GERARD E. LYNCH, Circuit Judge:

Petitioner Carlos Evans was convicted by a jury of burglarizing a Brooklyn apartment and sentenced to fifteen years in prison. He was tried along with two codefendants, Hudson Merzier and Anthony Foster, on the strength of evidence recovered from the scene as well as the testimony of, among others, Aisha Walker. Walker was both an acquaintance of the defendants and a neighbor and acquaintance of the burglary victim, Olujimni Omitogun. One week before Evans's trial, Walker agreed to testify against the defendants in exchange for a non-custodial sentence for her own role in the burglary.

On October 22, 2002, in New York Supreme Court in Kings County, a jury convicted Evans of burglary in the first degree, two counts of criminal possession of a weapon in the second degree, and assault in the second degree. see N.Y. Penal Law §§ 140.30; 265.03; 120.05. He was sentenced to concurrent terms of fifteen years' imprisonment (on the burglary and weapons possession counts) and seven years' imprisonment (on the assault count). Petitioner appealed his conviction and sentence, but the Second Department affirmed.

On October 31, 2006, petitioner filed the habeas petition at issue in this case in the United States District Court for the Eastern District of New York. Concluding that the trial judge had improperly admitted a hearsay document into evidence, the district court (Raymond J. Dearie, Judge) granted petitioner's application for the writ. The state appeals, arguing that the Appellate Division's affirmance of petitioner's conviction was not an "unreasonable application" of United States Supreme Court precedent within the meaning of 28 U.S.C. § 2254, as amended by the Antiterrorism and Effective Death Penalty Act of 1996, Pub.L. No. 104-132, § 104, 110 Stat. 1214 ("AEDPA"). We agree and reverse the grant of habeas corpus.

BACKGROUND

I. The Evidence at Trial

Because this case centers on Walker's various statements, including the hearsay statement admitted at trial, it will be most useful to describe the facts as she told them at trial, including the inconsistencies in her account revealed on cross-examination and through the admission of her written statement.

A. Walker's Testimony on Direct Examination

The account in this section relies only on Walker's sworn testimony given on direct examination at trial. Walker is a dancer who, at all times relevant to the facts of this case, worked part-time at an adult club called Sweet Cherry, located in the Sunset Park neighborhood of Brooklyn. Walker met Omitogun, the victim of the burglary, soon after moving into the apartment complex where they both resided in the Canarsie neighborhood of Brooklyn. She had visited his apartment on two occasions, observed that he had "fairly nice things," and heard him brag about his car, jewelry, and brand-name clothes.

Walker met Evans's co-defendant Merzier through a mutual friend three weeks to a month prior to the evening of the burglary. That meeting was arranged so that Walker could ask Merzier for a loan to pay her overdue rent, but Merzier was not able to lend her the money at the time. She met Evans a few weeks before the burglary, and Foster only one or two days before the crime.

On August 15, 2001, Walker was at her apartment with the three defendants and one of her coworkers, Diamond. During this gathering, Foster told the group that he intended to rob Omitogun. Foster then went to the roof of Walker's building to canvass Omitogun's apartment, which was accessible via the roof. He later commented on the similarity of the layout of Walker's and Omitogun's apartments. Over the course of the evening, the group planned the burglary. Foster was to be the ringleader and direct the burglary, Evans was to follow him into Omitogun's apartment, and Merzier was to stay behind in Walker's apartment as a lookout and getaway driver. The proceeds from the burglary were to be split among the defendants and Walker, whose share was promised in exchange for allowing the burglars to use her apartment as a staging ground.

The next day, in the evening of August 16, 2001,1 Walker was at home with Diamond, Evans, and Merzier. As she entered her apartment, Walker received a phone call from Omitogun, who said that he was at a friend's apartment in the same building. Omitogun asked Walker if she and other dancers from Sweet Cherry would be willing to entertain him and several friends from out of town. Walker told Omitogun that she had to be at work in approximately half an hour, but that she would come by his apartment afterward. Evans, having overheard this conversation, stated that he intended to rob Omitogun that night. Shortly thereafter, Merzier left the apartment, Walker and Diamond took a taxi to work at Sweet Cherry, and Evans stayed behind at Walker's apartment.

Upon her arrival at the club, Walker was told that she was not allowed to work that evening because she was late. Fearing for her safety, however, she decided to remain at the club. Walker called Omitogun's cell phone to arrange details related to her visit to Omitogun's apartment later that evening, particularly whether she and her coworkers would be paid for their services. About an hour after her conversation with Omitogun, Walker spoke on the phone with Merzier, who by that point had returned to Walker's apartment. Walker testified, over defense objections, that Merzier told her that Foster and Evans were in Omitogun's apartment robbing him. She also testified that she believed no weapons would be used in the robbery.

