Peterson, Justice.Following a jury trial in October 2010, Jerome Burgess was convicted of felony murder, three counts of aggravated assault, and possession of a firearm during the commission of a crime, and we affirmed his convictions. Burgess v. State, 292 Ga. 821 (742 SE2d 821) (2013). Burgess later filed a petition for a writ of habeas corpus, alleging that appellate counsel was ineffective for failing to argue on appeal that (1) trial counsel was ineffective for failing to cross- examine effectively a testifying co-defendant and (2) the State committed a Brady[1] violation for failing to disclose impeachment evidence against that co-defendant. The habeas court denied Burgess relief. We granted Burgess’s application for a certificate for probable cause, but we affirm because the habeas court correctly rejected Burgess’s claims.[2]1. Relevant backgroundThe crimes for which Burgess has been convicted stem from a drive-by shooting of three teenagers, one of whom died. Burgess, 292 Ga. at 822 (1). The State’s evidence showed that, in October 2008, Burgess drove fellow members of the Murk Mob gang, including his co-defendant Andre Weems, to a Clayton County neighborhood in search of the leader of a rival gang with whom they had had an altercation earlier that night. Id. at 821-822 (1). When that effort proved unsuccessful, the group instead decided to assault the three teenagers who happened to be in the vicinity, so that Weems could “get his stripes”; Weems opened fire as Burgess drove. Id. at 822 (1).Burgess and Weems were indicted together. Burgess pleaded not guilty, and Weems pleaded guilty and testified for the State at Burgess’s October 2010 trial. Weems testified that everyone in the vehicle knew about the plan to commit the drive-by shooting and that he never pointed a gun at Burgess. Weems admitted during his trial testimony that he had pleaded guilty to the shooting, but the jury did not hear that he pleaded guilty but intellectually disabled.Burgess testified and presented a different version of events. Burgess testified that he did not know Weems intended to commit a drive-by shooting, he did not want to drive the vehicle, and Weems coerced him by pointing the gun or nudging him with it and directing him to drive. Burgess also called Felix Irving to testify in his defense. Irving testified that Weems had called him after the shooting to say that the shooting was not planned, Burgess did not have anything to do with it, and Weems was going to “straighten it out” so Burgess would not get punished for something he did not do. At the conclusion of Burgess’s trial, the jury found him guilty of felony murder and other crimes, and we affirmed his convictions. Burgess, 292 Ga. 821.Burgess filed a habeas petition claiming that his appellate counsel was ineffective in his handling of issues regarding purported witness impeachment evidence that the State allegedly did not disclose and that trial counsel failed to uncover. The evidence Burgess cites as impeachment evidence relates to the testimony of two psychologists introduced at Weems’s competency trial that occurred about a month before Burgess’s criminal trial. The defense expert, Dr. James Powell, testified that Weems had a composite IQ of 53, a learning disability, a history of violent outbursts, and a seizure disorder. Dr. Powell also testified that Weems had given conflicting and incoherent accounts of the shooting and his prior criminal convictions, but Dr. Powell could not determine whether Weems was intentionally lying, confused, or simply could not remember.The State’s expert, Dr. Don Hughey, also testified at Weems’s competency trial that Weems scored low on an IQ test, but he did not consider the result to be valid because Weems had scored an 86 on a prior test and there was no evidence that Weems had an intervening factor, such as a serious head injury, to explain the drop in his IQ score. Dr. Hughey also performed a malingering test on Weems after Weems reported auditory hallucinations, and Dr. Hughey concluded that there was a 99.9% chance that Weems was malingering.Burgess argued that the experts’ testimony provided information that would have affected the jury’s assessment of Weems’s credibility, including whether he acted alone or whether Burgess participated in the shooting. Following a hearing, the habeas court denied Burgess’s habeas petition, concluding that Burgess failed to show that appellate counsel was deficient as to Weems’s cross-examination or that any deficiency prejudiced him. The habeas court also denied relief on Burgess’s claim that appellate counsel was ineffective for failing to raise a Brady claim on appeal, concluding that appellate counsel, despite being aware of Weems’s guilty plea, made a considered choice to raise the issues that were most likely to lead to a reversal of Burgess’s convictions; the habeas court also concluded that Burgess made no showing of