OPINION
PER CURIAM.
Petitioner Darick Demorris Walker was convicted by a Virginia state court jury of capital murder for the killings of Stanley Beale and Clarence Threat, use of firearm in the commission of a felony, and two counts of burglary. He was sentenced to death on the capital murder count and to prison terms on the other counts. The Supreme Court of Virginia affirmed Walker’s conviction and death sentence on direct appeal and denied Walker’s petition for state habeas relief. The district court dismissed Walker’s federal habeas petition and declined to grant a Certificate of Appealability (COA).
[760]*760Walker now seeks a COA to bring an appeal of the district court’s dismissal. Specifically, he asserts that he has made the required substantial showing that his Sixth Amendment right to counsel was violated at the guilt phase of his trial when his counsel failed to challenge his single trial for two murders, that his due process rights were violated when the Commonwealth failed to timely disclose Brady materials, and that his Sixth Amendment rights were violated at the sentencing phase of his trial when his counsel failed to investigate and present compelling mitigating evidence. Because reasonable jurists could debate the district court’s assessment of the first two of these claims (the right to counsel at the guilt phase of trial claim and the Brady claim) we grant a COA as to these claims; however, upon review of their merits, we affirm the district court’s dismissal. Because reasonable jurists could not debate the district court’s assessment of the right to counsel at the sentencing phase of his trial claim, we deny a COA as to this claim and dismiss.
I.
Stanley Beale lived with Catherine Taylor and their children, Monique, Bianca, and Sidney, in the University Terrace Apartments.1 On November 22, 1996, Taylor was in the bedroom with Sidney, an infant, when she heard “a boom like noise” coming from the living room. As she entered the living room to investigate, she saw a man, whom she identified as Walker, kick in the locked front door. Walker was holding a gun and began yelling, ‘Where is he?” Walker then asked Beale, who was standing in the doorway of the kitchen, “What you keep coming up to my door, what you look for me for?” Beale responded that he did not know Walker and did not know where he lived. Bianca, who was 13 years old at the time, began to shout at Walker, telling him that her father did not know him. When Walker began shooting at Beale, Taylor took Bianca and Monique into the bathroom to hide. Beale was shot three times and died. Bianca testified that she knew Walker as “Todd” and that she identified Walker in a photospread as the person who killed her father.
On the night of Beale’s murder, Tameria Patterson, a fourteen-year-old girl, was visiting a friend who lived in the University Terrace Apartments. Patterson testified that she saw a man she knew as “Todd” enter her friend’s apartment that night and say, “I shot him.” Patterson identified Walker in a photospread as the person who had entered the apartment and made the statement.
Approximately seven months later, on the night of June 18, 1997, Clarence Threat and Andrea Noble were sleeping in their bedroom. They were awakened by a “pop” coming from the screen door, which was followed by a knock at the door. Noble went to the door and looked outside through a small window in the door, but did not see anyone. Twice more she heard someone knocking but did not see anyone when she looked out the window. Sometime after the third knock, the door was “kicked open.” Noble went to the living room to find a person she knew as “Paul” standing there with a gun. “Paul” pointed the gun at Noble, who backed into the bedroom. When they reached the bedroom, “Paul” hit Noble with the back of the gun and then shot Threat in the leg. “Paul” and Threat “exchanged words” and [761]*761then “Paul” shot Threat six more times. Threat died from a gunshot wound to the chest. “Paul” warned Noble that if she told anyone “he would come back and kill [her] and [her] kids.” At trial, Noble identified Walker as the person she knew as “Paul.”
Walker was indicted on one count of capital murder for the killings of Beale and Threat within a three-year period in violation of Va.Code Ann. § 18.2-31.1(8) (Michie 1996), on four counts of the use of a firearm in the commission of a felony in violation of Va.Code Ann. § 18.2-53.1 (Michie 1996), and on two counts of burglary in violation of Va.Code Ann. § 18.2-90 (Michie 1996). On August 31 and September 1, 1998, Walker was tried before a jury in the Circuit Court for the City of Richmond and found guilty of all charges. He was sentenced to death for the capital murder conviction, life imprisonment for each of the burglaries, and a total of 18 years imprisonment for the firearms offenses.