While returning home from work, Walker received a call from Omitogun. Omitogun told her that he had been robbed. Another man, also on the phone, threatened her with harm unless Omitogun's money and belongings were returned. Shortly thereafter, Walker had a series of telephone conversations with Merzier. Walker testified (again over defense objections) that Merzier told her that he was unable to leave the apartment complex because police cars and helicopters had surrounded the block.

Rather than returning home, Walker and Diamond decided to go to the police precinct because Walker feared Omitogun's threats. She also feared that her role in the plan might be uncovered. Upon arriving at the 69th Precinct, Walker spoke with a police officer whose name she could not remember. She explained that she was being threatened and requested an escort home but did not mention anything about the burglary at Omitogun's home. The police officer asked where Walker lived and, when told, informed Walker there had been a homicide (apparently unrelated to the events at issue in this case) on her block. As a result, all the other officers were unavailable at that time. Walker left the station, but returned some time later, at which point she spoke with Detectives Ahern and Rivera.

Over the course of approximately two days, Walker gave varying statements about the events at issue in this case to the two detectives. Most importantly, she told Detective Rivera that Evans and Foster (but not Merzier) had discussed robbing Omitogun. She also gave details about the plan to Detective Rivera in a seven-page written statement, which omitted her role in the discussions.

B. Walker's Testimony on Cross-Examination

The facts in this section are drawn from Walker's testimony on cross-examination, during which defense counsel successfully elicited several inconsistencies in Walker's account, as well as contradictions between Walker's testimony on direct examination and various other statements she had given at different times about her role in the burglary. The defendants sought on cross-examination to demonstrate that Walker was willing to tell different stories at different times to serve her interests.

Walker admitted that, when giving a statement to Detective Ahern, she "basically lied and said [she] had nothing to do with" the burglary. She further testified that she did not mention any of the defendants in her initial statement to Detective Ahern. She told Detective Ahern that there was no one in her apartment and that nobody had her permission to be there.

Walker testified that, after she spoke with Detective Ahern, the police accompanied her back to her apartment. Upon arriving there, they found the three defendants, who were then arrested for burglary of Walker's apartment.2 When asked by the police officers, Walker denied knowing the defendants except for Merzier. She then swore out a complaint falsely stating that the defendants did not have permission to be in her apartment that evening.

Defense counsel did not ask Walker about the specific contents of the seven-page written statement other than to ask whether her comments to Detective Rivera were consistent with her testimony on direct examination. Walker did not testify about the contents of the written statement other than to say that the statement she gave to Detective Rivera was at least partially false.

Finally, Walker admitted that she agreed to testify against the defendants in exchange for a non-custodial sentence. Defense counsel also attempted to elicit contradictions in Walker's timeline of events and to raise questions about the true nature of her profession and her relationships with Omitogun and Merzier. However, Walker denied that she had misrepresented anything about those subjects.

C. Walker's Written Statement

The state then called Detective Rivera. Over the objections of defense counsel, Detective Rivera testified to the contents of Walker's written statement. Defense counsel argued that the statement's contents were inadmissible because Walker had already testified, because she could have been asked about the statement during her testimony, and because to admit the statement's contents as prior consistent statements would constitute improper bolstering under New York law. After hearing arguments outside the presence of the jury, the trial judge overruled the objections to Detective Rivera's testimony about the contents of the statement, and admitted the statement itself into evidence on the theory that, by asking Walker whether she had lied when she gave the statement to Detective Rivera, defense counsel had made a charge of recent fabrication. The trial judge did not redact the written statement and did not limit the jury's consideration of the statement as substantive evidence to the extent it was consistent with Walker's testimony.

The substance of the statement tracked much of Walker's version of events on direct examination, with the notable exclusion of any reference to Walker's role in facilitating the burglary. Walker stated that she had gone shopping the day of the incident with Diamond, Merzier, and Evans. After being dropped at home, Diamond, Walker, and Evans stayed at Walker's apartment as the two women prepared for work. After leaving for work, Walker received a phone call from Merzier informing her that Foster and Evans were inside Omitogun's apartment.

