalty Act (AEDPA) does not apply to Heishman’s petition for habeas corpus, which was filed nearly six years before AEDPA became law on April 24, 1996. See Lindh v. Murphy, 521 U.S. 320, 322, 327, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997).
II. Guilt Phase Error
Heishman first argues that the district court erred by finding that false testimony the prosecution failed to correct and Brady material the prosecution failed to disclose was immaterial. We agree with the district court and hold that there is no reasonable likelihood that the false testimony could have changed the jury’s verdict or that the cumulative impact of the false testimony and undisclosed Brady material would have changed the jury’s verdict. See Jackson v. Brown, 513 F.3d 1057, 1075-77 (9th Cir.2008).
*1035The district court assumed without deciding that the prosecution failed to correct false testimony under the obligations outlined in Napue v. Illinois, 360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959), and either found or assumed failure to produce categories of favorable discovery required by Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). Specifically, the district court found that the prosecution’s key witness — Nancy Gentry — testified falsely concerning both the scope of her prior criminal activity and remuneration for her testimony. The district court assumed without finding “that the prosecutor knowingly allowed Gentry to testify falsely that her criminal activity was limited to that discussed at trial and that she was receiving no consideration for her testimony other than immunity.” The district court also either found or assumed that the prosecution failed to turn over material concerning Gentry’s sexual relationships with law enforcement officers, police reports and a misdemeanor warrant concerning bad checks, a police report of a book theft and records of funds provided to cover costs incurred in connection with testifying.
Even adopting the district court’s assumption that the prosecution was aware that Gentry’s testimony was false, there is no reasonable likelihood that the false testimony could have changed the jury’s verdict or that the cumulative impact of the false testimony and undisclosed Brady material would have changed the jury’s verdict. See Jackson, 513 F.3d at 1075-77. Corrections of the false statements and the suppressed Brady material were similar to and cumulative of the extremely thorough impeachment during Gentry’s cross-examination, including proof that Gentry was an incorrigible liar and had lied numerous times during the proceedings, including while under oath. See United States v. Lopez, 577 F.3d 1053, 1059 (9th Cir.2009) (distinguishing between favorable evidence that must be produced under Brady and material evidence whose suppression requires a court to set aside the challenged conviction or sentence). Specifically, correcting testimony or disclosing information related to Gentry’s criminal activity would have been redundant with the history of passing bad checks, petty theft and theft of rental cars exposed during Gentry’s testimony. Payment for transportation, meals and lodging to facilitate testimony is petty in comparison to Gentry’s receipt of immunity. Cf. Hayes v. Brown, 399 F.3d 972, 986-87 (9th Cir.2005) (en banc) (holding that Napue error concerning a “critical deal” is material). Nor is it reasonably likely that cumulative consideration of Brady and Napue error would have swayed the jury in light of impeachment evidence concerning perjury, prior bad acts and Gentry’s involvement in the killing. A witness may be “so thoroughly impeached” that even evidence of perjury at trial is “merely cumulative.” United States v. Polizzi, 801 F.2d 1543, 1551 (9th Cir.1986).
III. Penalty Phase Ineffective Assistance of Counsel
Heishman also contends that his trial counsel rendered ineffective assistance of counsel at the penalty phase of the trial and failed to present an adequate case in mitigation. He alleges that counsel were deficient in two major respects. First, he maintains that counsel failed to conduct a timely and thorough investigation of his background and family relationships. Second, he contends that counsel failed to investigate his mental condition adequately. In particular, Heishman asserts that counsel provided ineffective representation by failing to follow a recommendation by *1036Dr. Hugh Winig that Heishman be evaluated by a psychologist. According to Heishman, such investigation would have revealed past psychological and physical trauma, namely alleged sexual abuse by his grandfather, Jack Schatt. He also maintains that a psychologist was likely to have diagnosed him with post-traumatic stress disorder (PTSD) stemming from the abuse. Heishman argues this information might have moved a juror to vote for life without parole instead of a death sentence.
