SUMMARY ORDER
ON CONSIDERATION WHEREOF, it is hereby ORDERED, ADJUDGED, and DECREED that the judgment of the district court be and hereby is AFFIRMED.
Petitioner-Appellant Jerome Mack appeals from a July 27, 2010 judgment of the United States District Court for the Southern District of New York (Swain, J.) denying his petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254. In his petition, Mack seeks to collaterally attack his conviction in New York State Supreme Court, following a jury trial, of two counts of criminal possession of a weapon. We *875presume the parties’ familiarity with the underlying facts and procedural history of this case, as well as with the issues on appeal.
“We review de novo a district court’s denial of a petition for a writ of habeas corpus.” Dixon v. Miller, 293 F.3d 74, 78 (2d Cir.2002).
We turn first to Mack’s contention that the State trial court erred in refusing to suppress Mack’s initial confession, which he made to police officers before he was issued the warnings required prior to custodial interrogations under Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). Assuming arguendo that Mack was “in custody” at the time of his initial un-Mirandized confession, and therefore that the statement should have been suppressed, we conclude that this is not a ground for habeas relief because Mack has not demonstrated that the error had a “substantial and injurious effect or influence in determining the jury’s verdict,” Penry v. Johnson, 532 U.S. 782, 795, 121 S.Ct. 1910,150 L.Ed.2d 9 (2001) (internal quotation marks and citations omitted). In determining whether a Miranda violation is harmless, “we consider the importance of the wrongly admitted evidence, and the overall strength of the prosecution’s case.” Wood v. Ercole, 644 F.3d 83, 94 (2d Cir.2011) (internal quotation marks, brackets, and ellipsis omitted). “The strength of the prosecution’s case, absent the erroneously admitted evidence, is probably the ... most critical factor in determining whether the error was harmless.” Id. (internal quotation marks and brackets omitted). “The importance of wrongly admitted evidence is determined by the prosecutor’s conduct with respect to the evidence, whether the evidence bore on an issue plainly critical to the jury’s decision, and whether it was material to the establishment of the critical fact, or whether it was instead corroborated and cumulative.” Id. (internal citation, quotation marks, ellipsis and brackets omitted).
Here, even absent Mack’s initial confession, the prosecution had a very strong case in support of Mack’s guilt. Most importantly, Mack’s second confession— which occurred after he had received Miranda warnings, and which was sufficiently attenuated from the first confession so as to be free from any taint — was virtually identical in substance to the first confession. In his second confession, Mack admitted, in writing, to possessing “a silver .380 auto gun in my jacket pocket” at the time that a rival gang member began shooting at Mack and his friends. Respondent’s Br. at 52. He also admitted to hiding the gun “under the cushion of the couch” at his friend’s apartment after the shooting, id. — precisely the location where the gun was later recovered by the police. Moreover, the prosecution presented considerable other evidence of Mack’s guilt at trial, including eyewitness testimony that Mack possessed a gun at the time of the shooting; testimony that Mack was involved in an ongoing, drug-related violent conflict with the shooter; and testimony that, after the shooting, Mack had been alone in the room where the gun was later found. Given the materially cumulative nature of Mack’s first confession, as well as the overall strength of the prosecutor’s case against Mack for unlawful possession of a weapon, we conclude that any Miranda violation emanating from Mack’s initial confession was harmless error and therefore cannot be a basis for habeas relief.
Next, we turn to Mack’s contention that he received ineffective assistance from his trial counsel. To prevail on an ineffectiveness claim, a petitioner must show that (1) “counsel’s performance was deficient,” defined as falling “below an objective standard of reasonableness,” and that (2) counsel’s “deficient performance prejudiced the *876defense,” meaning that “counsel’s errors were so serious [that they deprived] the defendant of a fair trial,” creating “a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Strickland v. Washington, 466 U.S. 668, 687-88, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). There is “a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance.” Id. at 689, 104 S.Ct. 2052. But where a counsel’s “omissions cannot be explained convincingly as resulting from a sound trial strategy, but instead arose from oversight, carelessness, ineptitude, or laziness, ... the quality of representation [is] sufficiently deficient to grant the writ” Eze v. Senkowslci, 321 F.3d 110, 112 (2d Cir.2003).
Here, Mack argues that his trial counsel was ineffective for failing to seek a jury instruction directing the jury that, under N.Y.Crim. Proc. L. § 710.70(3), it could disregard Mack’s confessions if it believed they were involuntarily made. Assuming arguendo that this error rendered trial counsel’s performance deficient under the first prong of Strickland, we nevertheless conclude that Mack’s ineffectiveness claim fails because Mack has not established that he was prejudiced thereby. 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, ... that course should be followed.”). Mack adduced no evidence at trial by which a reasonable jury could conclude that his second confession’was “involuntarily made” as defined under New York law. See N.Y.Crim. Proc. L. § 60.45(2). Moreover, in this ha-beas action, Mack points to no evidence that his trial counsel could have presented at trial on this matter but did not. And, for the reasons discussed above, to the extent that a jury instruction under N.Y.Crim. Proc. L. § 710.70(3) would have pertained to the relative voluntariness of Mack’s first confession, trial counsel’s failure to seek such an instruction was harmless error. Accordingly, the district court did not err in concluding that Mack had failed to establish that his trial counsel was constitutionally ineffective.
Finally, we turn to Mack’s contention that the prosecutors in his case violated his rights under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). To establish a Brady violation, a petitioner must show that: (1) the undisclosed evidence was favorable to him; (2) the evidence was in the state’s possession and was suppressed, even if inadvertently; and (3) the defendant was prejudiced as a result of the failure to disclose. See Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). Further, we have held that “new impeachment evidence is not material [for Brady purposes], and thus a new trial is not required ‘when the suppressed impeachment evidence merely furnishes an additional basis on which to impeach a witness whose credibility has already been shown to be questionable.’ ” United States v. Wong, 78 F.3d 73, 79 (2d Cir.1996) (quoting United States v. Payne, 63 F.3d 1200, 1210 (2d Cir.1995) (emphasis in original)); see also, e.g., United States v. Muja, 365 Fed.Appx. 245, 247 (2d Cir.2010) (summary order). Here, Mack contends that his Brady rights were violated because the prosecutors failed to disclose information relating to the alleged prior bad acts of one of the State’s primary witnesses at trial. However, the credibility of that witness had already been substantially undermined through impeachment evidence at trial. Among other things, the witness had admitted on cross-examination by Mack’s trial counsel that: (a) his trial testimony was in direct conflict with his prior sworn testimony before a grand jury in a related case; (b) he had lied to the police on numerous instances in the past, includ*877ing in connection with the instant case; (c) he had several previous criminal convictions and had absconded from a mandatory-drug treatment program; and (d) he was receiving favorable treatment with respect to a pending charge in exchange for his testimony against Mack. In light of the foregoing, we conclude that the undisclosed evidence identified by Mack was not material, in that Mack was not prejudiced by the prosecutors’ failure to disclose that evidence to him, and so the district court did not err in concluding that Mack had failed to establish that the prosecutors had violated his rights under Brady.
We have considered all of Mack’s other arguments on appeal and find them to be without merit. Accordingly, the judgment of the district court is hereby AFFIRMED.