
612 F.3d 118 (2010)
Johnny GUEITS, Petitioner-Appellee
v.
Robert KIRKPATRICK, Respondent-Appellant.
Docket No. 09-2335-pr.
United States Court of Appeals, Second Circuit.
Argued: November 30, 2009.
Decided: July 14, 2010.
*120 Lynn W.L. Fahey, Appellate Advocates, New York, N.Y., for Petitioner-Appellee.
Edward D. Saslaw, Assistant District Attorney, Queens County (Gary S. Fidel, Jill Gross-Marks, on the brief), for Richard A. Brown, District Attorney, Queens County, Kew Gardens, N.Y., for Respondent-Appellant.
Before WALKER, McLAUGHLIN, and RAGGI, Circuit Judges.
JOHN M. WALKER, JR., Circuit Judge:
Respondent Robert Kirkpatrick, Superintendent of New York State's Wende Correctional Facility, appeals from the judgment of the United States District Court for the Eastern District of New York (Brian M. Cogan, Judge) granting Johnny Gueits's petition for a writ of habeas corpus. Exercising de novo review, we hold that Gueits failed to demonstrate that the New York Supreme Court, Appellate Division, was unreasonable in its application of the ineffective assistance of counsel standard set forth in Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Accordingly, we reverse the district court's order granting Gueits's petition and remand with instructions that the petition be dismissed.

BACKGROUND
In the early hours of July 4, 2001, a woman was assaulted in the Harvard playground at 179th Place and Jamaica Avenue in Queens County, New York. Police officers and emergency medical personnel arrived at the scene at approximately 5:30 a.m. after Sunnita Jagpal called 911, from her apartment overlooking the playground, to report an ongoing assault. Police found the victim lying on the ground, naked, and seriously injured. At trial, an emergency medical technician testified that the victim told him that she had been raped by the same man who had beaten her; in a deposition, the arresting officer stated that the victim said the same thing to the nurse who treated the victim when she arrived at the hospital.[1]
Moments after finding the victim, police saw Gueits in another part of the playground with blood  later determined to be the victim's  on his shoes. An officer brought Gueits to the victim as she was awaiting transport to a hospital and asked her if Gueits was the man who had attacked her. The victim responded affirmatively by nodding her head. Gueits was arrested and taken to a police precinct where he agreed to answer questions. Gueits said that he had spent the evening of July 3 and the early morning of July 4 at a bar with a friend, and that he and his friend went to the Harvard playground *121 some time after 1:30 a.m. Gueits stated that, while he and his friend were there, an Hispanic woman entered the playground with a black man. He stated that the man attacked the woman. The woman then ran to Gueits, but Gueits pushed her away. After making that statement, Gueits provided the police with a sample of his DNA and his clothing.
Gueits was originally charged with both rape and assault. The prosecution later dropped the rape charge for lack of evidence. In particular, the DNA from semen found on the victim did not match Gueits's DNA. Thus, the state tried Gueits solely on the assault charge. He was convicted of first degree assault and sentenced to fifteen years of incarceration.
Gueits appealed his conviction to the New York Supreme Court, Appellate Division, claiming: insufficient evidence to support his conviction, erroneous admission of impeachment evidence, the use of impeachment evidence as evidence-in-chief, prosecutorial misconduct, and ineffective assistance of counsel. His ineffective assistance claim was based on the following claims that his trial counsel: 1) failed to present evidence of the DNA match between the semen found on the victim and that of a black male wanted for the rape of a thirteen-year-old girl in Maryland, notwithstanding trial counsel's awareness of this evidence prior to trial; 2) failed to properly object to grand jury testimony that the prosecution used to impeach Sunnita Jagpal's credibility; 3) failed to request a limiting instruction with respect to the introduction of this impeachment evidence; and 4) failed to object to alleged prosecutorial misconduct.[2] The Appellate Division denied Gueits's appeal in a brief order. People v. Gueits, 10 A.D.3d 732, 781 N.Y.S.2d 916 (N.Y.App. Div.2004).