We review this claim under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Heishman must establish that his counsel’s performance was deficient and that it prejudiced the outcome of his trial. Id. at 687-89, 694, 104 S.Ct. 2052. To establish deficiency, Heishman “must show that counsel’s representation fell below an objective standard of reasonableness.” Id. at 688, 104 S.Ct. 2052. To establish prejudice, he “must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 694, 104 S.Ct. 2052. “The legal question of whether a defendant received ineffective assistance of counsel is reviewed de novo, while any factual findings of the district court are reviewed for clear error.” Stankewitz v. Woodford, 365 F.3d 706, 714 (9th Cir.2004).
A. Unreasonable Delay in Investigation
Heishman first argues that trial counsel failed to begin the penalty phase mitigation investigation early enough. “The failure to timely prepare a penalty-phase mitigation case is ... error.” Allen v. Woodford, 395 F.3d 979, 1001 (9th Cir. 2005). Thus, “preparation for the sentencing phase of a capital case should begin early.” Id. In Allen, we held that counsel’s performance fell below professional standards when counsel “did not specifically prepare for the sentencing phase until after the guilt phase had concluded,” leaving “counsel one week in which to prepare the witnesses and evidence necessary to persuade the jury to spare [the defendant’s] life.” Id. at 1002; see also Williams v. Taylor, 529 U.S. 362, 395, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (“The record establishes that counsel did not begin to prepare for [the penalty] phase of the proceeding until a week before the trial.”).
Here, trial counsel opened the penalty phase investigation in August 1980, two months before trial, when they asked Heishman to prepare a list of potential witnesses. In September, counsel engaged Dr. Winig as their mental health consultant, directed their investigator to interview persons concerning Heishman’s background for the penalty phase and instructed the investigator to obtain Heishman’s Atascadero State Hospital, probation and prison records.
We find no constitutional error under 1980 professional standards in beginning the investigation two months before trial or in interviewing witnesses and retaining Dr. Winig only a month before trial. Although these efforts could have been initiated earlier, Heishman has not shown that counsel’s time-table was per se constitutionally deficient under professional norms existing in 1980.
Trial counsel’s failure to seek Heishman’s state mental hospital, probation and prison records before September 1980 presents a closer question of deficient performance. Because these records were not requested until September, counsel did not receive them until October — when trial was already beginning and perhaps too late to be useful for establishing investigative leads, identifying witnesses or informing Dr. Winig’s psychological evaluation. *1037See Allen, 395 F.3d at 1001. We need not determine whether this delay constituted deficient performance, however, because any error was not prejudicial. See Strickland, 466 U.S. at 697, 104 S.Ct. 2052 (“If it is easier to dispose of an ineffectiveness claim on the ground of lack of sufficient prejudice, which we expect will often be so, that course should be followed.”). The primary advantage of obtaining these records sooner would have been to provide them to Dr. Winig. Dr. Winig, however, recommended further psychological evaluation of Heishman even without reviewing the records. Absent prejudice, the delay does not amount to ineffective assistance of counsel.1
B. Failure to Investigate Heishman’s Family and Social History
Heishman contends that trial counsel failed to conduct a reasonable investigation into his family and social history. Professional standards in 1980 required counsel to investigate a capital defendant’s background, family relationships and mental condition as potential sources of mitigation evidence, in order to present “an individualized assessment of the appropriateness of the death penalty.” Ainsworth v. Woodford, 268 F.3d 868, 876-77 (9th Cir.2001); see also Smith v. Stewart, 189 F.3d 1004, 1009-14 (9th Cir.1999); Evans v. Lewis, 855 F.2d 631, 636-37 (9th Cir.1988); 1 ABA Standards for Criminal Justice 4-4.1 (2d ed.1980). A superficial investigation yielding “only rudimentary knowledge of[a defendant’s] history from a narrow set of sources” is constitutionally inadequate. Wiggins v. Smith, 539 U.S. 510, 524, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003).
Here, trial counsel’s primary approach to the penalty phase investigation was to ask Heishman to provide a list of schools, references, work experience and girlfriends and then to direct their investigator to use these witnesses to develop information “to make [Heishman] seem human to the jury.” Trial counsel did not, however, compile a comprehensive social history for Heishman and performed only limited interviews of Heishman’s family members in anticipation of the penalty phase.
