SUMMARY ORDER

Petitioner Charles Davis appeals from an April 17, 2003 judgment of the United States District Court for the Eastern District of New York (Spatt, J.) denying his petition for a writ of habeas corpus. Davis argues he was denied his Sixth Amendment right to effective assistance of counsel. The state trial court precluded counsel from calling a psychiatrist to testify on petitioner’s behalf because counsel had failed to give timely notification to the prosecution, as required by New York Criminal Procedure Law § 250.10, of his intention to present psychiatric evidence. We affirm the district court’s denial of Davis’s habeas petition. We conclude that the New York Appellate Division, which *354reviewed petitioner’s claim of ineffective assistance of counsel on direct appeal, did not unreasonably apply clearly established federal law in rejecting his claim. Familiarity with the facts and procedural history is assumed.

We review de novo a district court judgment denying habeas corpus. Sellan v. Kuhlman, 261 F.3d 303, 308 (2d Cir. 2001). Section 2254(d) of Title 28, United States Code, sets forth standards for federal habeas review of state court decisions applicable to this case. The statute provides in pertinent part:

(d) An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim—

(1) 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....

28 U.S.C.A. § 2254(d)(1) (West 1994 & Supp. 2004).

A Sixth Amendment ineffective assistance of counsel claim “necessarily invokes federal law that has been ‘clearly established’ by the Supreme Court within the meaning of AEDPA.” Sellan, 261 F.3d at 309.

We next determine whether the state court “adjudicated” Davis’s claim “on the merits,” and we find that it did. To do this we consider: “ ‘(1) what the state courts have done in similar cases; (2) whether the history of the case suggests that the state court was aware of any ground for not adjudicating the case on the merits; and (3) whether the state court’s opinion suggests reliance upon procedural grounds rather than a determination on the merits.’ ” Id. at 314 (quoting Mercar del v. Cain, 179 F.3d 271, 274 (5th Cir. 1999)). Although the Appellate Division’s decision regarding ineffective assistance of counsel consisted only of the words: “The defendant’s remaining contentions are without merit,” People v. Davis, 685 N.Y.S.2d 455, 456 258 A.D.2d 528, 529 (App.Div. 1999), this is sufficient to constitute an adjudication on the merits. Jenkins v. Artuz, 294 F.3d 284, 289, 291 (2d Cir. 2002). Because Davis’s claim in state court was adjudicated on the merits, we review the substance of that determination under the deferential standards mandated by § 2254(d)(1). See Sellan, 261 F.3d at 312.

Under § 2254(d), a federal court must deny a habeas corpus petition unless the state court’s adjudication “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.” 28 U.S.C.A. § 2254(d)(1). A decision is “contrary to” established law if the state court arrives at a legal conclusion “opposite” to that reached by the Supreme Court or if the state court confronts a set of facts that are “materially indistinguishable” from a decision of the Supreme Court and arrives at a different result. Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). There is no indication that either of these events occurred in this case.

We then turn to whether the Appellate Division’s decision was an “unreasonable application” of clearly established law. When making the “unreasonable application” inquiry, a federal habeas court “should ask whether the state court’s application of clearly established federal law was objectively unreasonable.” Id. at 409, 120 S.Ct. 1495. “[E]ven if the federal habeas court concludes that the state court decision applied clearly established federal *355law incorrectly, relief is appropriate only if that application is also objectively unreasonable.” Penry v. Johnson, 532 U.S. 782, 793, 121 S.Ct. 1910, 150 L.Ed.2d 9 (2001). For an application to be objectively unreasonable, “[s]ome increment of incorrectness beyond error is required.” Francis S. v. Stone, 221 F.3d 100, 111 (2d Cir. 2000). We cautioned, however, that “the increment need not be great; otherwise, habeas relief would be limited to state court decisions ‘so far off the mark as to suggest judicial incompetence.’ ” Id. (quoting Matteo v. Superintendent, SCI Albion, 171 F.3d 877, 889 (3d Cir. 1999) (in banc)).

Thus, the question is whether it was objectively reasonable for the Appellate Division to deny petitioner’s ineffective assistance of counsel claim, which he made on federal constitutional grounds. To prevail, Davis must demonstrate that his counsel performed deficiently and that the deficiency caused actual prejudice. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Because the record does not establish that any purported deficiency caused actual prejudice to the petitioner’s case, we hold that the Appellate Division’s ruling on the issue was objectively reasonable. For that same reason, we need not address whether counsel performed deficiently. See id., 466 U.S. at 697,104 S.Ct. 2052.

To establish prejudice, Davis must demonstrate that there is a “reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 694, 104 S.Ct. 2052. “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. At trial, petitioner’s counsel proffered that the psychiatrist’s proposed testimony “relates to Mr. Davis’ state of mind, his belief, his sense and his position once faced with those particular issues and facts that he was faced with on the evening of [the incident] looking at him as an individual and a psychiatric evaluation of him with regard to, the facts that relate to the incident.” Counsel stated further that the “intent” behind Dr. Dudley’s testimony “was to go more to the justification defense in this case, not looking at a mental infirmity or defect as stated by [N.Y.Crim. Proc. § 250.10].” Counsel’s proffer aside, there is nothing in the record to indicate the content of Dr. Dudley’s proposed testimony. Without more we cannot conclude with reasonable probability that, but for the exclusion of the proffered testimony, the outcome of petitioner’s trial would have been different. Because we cannot reach that conclusion, we cannot say that the Appellate Division unreasonably denied petitioner’s ineffective assistance of counsel claim.

For the foregoing reasons, we AFFIRM the judgment of the district court denying the petition for a writ of habeas corpus.