McLAUGHLIN, Circuit Judge.
Respondent Joseph Costello, Superintendent of the Mid State Correctional Facility, appeals from the grant of Sidney Hawkins’s petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254 by the United States District Court for the Eastern District of New York (Johnson, J.).
See Hawkins v. Costello,
No. 00 CV 1343(SJ), 2005 WL 946412 (E.D.N.Y. Apr.15, 2005). Because the state court adjudication was not contrary to, or an unreasonable application of, clearly established federal law, we reverse.
BACKGROUND
In June 1994, two New York City police officers were on patrol in Brooklyn. They saw two men running on the sidewalk, looking over their shoulders as they ran. The officers recognized one of the men as a man they knew by the sobriquet “Eddie-Ed.” The police officers also saw Sidney Hawkins standing behind the two men in front of a grocery store. Hawkins was holding a gun.
Hawkins ran into the grocery store. One of the officers pursued him and arrested him inside the store. The officers recovered the gun from behind a counter, and Hawkins was charged with criminal possession of a weapon.
In March 1995, the New York Supreme Court, Kings County, conducted a bench trial. Hawkins’s defense was that Eddie-Ed had brandished a gun at him during a dispute over a debt Hawkins owed Eddie-Ed. According to Hawkins, he grabbed the gun from Eddie-Ed in order to protect himself.
Mark McCormack, one of the officers who arrested Hawkins, testified about the events surrounding Hawkins’s arrest. He also testified that a few months after the arrest, he saw Eddie-Ed on a street corner. After the two exchanged pleasantries, Officer McCormack “mentioned” Hawkins’s arrest.
On cross-examination, Hawkins’s attorney attempted to explore the substance of Officer McCormack’s conversation with Eddie-Ed in order to support Hawkins’s innocent possession defense. The prosecution objected to the following question: “And during this conversation, isn’t it a fact that [Eddie-Ed] had told you ... that the weapon was his?” The court sustained the objection and struck the question from the record. Hawkins’s attorney then asked Officer McCormack, “And in this conversation that you had with [Eddie-Ed], didn’t he tell you that you were arresting the wrong person for ownership of the weapon?” The prosecution again objected. The court initially overruled the objection because it did not ask for “a direct quote.” The prosecution, however, explained why it believed the question called for hearsay. The court then reversed itself and sustained the prosecution’s objection to the question. Hawkins’s attorney also asked Officer McCormack if he knew “who the owner of that weapon is?” The prosecution once again objected, and the court sustained the objection, ruling that “owner” “is a legal term. The trier of facts has to determine who the
owner means.” Notably, Hawkins’s attorney never sought to make an offer of proof regarding why he thought Eddie-Ed’s putative out-of-court statements were admissible through Officer McCormack’s testimony.
At the close of trial, the court found Hawkins guilty of criminal possession of a weapon in the third degree. After finding that Hawkins was a persistent violent felony offender under New York law, the court sentenced him to eight years’ to life imprisonment.
Hawkins appealed his conviction to the Appellate Division, Second Department. He argued,
inter alia,
that the trial court improperly restricted his cross-examination of Officer McCormack. In 1999, the Appellate Division affirmed the conviction.
People v. Hawkins,
258 A.D.2d 472, 685 N.Y.S.2d 253 (2d Dep’t 1999). The court did not directly address Hawkins’s argument regarding Officer McCormack’s cross-examination. Instead, after addressing other arguments, the court said that all of Hawkins’s “remaining contentions ... are either unpreserved for appellate review or without merit.”
Id.
at 253-54.
The New York Court of Appeals denied Hawkins leave to appeal.
People v. Hawkins,
93 N.Y.2d 925, 693 N.Y.S.2d 508, 715 N.E.2d 511 (1999) (Wesley, J.).
In 2000, Hawkins filed a pro se petition for a writ of habeas corpus in the United States District Court for the Eastern District of New York. Among other things, the petition alleged that the trial court unconstitutionally restricted his cross-examination of Officer McCormack.
In January 2003, a magistrate judge (Chrein,
M.J.),
to whom the district court had referred Hawkins’s petition, construed Hawkins’s pro se claim as a contention that he was unconstitutionally prohibited from presenting exculpatory evidence. The magistrate found that
if
Eddie-Ed had told Officer McCormack that the gun belonged to him, Officer McCormack’s testimony to that fact would have been admissible hearsay as a statement against penal interest and the trial court’s refusal to allow such testimony would have been a denial of Hawkins’s due process right to introduce exculpatory evidence. The magistrate ordered a hearing to determine what Eddie-Ed told Officer McCormack. At the same time, he recommended rejection of Hawkins’s other claims, and he appointed counsel to represent Hawkins.