According to Heishman, had trial counsel conducted a more comprehensive investigation, and begun the penalty phase investigation earlier, they might have discovered additional mitigation evidence of Heishman’s difficult childhood (even distinct from the sexual abuse we address separately below). A declaration submitted by Dr. Leslie Lebowitz, a clinical psychologist retained by Heishman in connection with these habeas proceedings, describes several aspects of Heishman’s background that might have been offered as mitigation evidence, including his sickly childhood, the family’s favoritism toward his sister and infliction of emotional and physical abuse, including whippings inflicted by his father and beatings from his grandfather. According to Dr. Lebowitz, Heishman’s “fundamental relation*1038ships were uniformly abusive, terrorizing and denigrating,” and “left him damaged, needy to the point of desperation and self-loathing.” In comparison to the picture painted by Dr. Lebowitz’s declaration, the jury heard very little of Heishman’s troubled childhood.
Whether trial counsel adequately investigated Heishman’s background under 1980 standards presents a close question. On the one hand, counsel conducted some investigation into Heishman’s background, presented some mitigation evidence of his troubled childhood and offered some evidence designed to humanize him to the jury. On the other hand, the investigation was limited. Neither Heishman nor his family were interviewed extensively about his background, and a more complete investigation might have revealed additional mitigating evidence.
Even assuming counsel’s performance was deficient in this respect, however, we conclude that there was no constitutional error because Heishman has not shown prejudice. Putting aside the history of sexual abuse discussed separately below, the additional mitigation evidence that might have been uncovered is not compelling when weighed against the case in aggravation. The compelling aggravation case included evidence of eight sexual assaults, and the jury had just convicted Heishman of a calculated, cold-blooded murder of another rape victim to prevent her from testifying-a truly heinous crime. Thus, even if Heishman had offered the additional evidence of his difficult upbringing, he has not shown a reasonable probability that the jury would have imposed a sentence of life without parole. See, e.g., Wong v. Belmontes, — U.S. -, 130 S.Ct. 383, 390, 175 L.Ed.2d 328 (2009) (per curiam) (finding no prejudice where the aggravation evidence was “simply overwhelming”); Rhoades v. Henry, 596 F.3d 1170, 1195 (9th Cir.2010) (holding “that [petitioner’s] newly proffered facts ... add too little, and the aggravating circumstances are too strong, to make it reasonably probable that the sentencing decision would have been different but for counsel’s performance”). Counsel’s investigation of Heishman’s background thus does not establish a Sixth Amendment violation.2
C. Failure to Follow Dr. Winig’s Recommendation for Further Evaluation
Heishman also contends that counsel provided ineffective assistance of counsel by disregarding Dr. Winig’s recommendation to have Heishman evaluated by Dr. Paul Berg, a psychologist. We hold that counsel’s performance was deficient, but Heishman has not shown prejudice.
1. Relevant Facts
Trial counsel retained Dr. Winig to perform a psychological evaluation of Heish*1039man and to determine whether Heishman had any mental health defenses. On the first day of trial, after meeting briefly with Heishman, Dr. Winig reported to Costain, junior defense counsel, that Heishman was “evasive” and could “give us nothing re mitigation” but recommended that counsel obtain further “psychological evaluation.” Dr. Winig recommended two psychologists, including Dr. Paul Berg.
In response to Dr. Winig’s recommendation, trial counsel asked for and obtained authorization from the public defender’s office to retain Dr. Berg. But counsel inexplicably failed to retain him. At the evidentiary hearing in the district court, Costain testified that he likely advised Keep, his superior, of Dr. Winig’s recommendation. Keep, on the other hand, testified that he could not recall Costain having discussed the recommendation with him. Keep asserted that had Costain conveyed the recommendation to him, he would have instructed Costain to retain Dr. Berg.