Gueits then sought leave to appeal to the New York Court of Appeals on two grounds. First, he argued that the prosecution should not have been permitted to impeach Jagpal with her prior grand jury testimony. Second, he argued that his trial counsel had been ineffective in: 1) failing to present the DNA match evidence; 2) failing to properly object to the introduction of the grand jury impeachment evidence; and 3) acquiescing in the jury's consideration of that impeachment evidence as evidence-in-chief. Leave to appeal was denied. People v. Gueits, 4 N.Y.3d 744, 790 N.Y.S.2d 657, 824 N.E.2d 58 (2004).
Gueits then filed a timely habeas corpus petition in the U.S. District Court for the Eastern District of New York, arguing that the Appellate Division had unreasonably applied the Strickland standard for determining ineffective assistance of counsel. Reiterating his previous arguments, Gueits claimed that his trial counsel was ineffective in failing to put forth evidence of the DNA match, in failing to properly object to the impeachment of Jagpal, and in failing to request a limiting instruction with respect to the impeachment testimony. Magistrate Judge Orenstein found that these grounds for relief were properly exhausted and warranted habeas relief. Gueits also claimed that his trial counsel was ineffective in failing to object to the *122 prosecutor's injection of his personal views on Jagpal's credibility during Jagpal's examination and in failing to object to improper statements made by the prosecutor in summation. The magistrate judge assumed that these last two grounds were properly exhausted, but found that, standing alone, they did not warrant the requested relief. The district court adopted the magistrate judge's report and recommendation in full, issued the writ, and ordered the State to retry Gueits within forty-five days or release him from custody. Gueits v. Kirkpatrick, 618 F.Supp.2d 193, 198 (E.D.N.Y.2009).
The respondent appealed.

DISCUSSION
Our review of the district court's decision to grant Gueits's petition for habeas relief is de novo. Palacios v. Burge, 589 F.3d 556, 560-61 (2d Cir.2009). Under the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), 28 U.S.C. § 2254(d)(1), a federal court may not grant a state prisoner's habeas application unless the relevant state-court decision "was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States." See Knowles v. Mirzayance, ___ U.S. ___, ___, 129 S.Ct. 1411, 1418, 173 L.Ed.2d 251 (2009). Where, as here, "a state court fails to articulate the rationale underlying its rejection of a petitioner's claim, and when that rejection is on the merits, the federal court will focus its review on whether the state court's ultimate decision was an unreasonable application of clearly established Supreme Court precedent." Eze v. Senkowski, 321 F.3d 110, 125 (2d Cir.2003) (internal quotation marks omitted).
The respondent argues that the district court, in deciding whether state appellate review of the ineffective assistance of counsel claims was reasonable, failed to accord sufficient deference to the Appellate Division. Under the ineffective assistance of counsel standard set forth in Strickland, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674, a petitioner must demonstrate both that counsel's performance was deficient and that prejudice resulted from the deficient performance. Id. at 687, 104 S.Ct. 2052. To establish the former, the petitioner must show that "counsel's representation fell below an objective standard of reasonableness." Id. at 668, 104 S.Ct. 2052. We have recognized, however, that "[u]nder Strickland, there is a `strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance.'" Palacios, 589 F.3d at 561 (quoting Strickland, 466 U.S. at 689, 104 S.Ct. 2052). To establish prejudice, the petitioner "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, 104 S.Ct. 2052. "Furthermore, on habeas appeal it is not enough for [Gueits] to show a constitutional violation. He must also show that the state court's application of Strickland was not merely incorrect, but objectively unreasonable." Palacios, 589 F.3d at 561-62 (internal quotation marks omitted); see also Brisco v. Ercole, 565 F.3d 80, 87-88 (2d Cir.2009) ("A federal habeas court cannot issue the writ simply because that court concludes, in its independent judgment, that the state court applied clearly established federal law erroneously or incorrectly; conflating `unreasonableness' with `clear error' is improper because [t]he gloss of clear error fails to give proper deference to state courts." (internal quotation marks and citations omitted, alteration in original)).