prejudice.2. Burgess argues that the habeas court erred in denying his claim that appellate counsel was ineffective regarding trial counsel’s failure to investigate Weems’s competency and guilty pleas and then cross-examine Weems with the information introduced at Weems’s competency trial. We disagree.For Burgess to prevail on an ineffective assistance of counsel claim, he must satisfy the familiar standard of Strickland v. Washington, 466 U. S. 668 (104 SCt 2052, 80 LE2d 674) (1984). Under that standard, Burgess must prove that his lawyer’s performance was constitutionally deficient and that he was prejudiced by the deficient performance. Id. at 687. To show deficient performance, Burgess must prove that his counsel acted or failed to act in an objectively unreasonable way, considering all the circumstances and in the light of prevailing professional norms. See id. at 687-690. “This is no easy showing, as the law recognizes a strong presumption that counsel performed reasonably,” and to overcome this presumption, Burgess “must show that no reasonable lawyer would have done what his lawyer did, or would have failed to do what his lawyer did not.” Davis v. State, 299 Ga. 180, 183 (2) (787 SE2d 221) (2016) (citation and punctuation omitted).“Where the issue is the ineffective assistance of appellate counsel, the showing of prejudice calls for a demonstration that a reasonable probability exists that, but for appellate counsel’s deficient performance, the outcome of the appeal would have been different.” Gramiak v. Beasley, 304 Ga. 512, 513 (I) (820 SE2d 50) (2018) (citing Humphrey v. Lewis, 291 Ga. 202, 211 (IV) (728 SE2d 603) (2012)). When a defendant claims that his appellate counsel was ineffective for failing to raise a claim on direct appeal that trial counsel was ineffective, there are two layers of Strickland analysis. Gramiak, 304 Ga. at 513 (I). To show that appellate counsel was ineffective for failing to argue that trial counsel was ineffective, a defendant must show that trial counsel was deficient and the deficiency prejudiced the trial.Here, Burgess’s appellate counsel did raise the issue of trial counsel’s ineffectiveness in Burgess’s motion for new trial and questioned trial counsel about his cross-examination of Weems during the motion for new trial hearing. Trial counsel testified at the motion for new trial hearing that prior to trying Burgess’s case, he became aware that there had been a trial on Weems’s competency and that Weems had pleaded guilty but intellectually disabled. Trial counsel stated that he did not believe Weems’s guilty plea would have influenced the jury’s credibility determination in any way, and that he had more effective points on which to cross-examine Weems, including Weems’s statements to a detective.The transcript from Burgess’s trial reflects that trial counsel indeed impeached Weems’s credibility extensively. In particular, through cross-examination, Weems admitted that he first told the detective he did not know anything about the shooting, then said Burgess and a young woman “set[] everything up,” claimed that Burgess was the shooter, and finally admitted that he was the shooter. Trial counsel also elicited testimony from Weems that he told the detective, “if I’m going down, everybody’s going down,” because he was mad that people had “ratted [him] out.” While cross- examining the detective, trial counsel elicited testimony that the detective knew that Weems was lying when he claimed to not be involved in the shooting and named Burgess as the shooter, and the detective described Weems’s initial statements as being part of his “lies and deception.”Appellate counsel testified at the habeas hearing that he did not pursue the ineffectiveness claim on appeal because trial counsel had claimed that his cross-examination of Weems was a matter of trial strategy, and appellate counsel did not believe he could satisfy both Strickland prongs on appeal. Appellate counsel also stated that had he known about Weems’s low IQ, he “would have done a great deal more” and that he backed away from the ineffectiveness issue a little too quickly in retrospect. Trial counsel similarly testified at the habeas hearing that had he known about Weems’s diminished mental abilities, he would have used that information to cross- examine Weems “a whole lot more” and “maybe” show that even the State did not believe Weems. Trial counsel considered his failure to investigate Weems’s records to amount to ineffective assistance of counsel.Trial counsel’s hindsight assessment of his own performance does not control. See Kennedy v. State, 304 Ga. 285, 288 (2) (818 SE2d 581) (2018). But even if we agreed with trial counsel that he was deficient on this point, Burgess cannot show prejudice. Weems’s credibility was severely impeached at trial with his prior inconsistent statements to the detective, so much so that trial counsel got the detective to say that