2. Reasonable Tactical Decision versus Deficient Performance
Counsel’s failure to follow Dr. Winig’s advice to investigate Heishman’s mental condition constitutes deficient performance unless it can be justified as a reasonable tactical decision. See Hendricks v. Calderon, 70 F.3d 1032, 1043 (9th Cir.1995) (“[W]here counsel is on notice that his client may be mentally impaired, counsel’s failure to investigate his client’s mental condition as a mitigating factor in a penalty phase hearing, without a supporting strategic reason, constitutes deficient performance.”); see also Bean v. Calderon, 163 F.3d 1073, 1078-80 (9th Cir.1998) (finding penalty-phase ineffective assistance of counsel where counsel waited 10 months to follow the recommendation of two mental health experts for further neuropsychological testing, because “when testing requested by expert witnesses is not performed, ... a capital defendant has not received effective penalty phase assistance of counsel”); cf. Hendricks, 70 F.3d at 1037 (rejecting a guilt-phase ineffective assistance of counsel claim where counsel followed a psychiatrist’s advice to obtain additional psychological evaluation). We therefore turn to whether counsel’s actions can be justified as a reasonable tactical decision, as the state argues and the district court found.
The district court concluded that counsel’s failure to follow Dr. Winig’s advice was a reasonable tactical decision because it was a byproduct of a reasonable decision on the part of counsel not to offer any psychological evidence at the penalty-phase trial. According to the district court, if counsel were justified in ruling out a psychological defense, they necessarily were also justified in cutting off further investigation of such defenses. We cannot agree with that assessment. A decision by counsel not to present mitigating evidence at trial cannot be excused as a strategic decision unless it is supported by reasonable investigations. Correll v. Ryan, 539 F.3d 938, 948 (9th Cir.2008). Here, counsel did not know what psychological evidence Dr. Berg’s evaluation might have produced. Hence, their decision to rule out a psychological defense cannot have been reasonable.
The state alternatively argues that we should presume that trial counsel made a reasonable tactical decision not to follow Dr. Winig’s recommendation because counsel can no longer remember the actual reasons for their actions. We need not decide whether to adopt such a presumption, cf. Sallahdin v. Mullin, 380 F.3d 1242, 1251 (10th Cir.2004); Williams v. Head, 185 F.3d 1223, 1228 (11th Cir.1999); Fretwell v. Norris, 133 F.3d 621, 624 (8th Cir.1998), because Keep has no memory *1040of receiving Winig’s recommendation. Presuming that Costain told Keep of the recommendation that Heishman be evaluated and that Keep then made a tactical decision not to follow Dr. Winig’s advice would contradict Keep’s testimony rather than filling a gap in memory, contravening the Supreme Court’s admonition against adopting “a post hoc rationalization of counsel’s conduct” instead of relying on an “accurate description of their deliberations.” Wiggins, 539 U.S. at 526-27, 123 S.Ct. 2527. We therefore hold that counsel’s failure to investigate his client’s mental condition, without a supporting strategic reason, constitutes deficient performance. See Hendricks, 70 F.3d at 1043.
3. Prejudice
We nonetheless conclude that Heishman has not shown prejudice. The district court found that Heishman would not have revealed his sexual abuse in 1980 even if counsel had referred him to Dr. Berg. That finding is entitled to deference. See Silva v. Woodford, 279 F.3d 825, 835 (9th Cir.2002) (“Our review for clear error is ‘significantly deferential,’ in that we must accept the district court’s factual findings absent a ‘definite and firm conviction that a mistake has been committed.’ ” (quoting United States v. Syrax, 235 F.3d 422, 427 (9th Cir.2000))); see also Strickland, 466 U.S. at 698, 104 S.Ct. 2052; Cullen v. United States, 194 F.3d 401, 405 (2d Cir.1999) (distinguishing “a factual issue, albeit a hypothetical one” from the ultimate issue of prejudice). We find no clear error here because, as we shall explain, the evidence on this question was equivocal.
On one hand, some evidence presented to the district court supports a conclusion that Dr. Berg would have uncovered Heishman’s history of sexual abuse and diagnosed him with PTSD. Melody Ermachild, a trained habeas investigator, was able to elicit Heishman’s history of what appears to be shocking sexual abuse by his grandfather (since deceased) by conducting 10, two-hour interviews with Heishman over a six-month period in 1990, using techniques similar to those which would have been used by Dr. Berg in 1980. Dr. Berg himself testified about the methods he would have used to extract information from Heishman and about a number of “red flags” in Heishman’s records that would have alerted him to the possibility of sexual abuse and PTSD, and opined that it was reasonably likely that he would have been able to elicit the sexual abuse history and to diagnose PTSD in 1980. Dr. Jay Jack-man, another expert testifying on Heishman’s behalf, concurred in those opinions.