At that point, Walker's statement departed from the version she gave at trial. In the written statement, Walker claimed that she had told them to leave Omitogun's apartment, and that Merzier assured her that they would. Additionally, she stated that Evans did have permission to be in her apartment, which contradicted what she had told police at the apartment. The written statement also described in significant detail the meeting during which the defendants discussed the proposed burglary and mentioned that Evans had talked the week before about robbing her neighbor. The rest of Walker's statement was in line with the account given on direct examination, including the threatening phone call from Omitogun and the threats made by Omitogun's friend.3

D. Other Evidence at Trial

Also testifying at trial were the three victims: Omitogun and two of his friends, who were at Omitogun's apartment when the burglary took place. According to their testimony, when the masked burglars entered the apartment, Omitogun was on the phone with his girlfriend, who heard the burglary over the phone and informed the police. The victims testified that the burglars restrained them with telephone cords as they took valuables from the apartment. The burglars inflicted injuries on the victims that caused broken bones and required stitches. Omitogun testified that, when the police arrived in response to his girlfriend's call, the burglars left the apartment through the upstairs window, onto the roof. Further investigation showed footprints leading from Omitogun's window, including some in the direction of Walker's apartment.

Although the victims testified that the burglars had the same general build as Foster and Evans, the victims did not see the burglars' faces. Moreover, police were unable to match fingerprints found at the scene with any of those of the defendants. Although footprints found on the roof were consistent with the boots worn by Evans and Foster, a police expert was unable to conclude that they were in fact made by any of the defendants.

A few hours after finding the defendants in Walker's apartment (during which time the crime scene was unsecured), the police also found in Walker's apartment Omitogun's briefcase (in the broiler of the stove), two loaded nine-millimeter handguns (underneath the refrigerator, obscured by several articles of men's clothing), $90,000 in cash (the same amount Omitogun had reported missing), seven wristwatches (which Omitogun had also reported missing), approximately twenty British pounds, and other personal effects of Omitogun.

II. Procedural History

After hearing the evidence recounted above, the jury returned a verdict convicting Foster (who had fled during trial) and Evans; Merzier was acquitted of all charges. Evans appealed, arguing that the admission of Walker's statement into evidence represented improper bolstering. The prosecution argued that the statement was admissible as a prior consistent statement to refute a charge of recent fabrication.

The Appellate Division held that the admission of Walker's statement was error because the statement did not predate her motive to lie. It additionally held that the statement could not be admitted as a prior consistent statement, even if it had postdated her motive to lie, since it was not entirely consistent with her testimony at trial. Finally, it held that, during their cross examination of Detective Rivera, defense counsel had refrained from asking about the specific contents of the statement and therefore had avoided "open[ing] the door" to the issue. People v. Evans, 16 A.D.3d 517, 792 N.Y.S.2d 112, 113 (2d Dep't 2005).

The Appellate Division further held, however, that the error was harmless and did not require reversal of petitioner's sentence "because there is no reasonable probability that the defendant would have been acquitted had the error not occurred," as the additional evidence adduced at trial "was overwhelming in establishing" petitioner's guilt. Id.

Evans petitioned the district court for a writ of habeas corpus on October 31, 2006. On September 22, 2011, the district court granted the petition. Evans v. Fischer, 816 F.Supp.2d 171 (E.D.N.Y.2011). In granting the writ, the district court relied on what it called the "due process guarantee of trial fairness." Id. at 185. The district court concluded that this federal constitutional guarantee is violated where the state trial court misapplies state-law evidence rules in such a fundamental way that it interferes with a criminal defendant's ability to put on a defense. In particular, the district court concluded that the cumulative effects of the admission of the hearsay statement were so prejudicial to the outcome of the case that the statement's admission was "not reconcilable with basic conceptions of justice." Id. at 204. In finding that AEDPA authorized relief under such circumstances, the district court identified four Supreme Court cases that, in its view, the Appellate Division unreasonably applied: Estelle v. McGuire, 502 U.S. 62, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991); Dowling v. United States, 493 U.S. 342, 110 S.Ct. 668, 107 L.Ed.2d 708 (1990); Lisenba v. California, 314 U.S. 219, 62 S.Ct. 280, 86 L.Ed. 166 (1941); and Chambers v. Mississippi, 410 U.S. 284, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973). According to the district court, McGuire, Lisenba, and Dowling together stand for the proposition that serious evidentiary errors can go to the fundamental fairness of a trial. The district court read Chambers to say that "the cumulative nature of ... errors embedded in [a] single evidentiary ruling and their cumulative effect" can render a trial unfair. Evans, 816 F.Supp.2d at 203-04. On the basis of these principles, which it took to be "embodied" in clearly established federal law, Thaler v. Haynes, 559 U.S. 43, 130 S.Ct. 1171, 1173, 175 L.Ed.2d 1003 (2010), the district court granted the petition and ordered the state either to retry or release petitioner within ninety days. Evans, 816 F.Supp.2d at 204.