In April 2003, the State submitted an affidavit from Officer McCormack in which he stated that he did not remember his near-decade-old conversation with Eddie-Ed. Thus, Officer McCormack had no “recollection whatsoever of anything [Eddie-Ed] said to [him].” The State filed an additional affidavit in which it included Eddie-Ed’s last known address.
In May 2003, the magistrate rescinded the hearing order and gave Hawkins time to develop evidence regarding the substance of Eddie-Ed’s statements to Officer McCormack. When Hawkins failed to do so, the magistrate issued a report and recommendation in which he recommended that Hawkins’s habeas petition be denied in full.
Hawkins objected to the report and recommendation, arguing that the “Magistrate Judge unconstitutionally placed the burden on petitioner to offer proof as to what [Officer McCormack] would have testified.” In April 2005, the district court rejected the magistrate’s recommendation and granted in part Hawkins’s petition for a writ of habeas corpus. The district court essentially assumed that if the trial court permitted Officer McCormack to answer Hawkins’s counsel’s questions, he would have testified that Eddie-Ed stated that the gun was his, and therefore Hawkins
was prevented from presenting exculpatory evidence. The court based this assumption on its finding that the lack of evidence regarding what Eddie-Ed actually said to Officer McCormack is “entirely attributable” to the State because the trial court sustained the prosecution’s objections to Hawkins’s counsel’s questions. The district court ordered the State to immediately release Hawkins.
The State moved for a stay of Hawkins’s release pending appeal. The district court granted an interim stay pending its decision on the State’s motion. Seven months later, the district court denied the State’s motion for a stay pending appeal, lifted its interim stay, and ordered the State to release Hawkins within fifteen days.
Hawkins v. Costello,
No. 00 CV 1343, 2005 WL 3072019 (E.D.N.Y. Nov.1, 2005).
The State immediately moved this Court for a stay pending appeal, which we granted. Thus, Hawkins remains incarcerated during our consideration of this appeal.
DISCUSSION
The State argues that the district court erred in granting Hawkins’s habeas petition. We agree.
We review de novo a district court’s decision to grant or deny a habeas petition.
Jenkins v. Artuz,
294 F.3d 284, 290 (2d Cir.2002). In so doing, we review a district court’s factual findings for clear error.
Id.
I.
The Deference Afforded to the State Court Adjudication
When a state court adjudicates a habeas petitioner’s claim on the merits, we must afford that decision the deferential standard of review established by the Anti-terrorism and Effective Death Penalty Act of 1996 (“AEDPA”) in 28 U.S.C. § 2254(d).
Sellan v. Kuhlman,
261 F.3d 303, 310-11 (2d Cir.2001). In
Jimenez v. Walker,
we recently made clear that when a state court rejects a petitioner’s claim as either unpreserved or without merit, the conclusive presumption is that the adjudication rested on the merits. 458 F.3d 130, 146 (2d Cir.2006). Here, the Appellate Division rejected Hawkins’s claim regarding the exclusion of Officer McCormack’s answers to his counsel’s questions as “either unpre-served for appellate review or without merit.”
Hawkins,
685 N.Y.S.2d at 253-54. Thus, we owe that adjudication AEDPA deference.
Applying AEDPA deference, a federal court may grant a writ of habeas corpus if the state court’s adjudication on the merits “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. § 2254(d)(1). “Clearly established Federal law” “refers to the holdings, as opposed to the dicta, of [the Supreme] Court’s decisions as of the time of the relevant state-court decision.”
Williams v. Taylor,
529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000).
A state court adjudication is “contrary to” federal law if it “arrives at a conclusion opposite to that reached by [the Supreme] Court on a question of law” or if it “decides a case differently than [the Supreme] Court has on a set of materially indistinguishable facts.”
Id.
at 412-13, 120 S.Ct. 1495.
“Unreasonableness is determined by an ‘objective’ standard.”
Gersten v. Senkowski,
426 F.3d 588, 607 (2d Cir.2005) (quoting
Williams,
529 U.S. at 409, 120 S.Ct. 1495), cert.
denied,
— U.S. -, 126 S.Ct. 2882, 165 L.Ed.2d 894 (2006). An incorrect decision is not necessarily unreasonable. Instead, we look for “[s]ome increment of incorrectness beyond error.”