Other evidence is to the contrary, however. For instance, Heishman had never disclosed the sexual abuse to anyone prior to 1990, despite opportunities to do so. For example, although Heishman underwent treatment by psychiatrist Frederick Boyes for nearly a year in 1969, he did not reveal his grandfather’s abuse. Similarly, Heishman underwent extensive evaluation with psychologist D.L. Kuykendall over a five-month period in 1968 — “a detailed analysis of more than twenty hours of diagnostic and therapeutic work” — without revealing this information. Once, in 1967, Heishman affirmatively denied — to a probation officer — that he had been abused.
Heishman also might not have revealed the sexual abuse to Dr. Berg “out of loyalty to his beloved grandmother,” who was still alive in 1980, but who had passed away by the time Heishman revealed the alleged abuse in 1990. Dr. Lebowitz and Dr. Jackman also testified about “patterns of secrecy” and a “code of silence” within the Heishman family. Drs. Lebowitz, Jackman, Daniel Martell (the state’s ex*1041pert) and Berg all testified that men are more reticent to reveal sexual abuse than women. Drs. Jackman and Berg also testified about the reluctance of prisoners to reveal a history of sexual abuse based on fear that they will be sexually abused by other inmates. Each of these factors would have presented an obstacle in 1980.
We emphasize that the district court heard the testimony from Dr. Berg and Dr. Jackman first hand and was therefore in the best position to assess the weight to be accorded their opinions. Dr. Berg’s testimony was weakened in several respects: he conceded that he was unfamiliar with the Heishman family’s “code of secrecy”; he never personally interviewed Heishman; and, most significantly, his opinion was contradicted by Dr. Martell, who testified that it was unlikely Heishman would have revealed the sexual abuse in 1980.
Given the equivocal nature of the evidence, we cannot say that the district court’s finding that Heishman would not have disclosed the sexual abuse to Dr. Berg is clearly erroneous. Having so held, we necessarily must reject Heishman’s prejudice argument. If Heishman would not have disclosed the abuse, his attorneys could not have presented evidence of the abuse or PTSD to the jury, and no juror could have been swayed by such evidence to vote for life without parole. Heishman’s ineffective assistance claim therefore fails.3
IV. Strickland Expert
After the district court hearing concerning the ineffective assistance claim, Heishman moved to expand the record to include testimony of a Strickland expert and for authorization of funds to retain the expert. In the alternative, Heishman moved to supplement the record with a declaration from the proposed expert. The district court denied these requests, concluding that “expert testimony on the standard of care is not required.” We hold that the district court did not abuse its discretion by concluding that it was “in a position to evaluate counsel’s performance” and “that petitioner’s proffered expert would not assist the court in determining the issues before it.”
*1042A federal court may determine that it does not require expert assistance “to understand the legal analysis required by Strickland.” Bonin v. Calderon, 59 F.3d 815, 838 (9th Cir.1995); see also Fed. R.Evid. 702, 1972 Comm. Note (directing courts to ask whether the finder of fact “would be qualified to determine intelligently and to the best possible degree the particular issue without enlightenment from those having a specialized understanding of the subject involved in the dispute”). Although some judges may find expert testimony helpful, see, e.g., Sims v. Brown, 425 F.3d 560, 584 (9th Cir.2005) (upholding denial of a Strickland claim where eight experts testified but none addressed “prevailing legal norms”), it is within a district court’s discretion to exclude proposed expert testimony concerning a legal standard of care and to rely solely on the briefs, see LaGrand v. Stewart, 133 F.3d 1253, 1271 n. 8 (9th Cir.1998); see also Williams v. Woodford, 384 F.3d 567, 613 n. 17 (9th Cir.2004) (holding that rejection of a proposed Strickland expert was not a prejudicial abuse of discretion). Because the district court was in the best position to determine whether it would benefit from expert testimony concerning prevailing death penalty defense standards, it did not abuse its discretion by declining to authorize payment for a Strickland expert and excluding the expert’s declaration.