The state filed a timely notice of appeal, and the district court's order was stayed pending appeal.

DISCUSSION

I. Legal Principles

We review a district court's grant of a habeas application de novo. Langston v. Smith, 630 F.3d 310, 314 (2d Cir.2011). We focus on the state appellate court's decision and, for issues adjudicated on the merits in state court, we apply a "highly deferential standard for evaluating state-court rulings." Renico v. Lett, 559 U.S. 766, 130 S.Ct. 1855, 1862, 176 L.Ed.2d 678 (2010) (internal quotation marks omitted).

AEDPA authorizes a district court to grant an application for a writ of habeas corpus based on an issue adjudicated on the merits by a state court only if the state proceedings "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" or if they "resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d)(1)-(2). Before the district court, petitioner effectively challenged only the state court's conclusions of law and its application of those principles to the facts of his case.

The Supreme Court has made clear that when, as in this case, a petitioner seeks to overturn a state court's decision regarding "clearly established Federal law," he may pursue two distinct paths. First, a petitioner may show that a state court's decision was "contrary to" federal law, by demonstrating either (1) that the state court reached a conclusion of law that directly contradicts a holding of the Supreme Court, or (2) that, when presented with "facts that are materially indistinguishable from a relevant Supreme Court precedent," the state court arrived at a result opposite to the one reached by the Supreme Court. Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000).

Alternatively, a petitioner may prevail by showing that a state court's decision involved an "unreasonable application" of federal law. A state court decision involves an "unreasonable application" of federal law "if the state court identifies the correct governing legal principle ... but unreasonably applies that principle to the facts" of the case before it. Id. at 413, 120 S.Ct. 1495. An application of law is "unreasonable" only if it involves "[s]ome increment of incorrectness beyond error." Overton v. Newton, 295 F.3d 270, 277 (2d Cir.2002) (internal quotation marks omitted). Additionally, the Supreme Court has made clear that the phrase "clearly established Federal law" refers to holdings, and not dicta, of cases decided by the Supreme Court, as opposed to lower federal courts. Williams, 529 U.S. at 412, 120 S.Ct. 1495.

Even apart from the requirements of AEDPA discussed above, to establish that an erroneous application of state rules of evidence violates the federal guarantee of due process, Evans must also demonstrate that the state court's erroneous conclusions about New York evidence law were so egregious as to implicate the Fourteenth Amendment's guarantee of due process. That guarantee, in this case, is one of "fundamental fairness," a principle that the Supreme Court has "defined ... very narrowly." Dowling, 493 U.S. at 352, 110 S.Ct. 668; see also McGuire, 502 U.S. at 72-73, 112 S.Ct. 475.

In short, in this case Evans faces a doubly difficult challenge. The combination of the Supreme Court's "fundamental fairness" cases and the limited habeas jurisdiction granted by AEDPA means that Evans must demonstrate that the effect of the admission of Walker's statement was so prejudicial to his defense that he was deprived of due process and he must identify a Supreme Court case that clearly establishes that the admission of evidence that improperly bolsters a prosecution witness's testimony constitutes a violation of the Fourteenth Amendment. Because no Supreme Court case requires such a conclusion, we reverse the judgment of the district court.4

II. Application

In this case, Evans does not identify any Supreme Court holding that the Appellate Division's decision might be "contrary to" in AEDPA's sense. Rather, he contends that the district court was correct in holding that the decision was an "unreasonable application" of Supreme Court precedent. We thus turn to the district court's analysis, which we find unpersuasive.

In granting petitioner's application, the district court pointed to four Supreme Court cases that it thought embodied principles that the Appellate Division unreasonably applied. Evans, 816 F.Supp.2d at 203. In McGuire and Dowling, the Supreme Court rejected habeas petitions claiming violations of due process in cases that involved evidentiary violations. In McGuire, the Court rejected the petitioner's claim that the admission as substantive evidence of prior-injury evidence — which would have been properly used only to prove battered-child syndrome — "`so infused the trial with unfairness as to deny due process of law.'" 502 U.S. at 75, 112 S.Ct. 475, quoting Lisenba, 314 U.S. at 228, 62 S.Ct. 280. The Court found, in view of additional evidence presented at trial and the judge's instructions to the jury, that the evidentiary violations did not fall into the narrow "category of infractions that violate fundamental fairness." Id. at 73, 112 S.Ct. 475 (internal quotation marks omitted).