For the reasons that follow, we find that the Appellate Division's denial of Gueits's *123 ineffective assistance claims did not constitute an unreasonable application of the Strickland standard for each of his trial counsel's alleged failures.

I. Trial Counsel's Failure to Object to the Use of Impeachment Evidence
The respondent argues that the Appellate Division reasonably applied Strickland with respect to Gueits's claim that his trial counsel failed to properly object to the introduction of grand jury testimony used to impeach the prosecution's witness, Sunnita Jagpal. The district court determined that Jagpal's grand jury testimony prejudiced Gueits's defense by undermining her trial testimony that she was unable to identify Gueits as the victim's attacker.
At trial, Jagpal testified that she did not know the defendant or his family. She testified that, on July 4, 2001, she saw a woman and two men sitting in the playground when she arrived home around 4:00 a.m. Jagpal testified that around 5:00 a.m. she heard screaming from the playground, and that from her apartment window she saw "someone there ... kicking" the victim. Trial Tr., 433:5-6, Apr. 2, 2002. She testified that there was one person kicking the victim, that she could no longer see a second man, and that she saw the attacker kick the victim four or five times, but was unable to describe the attacker because the playground was dark.
After eliciting that testimony, the prosecution attempted, over objections by Gueits's counsel, to contradict portions of Jagpal's trial testimony with statements she made to the grand jury. Specifically, while Jagpal testified at trial that she had not known anyone named John Gueits, before the grand jury she indicated that she did know someone by that name. The prosecution then read to Jagpal a portion of her grand jury testimony in which, contrary to her trial testimony, she stated that she saw "John Gueits" kick the victim about "7, 10 times." Id., 445:12-16. Finally, Jagpal's trial testimony that she was unsure if the man she saw sitting on a park bench in the playground was the same man that had attacked the victim was contradicted by grand jury testimony in which she stated that she had told the 911 dispatcher that she was observing the police speaking to the attacker as he sat on a park bench.
New York Criminal Procedure Law § 60.35(1) states:
When, upon examination by the party who called him, a witness in a criminal proceeding gives testimony upon a material issue of the case which tends to disprove the position of such party, such party may introduce evidence that such witness has previously made either a written statement signed by him or an oral statement under oath contradictory to such testimony.
Gueits's counsel, after having reviewed the language of that statute with the trial court, objected to the introduction of Jagpal's grand jury testimony on the ground that there was no "contradiction to her testimony." Trial Tr., 440:15, Apr. 2, 2002. The trial court disagreed, stating that "[i]f she now gives testimony [that] she doesn't know whatever, can't see, that is material testimony which tends to disprove the People's position ... that the defendant was the person [who attacked the victim]." Id., 441:6-9. Gueits's counsel argued that the witness's reluctance to testify was insufficient to establish a basis for impeachment under § 60.35(1), but the trial court rejected this argument. Id., 441:22-442:7.
Gueits argues that his trial counsel failed to lodge the proper objection to Jagpal's impeachment, namely that Jagpal's trial testimony did not "tend to disprove" the prosecution's position. As Gueits asserts, *124 § 60.35(1) only permits impeachment where the trial testimony of a witness "affirmatively damage[s]" the case of the party calling that witness. Gueits Br. at 45 (citing People v. Fitzpatrick, 40 N.Y.2d 44, 52, 386 N.Y.S.2d 28, 351 N.E.2d 675 (1976) (holding that the testimony of a witness who states that he cannot recall the events in question does not "tend to disprove" the prosecution's case)).