Francis S. v. Stone,
221 F.3d 100, 111 (2d Cir.2000). That increment, however, “need not be great; otherwise, habeas relief would be limited to state court decisions so far off the mark as suggest judicial incompetence.”
Id.
(internal quotation marks omitted). “Moreover, the range of judgments that can be deemed ‘reasonable’ may vary with the nature of the rule in question.”
Serrano v. Fischer,
412 F.3d 292, 297 (2d Cir.2005),
cert. denied,
— U.S. -, 126 S.Ct. 1357, 164 L.Ed.2d 68 (2006). “The more general the rule, the more leeway 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).
AEDPA does not require that the state court adjudication under review cite Supreme Court cases.
Early v. Packer,
537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002) (per curiam). “[Ijndeed, it does not even require
awareness
of [Supreme Court] cases, so long as neither the reasoning nor the result of the state-court decision contradicts them.”
Id.
Where, as here, the state court “summarily rejected” the basis for a petitioner’s application for the writ, “we must focus on the ultimate decisions of [that] court[ ], rather than on the [court’s] reasoning.”
Aeid v. Bennett,
296 F.3d 58, 62 (2d Cir.2002). Thus, we consider whether the “ultimate decision was an ‘unreasonable application’ of clearly established Supreme Court precedent.”
Sellan,
261 F.3d at 311-12.
II.
Clearly Established Federal Law
Long before the Appellate Division’s adjudication of Hawkins’s claim, the Supreme Court made clear that a criminal defendant has a constitutional right— grounded in the Sixth Amendment’s Compulsory Process and Confrontation Clauses and the Fourteenth Amendment’s Due Process Clause — to “a meaningful opportunity to present a complete defense.”
Crane v. Kentucky,
476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986) (internal quotation marks omitted). Indeed, “[f|ew rights are more fundamental than that of an accused to present witnesses in his own defense.”
Chambers v. Mississippi,
410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973).
While a defendant has the right to present a complete defense, that right is not without limits and “may in appropriate cases, bow to accommodate other legitimate interests in the criminal trial process.”
Id.
at 295, 93 S.Ct. 1038;
Jimenez,
458 F.3d 147 (“As with many rights, the right to present a defense is not unlimited.”). A defendant “must comply with established rules of procedure and evidence designed to assure both fairness and reliability,”
Chambers,
410 U.S. at 302, 93 S.Ct. 1038, and the “accused does not have an unfettered right to offer testimony that is incompetent, privileged, or otherwise inadmissible under standard rules of evidence,”
Taylor v. Illinois,
484 U.S. 400, 410, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988);
see also Clark v. Arizona,
— U.S. -, -, 126 S.Ct. 2709, 2731, 165 L.Ed.2d 842, - (2006) (“[T]he right to introduce relevant evidence can be curtailed if there is a good reason for doing that.”). The Supreme Court, however, “has found unconstitutional the rigid application of state evidentiary rules prohibiting presentation” of exculpatory evidence.
See Wade v. Mantello,
333 F.3d 51, 57 (2d Cir.2003). In this vein,
“where constitutional rights directly affecting the ascertainment of guilt are implicated, the hearsay rule may not be applied mechanistically to defeat the ends of justice.”
Chambers,
410 U.S. at 302, 93 S.Ct. 1038.
III.
“Contrary to” or “Unreasonable Application of’
We can quickly dispense with AEDPA’s “contrary to” prong. In deciding Hawkins’s claim, the state court did not decide a question of law differently from the Supreme Court; and this case does not present a set of facts materially indistinguishable from a Supreme Court case. Thus, the state court adjudication is not “contrary to” clearly established federal law.
See Williams,
529 U.S. at 412-13, 120 S.Ct. 1495. Our focus here, then, is on AEDPA’s “unreasonable application” prong.
In considering whether the exclusion of evidence violated a criminal defendant’s right to present a complete defense, we start with “the propriety of the trial court’s evidentiary ruling.”
Wade,
333 F.3d at 59;
Washington v. Schriver,
255 F.3d 45, 57 (2d Cir.2001). Of course, “ha-beas corpus relief does not lie for errors of state law,”
Lewis v. Jeffers,
497 U.S. 764, 780, 110 S.Ct. 3092, 111 L.Ed.2d 606 (1990), and that necessarily includes erroneous evidentiary rulings. The inquiry, however, “into possible state evidentiary law errors at the trial level” assists us in “ascertainpng] whether the appellate division acted within the limits of what is objectively reasonable.”