On June 11, 1999, the Supreme Court of Virginia affirmed Walker’s conviction and death sentence. Walker v. Commonwealth, 258 Va. 54, 515 S.E.2d 565 (1999). The Supreme Court of the United States denied Walker’s petition for a writ of certiorari on January 18, 2000. Walker v. Virginia, 528 U.S. 1125, 120 S.Ct. 955, 145 L.Ed.2d 829 (2000). On March 23, 2001, the Supreme Court of Virginia dismissed Walker’s state petition for a writ of habeas corpus. The Supreme Court of the United States denied Walker’s petition for a writ of certiorari on October 29, 2001. Walker v. True, 534 U.S. 1003, 122 S.Ct. 481, 151 L.Ed.2d 395 (2001).
On February 1, 2002, Walker filed a petition for a writ of habeas corpus in the United States District Court for the Eastern District of Virginia. The district court dismissed Walker’s petition on July 26, 2002. On September 4, 2002, the district court denied Walker’s Motion to Alter or Amend Judgment and declined to grant a Certificate of Appealability (COA). Walker now seeks to appeal.
II.
To appeal the denial of habeas relief in the district court, a prisoner must first obtain a COA. See 28 U.S.C.A. § 2253(c)(1) (West Supp.2002). The first opportunity to obtain a COA is in the district court. When “an applicant files a notice of appeal, the district judge who rendered the judgment must either issue a certificate of appealability or state why a certificate should not issue.” Fed. R.App. Pro. 22(b)(1). In the present case, the district court denied Walker a COA. Because the requirement for a COA is jurisdictional, we may not consider the merits of Walker’s claims unless Walker has made the threshold showing required to obtain a COA. Miller-El v. Cockrell, 537 U.S. 322, 123 S.Ct. 1029, 1039, 154 L.Ed.2d 931 (2003) (“This threshold inquiry does not require full consideration of the factual or legal bases adduced in support of the claims. In fact, the statute forbids it.”). Thus our COA determination requires an overview of Walker’s claims and a general assessment of their merits.2
[762]*762To obtain a COA, a petitioner must make a “substantial showing of the denial of a constitutional right.” 28 U.S.C.A. § 2253(c)(2). “Under the controlling standard, a petitioner must ‘sho[w] that reasonable jurists could debate whether (or, for that matter, agree that) the petition should have been resolved in a different manner or that the issues presented were “adequate to deserve encouragement to proceed further.” ’ ” Miller-El, 123 S.Ct. at 1039 (quoting Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000), which in turn was quoting Barefoot v. Estelle, 463 U.S. 880, 893 n. 4, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983)). “A prisoner seeking a COA must prove something more than the absence of frivolity or the existence of mere good faith on his or her part. We do not require petitioner to prove, before the issuance of a COA, that some jurists would grant the petition for habeas corpus.” Id. at 1040 (internal quotation marks and citation omitted). ‘We look to the District Court’s application of AEDPA to petitioner’s constitutional claims and ask whether that resolution was debatable amongst jurists of reason.” Id. at 1039. “Where a district court has rejected [a petitioner’s] constitutional claims on the merits, ... [t]he petitioner must demonstrate that reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong” to obtain a COA. Slack, 529 U.S. at 484. Further, “[w]hen the district court denies a habeas petition on procedural grounds without reaching the prisoner’s underlying constitutional claim, a COA should issue when the prisoner shows, at least, that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right and that jurists of reason would find it debatable whether the district court was correct in its procedural ruling.” Id.
In his application for a COA, Walker raises three issues that were addressed by the district court. First, Walker argues that the state court’s conclusion that his trial counsel did not render ineffective assistance by failing to challenge his single trial for two murders was an objectively unreasonable application of federal law. He argues that the district court used an erroneous legal standard when it denied this claim. A COA is issued on this claim because Judge Gregory finds that reasonable jurists could debate whether the district court should have resolved this claim differently.3 We address the merits of the claim below.