The propriety of the trial court's decision to admit Jagpal's grand jury testimony is not the issue before us on habeas review. Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991) ("[I]t is not the province of a federal habeas court to reexamine state-court determinations on state-law questions."); Hawkins v. Costello, 460 F.3d 238, 244 (2d Cir.2006). Our inquiry is limited to 1) whether Gueits's trial counsel failed to raise a proper objection on the basis of applicable state law; 2) if so, whether that failure was objectively unreasonable and prejudicial to Gueits's defense; and 3) whether the Appellate Division unreasonably applied Strickland in answering those questions in the negative.
Assuming that Gueits's counsel in fact failed to properly object on the grounds that Jagpal's trial testimony had not tended to disprove the prosecution's position, the Appellate Division reasonably concluded that such a failure did not prejudice Gueits's defense. This is so because it was reasonable to conclude that any such objection would have been overruled by the trial court in this case. The trial court, after reading § 60.35(1) aloud to Gueits's trial counsel at sidebar, concluded that Jagpal's trial testimony met the standard provided in that statute. Specifically, the trial court noted that Jagpal's trial testimony that she was unable to see into the playground and did not know whether Gueits was the attacker was contradicted by her grand jury testimony. Trial Tr., 441:6-11, Apr. 2, 2002. It is clear from the trial record that the trial court understood the requirements of § 60.35(1), and, specifically, its prerequisite of trial testimony tending to disprove the case of the party attempting the impeachment. Thus, although Gueits's counsel never voiced the specific objection on which Gueits now relies, it is apparent that had such an objection been made, it would have been overruled. Assessing the propriety of such a ruling is a task left to the state courts, see Hawkins, 460 F.3d at 244, and for that reason we cannot conclude that the Appellate Division unreasonably applied Strickland's prejudice prong with respect to any failure by counsel to object to the admission of Jagpal's grand jury testimony.

II. Gueits's Counsel's Failure to Request a Limiting Instruction With Respect to Impeachment Evidence
Gueits was entitled to a limiting instruction that Jagpal's grand jury testimony was to be considered by the jury only with respect to its impeachment value and not as direct evidence of Gueits's guilt. See N.Y.Crim. Proc. Law, § 60.35(2).[3] Gueits's counsel, however, did not request such an instruction at the time of the introduction of Jagpal's grand jury testimony or prior to the trial court's final jury charge. The district court determined that the Appellate Division unreasonably failed to conclude that this lapse by trial counselin not requesting a limiting instructionconstituted *125 ineffective assistance under Strickland.
Although Gueits was entitled to a limiting instruction under state law, we cannot conclude that the Appellate Division unreasonably applied Strickland's prejudice prong with respect to trial counsel's failure to request such an instruction, either at the time of the testimony's presentation or prior to the final jury charge. Considerable direct evidence inculpated Gueits in the charged crime. Specifically, police responding to the 911 call testified that Gueits was the only other person in the playground when the body of the beaten victim was found. At that time, the victim's blood was on Gueits's shoes. Before leaving the playground, the victim identified Gueits as her assailant.[4] Further, in a post-arrest statement, Gueits admitted knowledge of the beating and interacting with the victim in the playground, though his exculpatory account of his own actions and explanation for how he came to have the victim's blood on him did not comport even with Jagpal's trial testimony, much less with her grand jury testimony. In light of this record strongly signaling Gueits's guilt, it was not unreasonable for the Appellate Division to conclude that failure to give a limiting instruction about the proposed use of Jagpal's grand jury testimony was not a sufficiently serious omission "as to deprive the defendant of a fair trial, a trial whose result is reliable." Strickland, 466 U.S. at 687, 104 S.Ct. 2052.
Although, as Gueits argues, New York law recognizes that jurors can understand the importance of distinguishing impeachment evidence from evidence in chief, see § 60.35(2), we reiterate that our review is not focused on the proper application of New York law. Our task is limited to assessing whether the Appellate Division unreasonably applied Strickland in determining that the absence of a limiting instruction was not prejudicial, even assuming that the state courts erroneously applied state law. See Hawkins, 460 F.3d at 244; see also Brisco, 565 F.3d at 87-88. We believe the Appellate Division's application of Strickland to trial counsel's failure to request this limiting instruction was reasonable.