Jones v. Stinson,
229 F.3d 112, 120 (2d Cir.2000).
If potentially exculpatory evidence was erroneously excluded, we must look to “whether ‘the omitted evidence [evaluated in the context of the entire record] creates a reasonable doubt that did not otherwise exist.’ ”
Justice v. Hoke,
90 F.3d 43, 47 (2d Cir.1996) (quoting
United States v. Agurs,
427 U.S. 97, 112, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976)) (alteration in original);
see also Wade,
333 F.3d at 59 (stating that “[t]his test applies post-AEDPA”).
On the other hand, if the evidentiary ruling was correct pursuant to a state evidentiary rule, our inquiry is more limited. We consider whether the evidentiary rule is “ ‘arbitrary’ or ‘disproportionate to the purposes [it is] designed to serve.’ ”
United States v. Scheffer,
523 U.S. 303, 308, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998) (quoting
Rock v. Arkansas,
483 U.S. 44, 56, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987));
see also Holmes v. South Carolina,
— U.S. -, -, 126 S.Ct. 1727, 1731, 164 L.Ed.2d 503 (2006). A state evidentiary rule is “unconstitutionally arbitrary or disproportionate only where it has infringed upon a weighty interest of the accused.”
Scheffer,
523 U.S. at 308, 118 S.Ct. 1261. Moreover, even before AEDPA required a more deferential review, the Supreme Court had a “traditional reluctance to impose constitutional constraints on ordinary evidentiary rulings by state trial courts.”
Crane,
476 U.S. at 689, 106 S.Ct. 2142. The Court has “never questioned the power of States to exclude evidence through the application of evidentiary rules that themselves serve the interests of fairness and reliability — even if the defendant would prefer to see that evidence admitted.”
Id.
at 690, 106 S.Ct. 2142.
A.
The Propriety of the Trial Court’s Evidentiary Ruling
We cannot say that the trial court’s exclusionary rulings were erroneous as a matter of New York evidentiary law. It appears that the trial court excluded Officer McCormack’s answers to Haw
kins’s counsel’s questions as hearsay.
Hearsay is inadmissible in New York courts unless it falls within an exception to the rule.
See People v. Huertas, 75
N.Y.2d 487, 492, 554 N.Y.S.2d 444, 553 N.E.2d 992 (1990). Hawkins’s attorney’s questions plainly called for out-of-court statements to be introduced for the truth of the matters asserted, and hence they called for hearsay.
See People v. Romero,
78 N.Y.2d 355, 361, 575 N.Y.S.2d 802, 581 N.E.2d 1048 (1991) (defining hearsay as an out-of-court statement “offered for the truth of the fact asserted in the statement” (internal quotation marks omitted)).
New York law does provide a potentially applicable exception to its hearsay rule for statements against a declarant’s penal interest so long as certain requirements are met.
See People v. Thomas,
68 N.Y.2d 194, 197-98, 507 N.Y.S.2d 973, 500 N.E.2d 293 (1986),
overruled on other grounds by People v. Hardy,
4 N.Y.3d 192, 791 N.Y.S.2d 513, 824 N.E.2d 953 (2005). The district court found that this exception applied here and therefore that the exclusion of Officer McCormack’s answers was a state evidentiary law error. But, as we discuss in greater detail below, Hawkins’s never gave the trial court any reason to find that the exception applied in this case.
Cf. People v. Houghton,
155 A.D.2d 883, 547 N.Y.S.2d 718, 718 (4th Dep’t 1989) (“In the absence of proof about the contents of the statements sought to be admitted, it is impossible to determine whether they came within any exception to the hearsay rule.”). Thus, the trial court’s evidentiary ruling was not erroneous. Cf.
Zarvela v. Artuz,
364 F.3d 415, 418 (2d Cir.) (per curiam),
cert. denied,
543 U.S. 879, 125 S.Ct. 140, 160 L.Ed.2d 132 (2004) (finding habeas relief unavailable where the state court excluded potentially exculpatory evidence as hearsay, in part, because “petitioner has not shown that the court’s ruling was contrary to” New York’s hearsay rule).
B.
Infringement on a “Weighty Interest”
As explained above, when a trial court has not made a state evidentiary error, we must consider whether the evidentiary rule the court applied is arbitrary or disproportionate to the purposes it is designed to serve, and we can only find the rule arbitrary or disproportionate if it infringes on a “weighty interest of the accused.”
