SUMMARY ORDER

UPON DUE CONSIDERATION, IT IS HEREBY ORDERED, ADJUDGED, AND DECREED that the judgment of the district court is AFFIRMED.

Petitioner-Appellant Roberto Ciaprazi (“Ciaprazi”) appeals the district court’s denial of his petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254. The sole issue for which this court issued a certificate of appealability is whether Cia-prazi’s trial counsel was constitutionally ineffective for failing to object to the trial court’s handling of an alternate juror’s allegation that another juror had slept through portions of the trial. We presume the parties’ familiarity with the facts, the procedural history, and the scope of the issues presented on appeal, which we reference only as necessary to explain our decision.

A defendant claiming ineffective assistance of counsel must satisfy both prongs of the test laid out in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). The defendant must show both that counsel’s performance “fell below an objective standard of reasonableness” and that “there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 688, 694, 104 S.Ct. 2052. In assessing counsel’s performance under the first prong of Strickland, “we must apply a ‘heavy measure of deference to counsel’s judgments.’ ” Greiner v. Wells, 417 F.3d 305, 319 (2d Cir. 2005) (quoting Strickland, 466 U.S. at 691, 104 S.Ct. 2052). ‘We will not normally fault counsel for foregoing a potentially fruitful course of conduct if that choice also entails a ‘significant potential downside.’ ” Id.

Ciaprazi argues that trial counsel should have sought further inquiry from the judge into the claim that one of the jurors was sleeping during key stages of the trial. See People v. Valerio, 141 A.D.2d 585, 529 N.Y.S.2d 350, 351 (1988); People v. Russell, 112 A.D.2d 451, 492 N.Y.S.2d 420, 422 (1985). Ciaprazi notes that if deliberations have begun with a “grossly unqualified” juror on the jury, the court must declare a mistrial unless the defendant consents to the replacement of the unqualified juror with an alternate. See N.Y.Crim. P.L. § 270.35(1).

If deliberations have not yet begun, however, the defendant’s consent is not required for the court to seat an alternate. Id. And it is anything but clear on this record that deliberations had begun in the sense contemplated by New York law. Although the transcript records the jury’s exit from the courtroom before the possibly sleeping juror was mentioned to the judge, see Transcript at 899, the transcript also specifically indicates, “Jury Deliberates,” at a later point in the proceedings, after the sleeping juror discussion had ended, see id. at 901. Accordingly, trial counsel’s decision not to object may well have been based on his desire to retain the inattentive juror rather than to seek to replace him with an alternate. As this decision is paradigmatically strategic, cf. *64United States v. Lawes, 292 F.3d 123, 128 (2d Cir. 2002) (“[Tjrial strategy and voir dire are inseparable.”), we cannot say that the state court acted unreasonably in failing to find counsel constitutionally ineffective for declining to request an inquiry.1 See Cox v. Donnelly, 387 F.3d 193, 197 (2d Cir. 2004) (stating that a state court defendant claiming ineffective assistance of counsel in a federal habeas petition “must show that the [state court] applied Strickland to the facts of his case in an objectively unreasonable manner” (quoting Bell v. Cone, 535 U.S. 685, 699, 122 S.Ct. 1843, 152 L.Ed.2d 914 (2002)) (internal quotation marks omitted)).

We note, moreover, that the evidence that the juror was actually dozing is thin. Some greater indication than is currently in the record that he was, in fact, asleep, as opposed to daydreaming or concentrating with eyes shut, would have significantly strengthened the argument that a hearing was warranted. This might have been established through an affidavit from Cia-prazi, his trial counsel, or any of the jurors, but no such evidence was produced.

We have considered all of Ciaprazi’s arguments and find them to be without merit. The decision of the district court is therefore AFFIRMED.