Second, Walker asserts that the Commonwealth failed to disclose exculpatory materials in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). Walker challenges the state court’s decision that a portion of his Brady claim is procedurally defaulted and that the remainder is without merit. He argues that the district court erred by concluding that he had not shown cause for the default and by concluding that the state court’s resolution of the remainder of his Brady claim was not an unreasonable application of federal law. A COA is also issued on this claim because Judge Gregory finds that reasonable jurists could debate whether the district court should have resolved this claim differently. We address the merits of the claim below.
[763]*763Third, Walker argues that the state court’s conclusion that his trial counsel did not render ineffective assistance during sentencing by failing to investigate and present compelling mitigating evidence was an objectively unreasonable application of federal law. Specifically, Walker claims that his trial counsel was ineffective because he failed to timely discover and effectively present school records and mental health history, failed to investigate and provide records to Dr. J. Randy Thomas of the Medical College of Virginia’s Forensic Evaluation Program, Walker’s court-appointed mental health expert, and failed to discover Walker’s brain dysfunction. The state court, applying the two-part test for evaluating claims of ineffective assistance of counsel, see Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2062, 80 L.Ed.2d 674 (1984) (“[T]he defendant must show that counsel’s performance was deficient ... [and] that the deficient performance prejudiced the defense.”), concluded that Walker’s claim failed to satisfy the performance prong. The state court determined that counsel’s delay in acquiring Walker’s school records resulted from Walker’s and his mother’s recalcitrance, and Walker presented no evidence to the district court to rebut this conclusion. The state court also rejected Walker’s claim that his counsel was ineffective by failing to further investigate Walker’s organic brain damage and concluded that counsel’s decision to use Walker’s school records to demonstrate that Walker would respond well in a structured environment, rather than arguing that Walker suffered from an organic mental deficiency, was a reasonable trial strategy. The district court determined that the state court’s decision was not an unreasonable application of Strickland because, as there is only one reference to possible organic brain damage in Walker’s school records, Walker’s counsel was justified in pursuing and preparing an alternative theory better supported by the evidence. Moreover, both the state court and district court determined that counsel’s choice not to forward Walker’s school records to the court-appointed mental health expert was reasonable because after he had diagnosed Walker as a sociopath, the mental health expert was removed from the defense witness list. Our threshold review of Walker’s claim of ineffective assistance of counsel at the sentencing phase of his trial reveals that reasonable jurists could not debate the district court’s resolution of this claim. We therefore deny a COA on this claim. We address below the two claims on which we have granted a COA.
III.
Walker was convicted of “[t]he willful, deliberate, and premeditated killing of more than one person within a three-year period.” Va.Code Ann. § 18.2-31.1(8). He was tried in a single trial before a single jury. Walker asserts that his conviction is invalid because his trial counsel rendered ineffective assistance by failing to challenge the constitutionality of § 18.2-31.1(8), move for separate trials on the two murders, or request a jury instruction that evidence of one murder could not be considered in determining Walker’s guilt in the other.
As stated above, to show ineffective assistance of counsel “the defendant must show that counsel’s performance was deficient ... [and] that the deficient performance prejudiced the defense.” Strickland, 466 U.S. at 687. The state court held that Walker’s claim of ineffective assistance of counsel in the guilt phase satisfied neither the performance prong nor the prejudice prong of the Strickland test. Because the state court adjudicated this claim on the merits, we may not grant habeas relief unless the state court’s adju[764]*764dication “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.” 28 U.S.C.A. § 2254(d)(1) (West Supp.2002). Walker asserts that he is entitled to federal habeas relief because the state court’s decision was an unreasonable application of Strickland. (Appellant’s Br. at 14.) “ ‘[U]nder the “unreasonable application” clause, a federal habeas court may grant the writ if the state court identifies the correct governing legal principle from this Court’s decision but unreasonably applies that principle to the facts of the prisoner’s case.’ ” Lockyer v. Andrade, — U.S. -, 123 S.Ct. 1166, 1174, 155 L.Ed.2d 144 (2003) (citing Williams v. Taylor, 529 U.S. 362, 413, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)); see also Bell v. Cone, 535 U.S. 685, 122 S.Ct. 1843, 1850, 152 L.Ed.2d 914 (2002). “The ‘unreasonable application’ clause requires the state court decision to be more than incorrect or erroneous.” Lockyer, 123 S.Ct. at 1174; see also Williams, 529 U.S. at 411 (“[A] federal habeas court may not issue the writ [under the unreasonable application clause] simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly.”). Instead, “[t]he state court’s application of clearly established federal law must be objectively unreasonable.” Lockyer, 123 S.Ct. at 1174 (citation omitted). Walker, therefore, “must do more than show that he would have satisfied Strickland’s test if his claim were being analyzed in the first instance.” Bell, 122 S.Ct. at 1852. Rather, he must demonstrate that the state court applied Strickland in “an objectively unreasonable manner.” Id. This he cannot do. Because, as discussed below, the state court’s conclusion that Walker could not satisfy the prejudice prong was not unreasonable, we need not address the state court’s determination under the performance prong of Strickland.