III. Trial Counsel's Alleged Failure to Present DNA Match Evidence
The respondent challenges the district court's holding that the Appellate Division unreasonably failed to find that his trial counsel was constitutionally ineffective in failing to present evidence that the DNA recovered from the victim matched that of an unknown black male suspected of having committed a rape in Maryland. Gueits argues that this evidence would have been exculpatory in that Sunnita Jagpal had testified that she saw only one man attacking the victim,[5] and that the victim had made two statements indicating that the same person who had assaulted her had also raped her. Gueits also argues that this evidence would have corroborated his initial statement to the police that he had seen the victim enter the Harvard playground accompanied by a black male.
Prior to trial, Gueits's counsel learned from the prosecution that the DNA in the semen recovered from the victim matched that of a man wanted for rape in Maryland. *126 Counsel for each side thereafter agreed to a stipulation that "the result [of the DNA test] is that the semen that is recovered does not match [Gueits's DNA]." Trial Tr., 354:16-21, March 25-27, 2002. The prosecution, during a conference regarding the instructions and stipulations to be read to the jury, reaffirmed this stipulation when it further stipulated that Gueits's friend with whom he spent the morning of July 4, 2001 was not the source of the DNA. The prosecution, however, refused to stipulate that the DNA was that of a black male wanted for rape in Maryland despite information from Maryland investigators that the DNA matched that of such a person. Trial Tr., 676-77, Apr. 2, 2002. Despite having knowledge of the existence of this evidence, Gueits's counsel made no attempt to contact the Maryland authorities and made no preparations to present that evidence in the event the prosecution refused to stipulate to the DNA match.
Even assuming that unjustified reliance on the possibility of a stipulation as to the DNA evidence, coupled with the absence of any attempt to independently present such evidence, constitutes a constitutionally deficient performance by trial counsel, we hold that the Appellate Division reasonably applied Strickland's prejudice prong with respect to the DNA match evidence. In order for Gueits's trial counsel's deficient performance to have prejudiced Gueits, the DNA match evidence would have to have been admissible under New York's evidentiary rules. Hawkins, 460 F.3d at 243-44. Under New York law, the admissibility of evidence of third-party culpability is reviewed "under the general balancing analysis that governs the admissibility of all evidence," which takes into account risks of "prejudice, delay and confusion," People v. Primo, 96 N.Y.2d 351, 728 N.Y.S.2d 735, 753 N.E.2d 164, 168 (2001); see also id. at 169 ("The admission of evidence of third-party culpability may not rest on mere suspicion or surmise."), and lies within the discretion of the trial judge, id. at 167.
The Appellate Division could have reasonably concluded that the DNA match evidence would not have been admitted under this balancing test. Initially, any advantage to Gueits of presenting the fact of the DNA match would have been incremental in light of the stipulation actually presented to the jury that the DNA recovered from the victim belonged to someone other than Gueits. This factual overlap consequently lowers the probative value of an independent introduction of the DNA match evidence.
Gueits also suggests that the match of the DNA with that of a suspected rapist makes more likely his claim that another man raped the victim. The DNA match evidence, however, implicated a person who, while suspected of rape, had not been convicted, again lowering its probative value. In addition, the parties presented conflicting evidence as to whether the victim here was raped and assaulted by the same man: police reports and emergency medical technician testimony indicating that the victim stated that she was raped by the same person who assaulted her; the victim's trial testimony that she did not make those statements and that she had meant to indicate only that Gueits was present when she was raped; and, finally, the victim's trial testimony that she had no memory of having been raped.
Lastly, the admissibility of the Maryland evidence was reasonably in doubt on the basis of jury confusion, particularly when coupled with its questionable probative value in a case that charged only assault. The evidence could have exculpated Gueits only if he established that a single person had both assaulted and raped the victim. *127 As indicated above, however, the evidence was nowhere conclusive on this point.
