SUMMARY ORDER

Adalberto Fernandez appeals from a denial of a petition for a writ of habeas corpus, by the United States District Court for the Southern District of New York (Miriam Goldman Cedarbaum, Judge). The petition challenged his October 1988 conviction in the New York State Supreme Court, New York County, on two counts of second-degree murder.2 The district court dismissed four of Fernandez’s five claims on the ground that he had failed to exhaust them. See 28 U.S.C. § 2254(b)(1)(A). The remaining claim— that Fernandez’s rights under the Confrontation Clause of the Sixth Amendment were violated by the trial court’s evidentiary rulings — was considered and rejected by the district court.

On appeal, Fernandez challenges three specific evidentiary rulings. The first challenge concerns his counsel’s attempt to ask Miguel Tejada, one of the prosecution’s witnesses, whether he had ever fired *50gunshots at either Fernandez or Fernandez’s friend. Upon being informed that Tejada intended to invoke his Fifth Amendment privilege against self-incrimination, the trial court ruled that the defense could not inquire into this area. The second challenge concerns defense counsel’s attempt to question Tejada on whether he had murdered an individual named Sting. The trial court found that defense counsel failed to articulate a good faith basis for his belief that Tejada had killed Sting, and it prohibited the inquiry. The third challenge concerns the trial court’s refusal to permit defense counsel to elicit testimony suggesting that the charges against Jorge Gonzales — with whom Fernandez was originally indicted — were dismissed by the prosecution. Fernandez also takes issue with the trial court’s instruction to the jury that they were not to speculate as to why no charges were pending against Gonzales.

We recognize that “[t]he right of cross-examination, though not absolute, is one of the most firmly established principles under Supreme Court law.” Cotto v. Herbert, 331 F.3d 217, 248 (2d Cir. 2003). The Confrontation Clause is violated when a defendant is “prohibited from engaging in otherwise appropriate cross-examination designed ... to expose to the jury the facts from which the jurors ... could appropriately draw inferences relating to the reliability of the witness.” Delaware v. Van Arsdall, 475 U.S. 673, 680, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986) (internal quotation marks omitted). In some instances, an adverse witness’s invocation of the Fifth Amendment privilege may violate the Confrontation Clause. See Bagby v. Kuhlman, 932 F.2d 131, 135 (2d Cir. 1991).

Although we review a district court’s denial of a writ of habeas corpus de novo, see Cotto, 331 F.3d at 229, the ability of federal courts to grant habeas relief is limited by the Antiterrorism and Effective Death Penalty Act of 1996, Pub.L. 104-32, 110 Stat. 1214 (codified principally at 28 U.S.C. §§ 2254(d)) (“AEDPA”). Under AEDPA, habeas relief on any claim adjudicated on the merits in state court proceedings may not be granted unless the adjudication of the claim resulted in a decision that was either “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court,” or “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” Id.

We cannot find that the adjudication of Fernandez’s claim in New York state court proceedings offended this deferential standard. Here, the trial court appropriately limited Fernandez’s cross-examination of Tejada to avoid infringing on Tejada’s privilege against self-incrimination and to eliminate questions lacking a good faith basis, and also properly restricted Fernandez from asking questions of Gonzales which would have called for speculative responses. Because the adjudication of Fernandez’s claim in New York state courts resulted in a decision that was neither contrary to clearly established federal law nor reflective of an unreasonable application of such law, the petition was properly denied.

The judgment of the District Court is AFFIRMED.