To establish prejudice, a defendant “must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Strickland, 466 U.S. at 694. “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. It was not objectively unreasonable for the state court to conclude that there was no reasonable probability that a challenge to the constitutionality of § 18.2-31.1(8) would have produced a different result.
In Commonwealth v. Smith, 263 Va. 13, 557 S.E.2d 223, 226 (2002), the Supreme Court of Virginia rejected a claim that a single trial under § 18.2-31.1(8) constitutes a misjoinder of different offenses. The court explained that murders charged under § 18.2-31.1(8) are connected by the “fact that the capital murder and the predicate murder or murders occur within a three-year period.” Id. at 226. This “connection [is] similar to the link the General Assembly has established between capital murders and predicate offenses in other subsections of Code § 18.2-31.” Id. For example, Va.Code Ann. § 18.2-31(5) (Michie 1996) provides that “[t]he willful, deliberate, and premeditated killing of any person in the commission of, or subsequent to, rape or attempted rape” constitutes a capital murder offense. The Supreme Court of Virginia thus concluded in Smith that “the Commonwealth may join two or more counts or charges of murder in a prosecution under Code § 18.2-31.1(8) despite the prejudice that may result thereafter ... [if] the murders shall have occurred within a three year period.” Id. at 227. Because the Supreme Court has never addressed whether it is a misjoinder to have a single trial for a capital offense [765]*765involving the commission of two murders within a set period of time, the Smith decision does not contradict clearly established federal law.4 Walker, therefore, has failed to show that there is a reasonable probability that his challenge to § 18.2-31.1(8) would have been successful.
It was also not objectively unreasonable for the state court to conclude that there was no reasonable probability that moving for separate trials or requesting an additional jury instruction would have produced a different result. Even assuming that the trial court would have granted either motion, Walker has failed to establish prejudice. The risk created by joinder is that a jury may confuse the evidence and return a conviction against a defendant on a charge on which it would have acquitted if the evidence had been properly segregated. See Zafiro v. United States, 506 U.S. 534, 539, 113 S.Ct. 933, 122 L.Ed.2d 317 (1993) (explaining that the risk of joining defendants is that the jury will consider evidence against a defendant that would not be admissible if a defendant were tried alone). To show prejudice, Walker must demonstrate that there is a reasonable probability that the jury confused evidence of the predicate murder and evidence of the capital murder. It is not enough to show that he might have had a better chance for acquittal if the guilt phase of his trial had been bifurcated. See id. at 540 (“[I]t is well settled that defendants are not entitled to severance merely because they may have a better chance of acquittal in separate trials”). Of course, some of the risk posed by joinder can be cured with proper instructions to the jury. Id. In this case, the risk of the jury confusing the evidence was minimal. As the district court noted, “the joint trial was not unduly lengthy or complex and the evidence with respect to each murder was distinct and easily compartmentalized.” (J.A. at 965.) The transcript shows that in presenting its case against Walker, the Commonwealth kept its evidence regarding each murder separate. First it presented its case regarding the Beale murder and then put on its evidence about the Threat murder. Paul Tuttle, the only witness to testify about both murders, testified first about the Beale murder, was excused, and then recalled during the Threat portion of the trial.