Similarly, in Dowling, the Supreme Court rejected the petitioner's claim that the admission, pursuant to Fed.R.Evid. 404(b), of evidence of his role in a prior burglary and assault, for which he was acquitted, violated the guarantee of fundamental fairness. 493 U.S. at 354, 110 S.Ct. 668. While the Court recognized "that the introduction of [this] evidence ... ha[d] the potential to prejudice the jury," it framed the question as "whether it is acceptable to deal with the potential for abuse through nonconstitutional sources like the Federal Rules of Evidence, or whether the introduction of this type of evidence ... violates fundamental conceptions of justice." Id. at 352, 110 S.Ct. 668 (internal quotation marks and footnote omitted). At least in Dowling, the Supreme Court opted not to constitutionalize this sort of evidentiary error. McGuire and Dowling therefore set precedents as to what evidentiary errors would not violate due process, but they provide very limited guidance as to which evidentiary errors would do so.

These cases are consistent with Lisenba, in which the Supreme Court had earlier considered whether due process was violated when evidence was admitted in violation of state-law evidence rules. On the evidentiary issues, the Supreme Court rejected petitioner's claims and noted that it did "not sit to review state court action on questions of the propriety of the trial judge's action in the admission of evidence." 314 U.S. at 228, 62 S.Ct. 280. What the Court found most relevant to the petitioner's claims in Lisenba was the admission of confessions, allegedly obtained under duress, made by petitioner regarding crimes for which he was convicted; the question is therefore wholly distinct from the one presented in the instant case. But even as to the admissibility of coerced confessions, the Court rejected petitioner's claims. Id. at 240-41, 62 S.Ct. 280. Not only does Lisenba not stand for the proposition that the admission of hearsay evidence violates due process, its holding does not embody a principle that could guide a federal court when granting an application for habeas under AEDPA in a case such as this one.

The district court also relied on Chambers v. Mississippi, which it took to embody the principle that the erroneous admission of hearsay can defeat a defendant's fundamental right to present his own defense. But Chambers stands for the inverse proposition: that in some cases the exclusion of hearsay proffered by a defendant in a correct application of state rules of evidence can violate the guarantee of due process by denying a defendant his right to present witnesses in his own defense. 410 U.S. at 302, 93 S.Ct. 1038. In that case, Mississippi's "voucher" rule prohibited litigants from impeaching their own witnesses. Because the state refused to call a witness who had previously confessed to the crime for which Chambers was then being tried, he sought to introduce other evidence of those prior third-party confessions. The operation of Mississippi's hearsay rule prohibited Chambers from doing so. Id. at 294, 93 S.Ct. 1038. In these circumstances, the Court held, the state's evidence rules produced an unconstitutional result. Id. at 302, 93 S.Ct. 1038. To rely on Chambers for more than that is to ignore the Supreme Court's interpretation of AEDPA's "as determined by the Supreme Court" language to include only the holdings of — and not the dicta contained in — its cases. see Williams, 529 U.S. at 412, 120 S.Ct. 1495.5

Finally, to the extent any of the cases on which the district court relied can be said to provide a principle the Appellate Division unreasonably applied, such a principle would be broad in nature. "[E]valuating whether a rule application was unreasonable requires considering the rule's specificity. The more general the rule, the more leeway [state] courts have in reaching outcomes in case-by-case determinations." Yarborough v. Alvarado, 541 U.S. 652, 664, 124 S.Ct. 2140, 158 L.Ed.2d 938 (2004). We may assume, arguendo, that the admission of hearsay statements, in some egregious instance, could render a trial fundamentally unfair — though in most cases, the more specific provisions of the Confrontation Clause would remedy such abuses.6 But the ruling in this case was hardly a clean example of such abuse. The declarant, Walker, testified at trial and was extensively cross-examined about the inconsistencies in her various statements; the hearsay statement added little of an incriminating nature to Walker's sworn and cross-examined in-court testimony, and its inconsistencies with some details of that testimony added grist to the defense argument that Walker was an unreliable witness; and Walker's testimony (and thus the hearsay statement) was corroborated by a wealth of other evidence. Under these circumstances, assuming arguendo that Supreme Court cases establish a general principle that the reliance on hearsay testimony to support a conviction can violate the requirement of due process, we could not conclude that the state court's affirmance of Evans's conviction, finding any state evidentiary error harmless and Evans's trial fundamentally fair, was an unreasonable application of that principle.

CONCLUSION

For the foregoing reasons, we conclude that the district court erred by granting Evans's application for the writ of habeas corpus. The judgment of the district court is accordingly REVERSED, and the case remanded with instructions to dismiss the petition.