Jagpal testified to hearing screams while the victim was with two men, and, while the victim's blood was on Gueits's shoes, it was stipulated that semen recovered from the victim was not Gueits's. In this situation, the trial court faced a significant possibility of jury confusion as to the facts necessary for a conviction of the assault. Specifically, the jury could have been confused as to whether it needed to find that Gueits was implicated in a contemporaneous rape of the victim, even though the prosecution was under no obligation to establish that such a rape occurred and the evidence at trial admitted to the possibility, indeed the probability, of Gueits having assaulted the victim and another having had intercourse with her, forcibly or otherwise. Additional confusion could reasonably have arisen from the fact that the DNA match was to a person who was only accused of rape; admission of that evidence would have invited an argument in rebuttal that in fact there had been no rape in Maryland, leading to a confusing and cumbersome de facto trial of that issue within this case.
Given the broad discretion available to a trial court in properly balancing the probative value of proffered evidence against the risks of confusion and prejudice, there is no basis to conclude that the DNA match evidence necessarily would have been admissible at trial. See Hawkins, 460 F.3d at 243 ("[T]he range of judgments that can be deemed reasonable may vary with the nature of the rule in question. The more general the rule, the more leeway courts have in reaching outcomes in case by case determinations." (internal quotation marks and citations omitted)). In light of the considerable leeway inherent in assessing a state court's balancing determination, viewed through the prism of the deference appropriately accorded to state courts on federal habeas review, we cannot conclude that the Appellate Division's application of Strickland was unreasonable with respect to trial counsel's failure to present independent evidence of the DNA match.

IV. Gueits's Remaining Challenges
Gueits's habeas petition further claims that his trial counsel was ineffective in failing to object to the prosecutor's statement of his personal views of the evidence during his examination of Jagpal and to improper statements made by the prosecutor during summation. Neither ground for relief was presented in Gueits's letter seeking review by the New York Court of Appeals, and, therefore, each is procedurally defaulted. See 28 U.S.C. § 2254(b)(1); Jimenez v. Walker, 458 F.3d 130, 148-49 (2d Cir.2006). A petitioner may overcome procedural default only with a demonstration of "cause and prejudice" or a "fundamental miscarriage of justice," see Murray v. Carrier, 477 U.S. 478, 495-97, 106 S.Ct. 2639 (1986), neither of which is met in this case.

CONCLUSION
For the foregoing reasons, we REVERSE the district court's judgment granting Gueits's petition for a writ of habeas corpus and REMAND with instructions to dismiss the petition.
NOTES
[1]  At trial, the victim denied having made these statements and testified that she only indicated to the police that Gueits "was there" during the attack. Trial Tr., 589:6-19, Apr. 2, 2002.
[2]  With respect to prosecutorial misconduct, Gueits claimed that the prosecutor 1) suggested that Jagpal had been threatened by Gueits and his family; 2) knowingly advocated for a false position, i.e., Gueits's guilt; 3) suggested that Gueits was obligated to testify in his defense; 4) interjected his personal disbelief in Gueits's version of events; 5) suggested that Gueits was guilty of rape; 6) misrepresented the law to the jury in suggesting that Gueits could be convicted for failing to intervene in the attack on the victim; and 7) attempted to inflame the jury.
[3]  "Evidence concerning a prior contradictory statement introduced pursuant to [§ 60.35(1)] may be received only for the purpose of impeaching the credibility of the witness with respect to his testimony upon the subject, and does not constitute evidence in chief. Upon receiving such evidence at a jury trial, the court must so instruct the jury." N.Y.Crim. Proc. Law, § 60.35(2).
[4]  The reliability of this identification was challenged at trial, but not the fact that it was made.
[5]  As explained above, supra Part I, Jagpal was impeached on the stand through the use of her prior grand jury testimony, but that impeachment did not contradict her statement that only one person attacked the victim. Trial Tr., 444-50, Apr. 2, 2002.