Moreover, the jury instructions made it clear that each murder was a separate element that had to be proved beyond a reasonable doubt.
If you find from the evidence that the Commonwealth has proved beyond a reasonable doubt each of the above elements of the offense as charged, then you shall find the defendant guilty of capital murder.... If you find from the evidence that the Commonwealth has proved beyond a reasonable doubt that the defendant killed Clarence Threat, and that the killing was willful, deliberate and premeditated, but fail to find that the defendant killed Stanley Roger Beale, then you shall find the defendant guilty of first degree murder.... If you find from the evidence that the Commonwealth has proved beyond a reasonable doubt that the defendant killed Stanley Roger Beale, and that the kill[766]*766ing was willful, deliberate and premeditated, but fail to find that the defendant killed Clarence Threat, then you shall find the defendant guilty of first degree murder.... Ladies and gentleman of the jury, it’s simple. If you believe he killed both in a three year period that would meet the elements of capital murder. But, you might believe he killed one and not the other and that would be first degree murder. That would be a finding of not guilty as to one he is not guilty of.
(J.A. at 157-58.) Because the evidence for each murder was easily distinguishable and the jury was instructed to consider each murder separately, it was reasonable for the state court to conclude that under Strickland, Walker suffered no prejudice from his counsel’s failure to move for separate trials or request an additional jury instruction. Accordingly, the state court’s denial of relief on Walker’s claim of ineffective assistance of counsel at the guilt phase was not an unreasonable application of federal law.
IV.
Walker argues that the Commonwealth failed to disclose exculpatory evidence that would have impeached the trial testimony of three of its key witnesses: Bianca Taylor, Tameria Patterson, and Chris Miller. The state court concluded that Walker’s Brady claim regarding Bianca was procedurally barred and found Walker’s Brady claims regarding Patterson and Miller without merit. (J.A. at 348-49.) We will discuss the state court’s application of the procedural bar and determination on the merits in turn.
A.
Bianca testified at trial that she saw the shooter enter the house, yell at her father, and then shoot her father. Walker contends that the Commonwealth suppressed the following evidence that indicates that Bianca did not see the shooter: the Supplementary Offense Report of Officer Ernst (J.A. at 537), Supplementary Offense Report of Detective Mullins (J.A. at 489), handwritten notes of Detective Mullins (J.A. at 485), and statements made by Bianca and Catherine Taylor to Detective James Hickman (J.A at 543A). The state court, applying the rule in Slayton v. Parrigan, 215 Va. 27, 205 S.E.2d 680 (1974), concluded that because this issue “could have been raised and adjudicated at [Walker’s] trial and upon his appeal,” Walker “ha[s] no standing to attack his final judgment of conviction by habeas corpus.” 205 S.E.2d at 682. The district court refused to address the merits of this claim, concluding that this state procedural rule was independent and adequate and that Walker had failed to show cause and prejudice.
A federal court conducting habeas review is “precluded from reviewing the merits of a claim that was procedurally defaulted under an ‘independent and adequate’ state procedural rule, ‘unless the [applicant] can demonstrate cause for the default and actual prejudice as a result of the alleged violation of federal law, or demonstrate that failure to consider the claims will result in a fundamental miscarriage of justice.’ ” Fisher v. Lee, 215 F.3d 438, 455 (4th Cir.2000) (alteration in original) (quoting Coleman v. Thompson, 501 U.S. 722, 750, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991)). A state rule is “adequate” if it is regularly or consistently applied by the state court, see Johnson v. Mississippi, 486 U.S. 578, 587, 108 S.Ct. 1981, 100 L.Ed.2d 575 (1988), and “independent” if it does not “depend[ ] on a federal constitutional ruling,” Ake v. Oklahoma, 470 U.S. 68, 75, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985) (alteration in original). “We have re[767]*767peatedly recognized that the procedural default rule set forth in Slayton constitutes an adequate and independent state law ground for decision.” Fisher v. Angelone, 168 F.3d 835, 844 (4th Cir.1998) (internal quotation marks omitted) (citing cases). Walker does not dispute that the state court applied an adequate and independent procedural rule but rather asserts that he can demonstrate cause and prejudice to excuse the default.5
“Cause excuses the failure to raise a claim during a state proceeding if ‘the factual or legal basis for [the] claim was not reasonably available.’” Fisher, 163 F.3d 835, 845 (alteration in original) (quoting McCleskey v. Zant, 499 U.S. 467, 494, 111 S.Ct. 1454, 113 L.Ed.2d 517 (1991)). Walker contends that the Commonwealth’s interference, specifically its suppression of the documents listed above until eight months after direct appeal, prevented his counsel from raising the Brady claim regarding Bianca prior to state habeas. He correctly points out that “a defendant cannot conduct a ‘reasonable and diligent investigation’ [as] mandated by McCleskey to preclude a finding of procedural default when the evidence is in the hands of the State.” Strickler v. Greene, 527 U.S. 263, 287-88, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). If Walker, however, was aware or should have been aware that documents had been suppressed when he appealed his conviction, suppression of the documents would not constitute cause for failure to bring a Brady claim. Id. at 287 (holding that suppression of documents can constitute cause and distinguishing cases in which “the petitioner was previously aware of the factual basis for his claim but failed to raise it earlier”).