V. Uncertified Issues
We decline to issue a certificate of appealability concerning Heishman’s competency or cumulative error claims. Heishman has not made a substantial showing of a denial of a constitutional right based either on the likelihood that he would not have disclosed childhood abuse to defense counsel had he been asked or on cumulative error. See 28 U.S.C. § 2253(c)(2); see also Miller-El v. Cockrell, 537 U.S. 322, 335-38, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).
VI. Conclusion
For the preceding reasons, we hold that the district court did not err by denying Heishman’s Brady, Napue and Strickland claims and did not abuse its discretion by denying funds for an expert concerning death penalty defense standards or by declining to admit the opinion evidence of such an expert.
AFFIRMED.
. For similar reasons, we reject Heishman’s argument that trial counsel provided ineffective assistance of counsel by failing to provide these records to Dr. Winig after counsel obtained them. We agree with Heishman and with the district court that failure to provide these records to Dr. Winig constituted deficient performance. See Stanley v. Schriro, 598 F.3d 612, 624 (9th Cir.2010) (“[T]rial counsel has an affirmative duty to provide mental health experts with all information relevant to the formulation of their conclusions.”); Wallace v. Stewart, 184 F.3d 1112, 1117 (9th Cir.1999). Like the district court, however, we conclude that the error was not prejudicial given that Dr. Winig recommended further evaluation even without seeing the records.
. There is also no merit to Heishman’s related contention that counsel unreasonably disregarded “red flags” in Heishman’s prison, probation and state mental hospital records that should have prompted them to conduct a more extensive investigation into his mental health background. To be sure, an attorney has a duty to pursue investigatory leads suggested by a defendant's records. See, e.g., Wiggins, 539 U.S. at 526-27, 123 S.Ct. 2527; Stankewitz, 365 F.3d at 719-20. But "[a] fair assessment of attorney performance requires that every effort be made to eliminate the distorting effects of hindsight ... and to evaluate the conduct from counsel’s perspective at the time.” Strickland, 466 U.S. at 689, 104 S.Ct. 2052. With the benefit of hindsight, and in particular given Heishman's disclosure of childhood sexual abuse in 1990, the records in possession of trial counsel in 1980 seem to point to the possibility of such abuse. Trial counsel, however, had neither the benefit of those 1990 revelations nor training in psychology, and they had little reason at the time to suspect that Heishman had been sexually abused as a child.
. The concurrence posits that Heishman may be fabricating his claims of sexual abuse. We recognize that possibility, though we point out both that we need not reach that issue and that the possibility of prevarication is contrary to the weight of the evidence in the record before us. Even the state’s expert, Dr. Martell, acknowledged that the abuse likely occurred, see Martell Depo. 21-22, and the state has not meaningfully challenged that conclusion in these proceedings.
We also need not speculate about how Heishman’s alleged history of sexual abuse would, or would not, have been presented to the jury in 1980 had Heishman revealed the abuse to Dr. Berg. We note, however, that the jury could have heard about Heishman’s sexual abuse in one of two ways. First, trial counsel could have presented expert psychological testimony regarding Heishman’s diagnosis for post-traumatic stress disorder. If so, the expert would have been able to base her opinions on inadmissible hearsay — Heishman’s out-of-court statements regarding sexual abuse — and to discuss both those opinions and the underlying hearsay in court, just as Heishman’s experts have done in these habeas proceedings. See Cal. Evid.Code § 801(b). Second, Heishman himself might have testified about the alleged abuse. Putting Heishman on the stand would have presented risks, but would not necessarily have exposed him to sweeping cross-examination. See People v. Ramirez, 50 Cal.3d 1158, 270 Cal.Rptr. 286, 791 P.2d 965, 987-88 (1990) (holding that the scope of cross-examination did not extend to any bad acts committed by the defendant during his life where defendant presented evidence of adverse circumstances that he experienced in his early childhood rather than evidence of his general good character). It is therefore at least plausible that trial counsel would have chosen to have Heishman testify about the abuse.