Weems’s initial statements to the detective were “lies and deception.” Any additional attack on Weems’s credibility would have had marginal value.Before the habeas court, Burgess argued that evidence of Weems’s intellectual disabilities could have been used to impeach him. But a witness’s low IQ, by itself, does not make the witness incredible. Even considering IQ as a factor in an overall credibility determination, Burgess fails to show that Weems’s low IQ would have damaged Weems’s credibility any more than it already was.Although Burgess did not focus on the evidence of Weems’s malingering in questioning appellate or trial counsel, this evidence is probably the best impeachment evidence that could have been obtained from Weems’s competency trial. But even this evidence would have had marginal value to Burgess, as it would only have been additional evidence supporting the already well-established pattern of Weems’s “lies and deception.” See McCoy v. State, 303 Ga. 141, 143 (2) (810 SE2d 487) (2018) (evidence with marginal impeachment value does not establish prejudice). Even when considered cumulatively, the evidence from Weems’s competency trial would have made little difference to Weems’s noted lack of credibility.Moreover, despite his attempts to undercut Weems’s credibility, Burgess also simultaneously sought to rely on statements Weems made, and he continues to do so on appeal. To corroborate his own testimony that he had nothing to do with the crime, Burgess cites the testimony of Felix Irving that Weems told Irving that Burgess had nothing to do with the shooting and Weems was going to make sure Burgess did not get punished for something he did not do. Burgess wants to credit Weems’s statement that Burgess was not involved in the shooting but discredit Weems on other points. Given these circumstances, there is no reasonable probability that additional impeachment of Weems would have made any difference to the outcome of the trial. See Barrett v. State, 292 Ga. 160, 177-178 (3) (C) (iv) (733 SE2d 304) (2012) (given trial counsel’s cross-examination of witness regarding the inconsistencies between her testimony and prior statement to police, appellant failed to show a reasonable probability that result of trial would have been different with additional impeachment of witness).Because Burgess cannot demonstrate that he was prejudiced by trial counsel’s failure to obtain additional impeachment evidence and cross-examine Weems with it, he cannot establish that appellate counsel was ineffective for not pursuing an ineffectiveness claim against trial counsel. See Rozier v. Caldwell, 300 Ga. 30, 33 (3) (793 SE2d 73) (2016) (“Because appellate counsel could not have prevailed on a claim that trial counsel provided ineffective assistance by not pursuing such a cross-examination, appellant cannot show prejudice on his claim that appellate counsel was ineffective in failing to assert such a claim on appeal.”).3. Burgess next argues that appellate counsel was ineffective for failing to argue on appeal that the State violated Brady by failing to disclose the impeachment evidence noted above. Because Burgess’s claims relate to appellate counsel’s purported ineffectiveness, he must establish a reasonable probability that the outcome of the appeal would have been different but for appellate counsel’s deficient performance. See Gramiak, 304 Ga. at 513 (I). This he cannot do.To prove a Brady violation, a defendant must show that:(1) the State, including any part of the prosecution team, possessed evidence favorable to the defendant; (2) the defendant did not possess the favorable evidence and could not obtain it himself with any reasonable diligence; (3) the State suppressed the favorable evidence; and (4) a reasonable probability exists that the outcome of the trial would have been different had the evidence been disclosed to the defense.Anthony v. State, 302 Ga. 546, 552 (III) (B) (807 SE2d 891) (2017) (citation omitted).Burgess cannot establish the fourth Brady prong. Burgess claims the undisclosed information could have been used to impeach Weems, but, as discussed above, Weems’s testimony had been significantly impeached at trial and further impeachment would not necessarily have helped Burgess’s case. As a result, even if the relevant materials had been disclosed to Burgess, there is no reasonable probability that the outcome of his trial would have been different, and a Brady claim would have failed. See Whatley v. Terry, 284 Ga. 555, 560-561 (II) (B) (2) (668 SE2d 651) (2008) (finding no Brady violation from State’s failure to disclose police interview of eyewitness that the defendant claimed could have been used for “enhanced” cross-examination, because it was established at trial that eyewitness could not be relied upon). Accordingly, Burgess’s claim that appellate counsel was ineffective on this ground fails.Judgment affirmed. All the Justices concur.