In applying the Slayton procedural bar, the state court found that at the time Walker filed for direct review, Walker’s counsel was aware of the factual basis of Walker’s Brady claim, specifically, the Commonwealth’s suppression of the evidence that allegedly could have impeached Bianca’s testimony. This factual finding is presumed to be correct and petitioner has the burden of rebutting the presumption of correctness by clear and convincing evidence. See 28 U.S.C. § 2254(e)(1). Walker fails to satisfy this burden. Indeed, as Walker admitted in the first habeas petition he presented to the district court, shortly before trial the defense received a Presentence Report referencing two undisclosed police reports containing the same information as the documents listed above. This Presentence Report, by referencing these undisclosed documents, evidenced the Commonwealth’s suppression of the alleged Brady material.6 The factual basis [768]*768for the assertion of Walker’s Brady claim, therefore, was available not only before direct appeal, but before sentencing. Because Walker has failed to rebut the state court’s finding that he could have brought his claim on direct review, he cannot demonstrate that the alleged with-holding by the Commonwealth constitutes cause to excuse his failure to raise the claim.7
B.
We now turn to the remainder of Walker’s Brady claim regarding the Commonwealth’s alleged withholding of evidence that would have impeached Patterson and Miller. Patterson testified at trial that someone she knew as “Todd” entered the residence of Karen and Charles Randolph and Jennifer Stewart, an apartment at 1309 W. Graham Road, on the night of Beale’s murder and exclaimed, “I shot him.” (J.A. at 50-52.) Miller testified that he observed an unidentified person leave Beale’s apartment after the shooting and enter the Randolph apartment. Walker contends that the Commonwealth suppressed the following records that would have impeached the testimony of Miller and Patterson: (1) a handwritten note by Detective Mullins recording Karen Randolph’s statement that “Ty didn’t come into her apt. [1309 W. Graham Road] after the shooting”8 (J.A. at 486); (2) a statement to Detective Mullins by 1309 W. Graham Road resident Jennifer Stewart that she “didn’t see him [Todd] Friday evening” (J.A. at 486); (3) the Commonwealth’s witness synopsis sheet stating that Miller said he saw a black male “walk from scene putting something in his pocket. Didn’t see face can’t ID ... Walked to front of 1309 W. Graham Rd. didn’t go in. Got into a red Ford Escort and drove to Brook Rd.” (J.A. at 483); (4) the Supplementary Offense Report of Detective Mullins summarizing Miller’s account of what he witnessed, with no mention of the perpetrator entering 1309 W. Graham Road (J.A. at 488-89); and (5) the Supplementary Offense Report of Officer Ernst summarizing Miller’s account of what he witnessed, with no mention of the perpetrator entering 1309 W. Graham Road (J.A. at 537).