Scheffer,
523 U.S. at 308, 118 S.Ct. 1261. Here, there is no basis upon which to find that the application of New York’s hearsay rule infringed on any of Hawkins’s weighty interests.
If we knew — or perhaps more precisely if the trial court had reason to have known — that Eddie-Ed had confessed ownership of the gun to Officer McCormack, then we might well have found that the trial court’s exclusion of that evidence infringed on Hawkins’s weighty interest in presenting exculpatory evidence.
See People v. Almodovar,
62 N.Y.2d 126, 130, 476 N.Y.S.2d 95, 464 N.E.2d 463 (1984) (stating that a person who possesses an otherwise proscribed weapon is not guilty of unlawful possession if he took the weapon from an assailant in the course of a fight).
The problem, however, is that we do not know whether such exculpatory evidence ever existed. Hawkins “bears the burden of proving by a preponderance of the evidence that his constitutional rights have been violated.”
Jones v. Vacco,
126 F.3d 408, 415 (2d Cir.1997). Without some basis to find that the evidence did in fact exist or some reason to excuse the absence of such a basis, a writ of habeas corpus is inappropriate in this case.
See Wood v. Bartholomew,
516 U.S. 1, 8, 116 S.Ct. 7, 133 L.Ed.2d 1 (1995) (per curiam) (stating that a federal court cannot grant “habeas relief on the basis of little more than speculation with slight support”).
Significantly, neither Hawkins nor the district court has directed us to any cases in which a court found a violation of a criminal defendant’s right to a meaningful opportunity to present a defense where the court so ruling did not know the substance of the excluded evidence. And we have not found any cases in which the Supreme Court or this Court found a violation of that right where it was not “able to appreciate the significance of the excluded evidence.”
See Gov’t of the Virgin Islands v. Smith,
615 F.2d 964, 972 (3d Cir.1980).
C.
The Absence in the Record of the Substance of Eddie-Ed’s Out-of-Court Statements
Finally, we consider the district court’s conclusion that the absence of information in the record about Eddie-Ed’s conversation with Officer McCormack is “entirely attributable” to the State because the trial court sustained the prosecution’s objection to Hawkins’s counsel’s questions. The district court went on to find that “[t]o deny [Hawkins’s] claim on the basis of the fact that he has not presented such evidence when the trial court
erroneously
barred him from presenting exactly that evidence would be unreasonable and unjust.” (Emphasis added.) We disagree with this analysis.
First,
as we discussed above, the trial court did not “erroneously” exclude the evidence. Instead, it excluded hearsay evidence in accord with well-established New York evidentiary law designed to exclude unreliable evidence.
See Scheffer,
523 U.S. at 309, 118 S.Ct. 1261 (“State and Federal Governments unquestionably have a legitimate interest in ensuring that reliable evidence is presented to the trier of fact in a criminal trial,” and “the exclusion of unreliable evidence is a principal objective of many evidentiary rules.”).
Second,
as we have explained, when the trial court made its initial exclusion ruling, the proverbial ball was in Hawkins’s court. As a matter of New York law, it was incumbent upon his counsel to alert the trial court to a basis, if there was any, upon which the out-of-court statements were admissible.
See Tyrrell v. Wal-Mart Stores, Inc.,
97 N.Y.2d 650, 652, 737 N.Y.S.2d 43, 762 N.E.2d 921 (2001) (“Our law is well settled. The proponent of hearsay evidence must establish the applicability of a hearsay-rule exception.” (internal citation omitted)). He did not do so.
Whatever the reason, we cannot know how Officer McCormack would have
answered Hawkins’s counsel’s questions. We cannot — and do not — fault the State for that lack of knowledge.
Hawkins contends that his opening statement “clearly alerted the Court to the defense that the weapon was in temporary possession of [Hawkins], after having been removed from the true owner,” and thus the trial court had a sufficient offer of proof to allow Officer McCormack to answer Hawkins’s counsel’s questions. That is not correct. The opening statement certainly alerted the trial court to Hawkins’s defense of innocent possession. That is a far cry, however, from an indication that Eddie-Ed told Officer McCormack that the gun was his. Simply because a hoped-for answer would support an asserted defense does not indicate a basis for admission of that answer into evidence.
* * *
We cannot say that the state court adjudication was contrary to, or an unreasonable application of, clearly established federal law. Thus Hawkins’s habeas petition must be denied.
CONCLUSION
For the foregoing reasons, we reverse the district court’s grant of Hawkins’s ha-beas petition and remand with directions to dismiss the petition.