The state court concluded that this portion of Walker’s Brady claim was without merit. Specifically, the state court concluded that “no material, exculpatory evidence was withheld.” (J.A. at 348.) The state court reasoned that
[n]either Stewart nor Randolph testified at trial; a review of the investigating officer’s complete notes indicates that Christopher Miller would not have been impeached since he told the officer that he saw a person walk from the Taylor apartment and enter the Randolph apartment. Randolph would have placed Walker at the murder scene regardless of whether she would have testified that he did or did not enter her apartment, thereby destroying the exculpatory quality of the evidence alleged by petitioner to have been withheld.
(J.A. at 349.)
Under the Brady rule, the prosecution is required “to disclose evidence favorable to the accused that, if suppressed, would deprive the defendant of a fair trial.” United States v. Bagley, 473 U.S. 667, 675, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). “[Favorable evidence is material, and constitutional error results from its suppression by [769]*769the government, ‘if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.’ ” Kyles v. Whitley, 514 U.S. 419, 433-34, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (quoting Bagley, 473 U.S. at 682). While a court initially considers the materiality of undisclosed evidence item by item, it must ultimately consider the cumulative effect of all suppressed evidence. Id. at 435 & 436 n. 10.
First, Randolph’s statements to Detective Mullins that “Ty didn’t come into her [1309 W. Graham Road apartment] after the shooting” (J.A. at 486) cannot be characterized as impeachment evidence because Randolph did not testify. Moreover, even if it were potentially exculpatory evidence, it would not fall under the Brady rule because Walker’s defense counsel was aware before trial of the fact that Randolph did not see Ty enter her apartment after the shooting. Information known by the defense falls outside of the Brady rule. See, e.g., United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976) (explaining that Brady applies in situations in which information is known to the prosecution but unknown to the defense).
Second, Stewart’s statement to Detective Mullins that she “didn’t see [Todd] Friday evening” at 1309 W. Graham Road (J.A. at 486) also cannot be characterized as impeachment evidence because Stewart did not testify. Moreover, Stewart’s statement is not favorable to Walker because it does not contradict Patterson’s claim that she saw Walker enter the apartment. Patterson testified that she had been upstairs with Stewart and that she saw Walker as she was coming down the stairs. Patterson did not say whether Stewart was coming down the stairs with her and thus gave no indication that Stewart was also in a position to see Walker.
Finally, Walker claims that the following three documents contradict Miller’s testimony that the person Miller saw leave Beale’s apartment entered the Randolph apartment before driving away: the Commonwealth’s witness synopsis sheet (J.A. at 483), the Supplementary Offense Report of Detective Mullins (J.A. at 488-89), and Supplementary Offense Report of Officer Ernst (J.A. at 537). The witness synopsis sheet was created by the prosecution to summarize statements by the witnesses. The statement recorded on the witness synopsis sheet, that the person Miller observed the night of the shooting “didn’t go in” 1309 W. Graham Road (J.A. at 483), contradicts Miller’s testimony that the person he saw leave Beale’s apartment entered the Randolph apartment before driving away. Even if Brady requires a prosecutor to disclose work product,9 there is no indication that Miller adopted or approved this statement. Cf. Goldberg v. United States, 425 U.S. 94, 98 & n. 3, 96 S.Ct. 1338, 47 L.Ed.2d 603 (1976) (explaining that a prosecutor’s work product must be produced under the Jencks Act if it contains a statement relating to the testimony of a government witness that has been “signed or otherwise adopted or approved” by the government witness). Indeed, it is not even clear whether the prosecution recorded these statements during an interview of Miller or was merely attempting to summarize another report, such as Detective Mullins’s Supplementary Offense [770]*770Report. Detective Mullins’s report, created on December 16, 1996, contains no statement by Miller regarding whether the person he saw entered Randolph’s apartment before driving away. Detective Ernst’s description of his meeting with Miller on the day of the murder also does not indicate whether the person Miller saw entered the Randolph’s apartment. Miller’s statements reflected in the Supplementary Offense Reports, therefore, do not contradict his testimony at trial. Moreover, even if we assume that the Supplementary Offense Reports and the witness synopsis sheet fall under the Brady rule and would have had some impeachment effect, the prosecution would have been able to rehabilitate Miller with Officer Mullins’s contemporaneous notes of his interview of Miller on the day of the murder, which reflect that Miller made the following statements: “Car parked on grass 1309 W. Graham Rd. he went inside 1309 before he left.” (J.A. at 860.) It was therefore not an unreasonable application of federal law for the state court to conclude that the material allegedly withheld in violation of Brady was either not impeachment evidence or the cumulative effect of any material that was impeachment evidence did not make a different result reasonably probable.
V.
Walker also seeks to assert that his execution would violate the Eighth Amendment under Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 2252, 153 L.Ed.2d 335 (2002) (holding that executing a mentally retarded individual violates the Eight Amendment’s ban on cruel and unusual punishments), a claim he did not make in the district court and has not presented in state court. Because Walker’s Atkins claim is “a brand-new, free-standing allegation of constitutional error in the underlying criminal judgment,” United States v. Winestock, 340 F.3d 200, No. 02-6304, 2003 WL 1949822 (4th Cir. Apr. 25, 2003) (explaining how to identify a successive application), we construe Walker’s assertion of this claim as a motion for authorization to file a successive habeas corpus application under 28 U.S.C.A. § 2244(b) (West Supp.2002). See Fischer v. United States, 285 F.3d 596, 600 (7th Cir.2002) (“If the original [habeas] petition did not contain [a new rule of constitutional law as a] ground for relief, then that ground has been waived on appeal, ... and a prisoner’s habeas options are thereafter limited by the special rules that apply to second or successive collateral attacks.”). But see Hill v. Anderson, 300 F.3d 679, 682 (6th Cir.2002) (combining petitioner’s Atkins claim, raised for the first time on appeal, with habeas petition at issue in appeal). A successive habeas petition is allowed under § 2244(b)(2)(A) if “the claim relies on a new rule of constitutional law, made retroactive to cases on collateral review by the Supreme Court, that was previously unavailable.” Walker’s claim satisfies these requirements because the Court in Atkins announced a new rule of constitutional law that applies retroactively to cases on collateral review. See Teague v. Lane, 489 U.S. 288, 330, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989) (concluding that a holding that “the Eighth Amendment prohibits the execution of mentally retarded persons ... would fall under the first exception to [Teague’s] general rule of non-retroactivity and would be applicable to defendants on collateral review”); accord Hill, 300 F.3d at 681. We, therefore, grant Walker’s motion and authorize the district court to consider Walker’s successive habeas petition.10 The district court, of course, on [771]*771considering Walker’s petition, is free to dismiss it without prejudice to afford the Commonwealth of Virginia the first opportunity to assess Walker’s Atkins claim. See, e.g., Bell v. Cockrell, 310 F.3d 330, 332-33 (5th Cir.2002) (“[I]nferior federal courts have no useful role to play until and unless following Atkins, a death sentence is reaffirmed or again imposed on [the petitioner] by the state courts.... [T]he state must be given the first opportunity to apply the Supreme Court’s holding in order to insure consistency among state institutions and procedures and to adjust its prosecutorial strategy to the hitherto unforeseen new rule.”); Hill, 300 F.3d at 682 (“The Supreme Court’s decision to return Atkins’s case to state courts suggests that we should return [petitioner’s] Eighth Amendment retardation claim to the state for further proceedings.... [The state] should have the opportunity to develop its own procedures for determining whether a particular claimant is retarded and ineligible for death.”). Following state review of Walker’s Atkins claim, Walker would be free to refile his second petition should the need arise.
VI.
In summary, we grant a COA as to Walker’s claim that his Sixth Amendment right to counsel was violated at the guilt phase of his trial and his claim that his due process rights were violated when the Commonwealth failed to timely disclose Brady materials. Because we conclude that the resolution of these issues by the Supreme Court of Virginia does not constitute an unreasonable application of clearly established federal law, we affirm the district court’s dismissal of these claims. We deny a COA and dismiss Walker’s appeal with regard to his claim that his Sixth Amendment rights were violated at the sentencing phase of his trial because reasonable jurists could not debate the district court’s resolution of that issue.
DISMISSED IN PART AND AFFIRMED IN PART.