On July 7, 1989, the Supreme Court of the State of New York, New York County (Altman, /.), entered judgment convicting petitioner Thomas Beatty of Attempted Murder in the Second Degree, N.Y. Penal L. §§ 110.00, 125.25[1], Assault in the *495First Degree, id. at § 120.10[1], and Criminal Possession of a Weapon in the Second Degree, id. at § 265.03. Beatty was sentenced to a ten-to-twenty year term of imprisonment and to two seven-and-a-half-to-fifteen year terms, all three to run concurrently. Beatty has since been released on parole.

The State’s proof at trial established that, on August 16, 1988, Beatty purchased marijuana from Elvin Elliot. Apparently disappointed with these drugs, Beatty returned shortly thereafter to demand a refund. When Elliot refused, an argument ensued, Beatty drew a gun, and fired a gunshot at Elliot. Although Beatty’s gunshot missed his intended target, bullet fragments hit Elliott’s friend, DeShawn Flournoy, in the eye and arm, as she sat on an adjacent car. The prosecution’s trial evidence consisted predominantly of Flournoy and Elliot’s eyewitness testimony.

Beatty has pursued a multitude of state court avenues to challenge his conviction. On direct appeal, the New York Appellate Division, First Department, affirmed Beatty’s conviction in its entirety by an order entered on May 30, 1991. People v. Beatty, 173 A.D.2d 403, 570 N.Y.S.2d 39 (1st Dep’t 1991). On October 21, 1991, the New York Court of Appeals denied Beatty’s motion for leave to appeal. People v. Beatty, 78 N.Y.2d 1073, 577 N.Y.S.2d 236, 583 N.E.2d 948 (1991) (Table).

In February 1992, Beatty moved to vacate his conviction pursuant to New York Criminal Procedure Law (“CPL”) § 440.10[l][g], on the ground of newly discovered evidence. The motion was denied in a decision dated July 17,1992, and leave to appeal was denied on October 8, 1992.

Beatty next moved, pursuant to CPL § 160.50, to unseal the records in criminal proceedings involving Elliot and Flournoy, and, pursuant to CPL § 610.20[3], to subpoena the District Attorney’s records in these cases. At trial, Elliot admitted to a February 1989 arrest for robbery, forcible theft, unlawful imprisonment, and criminal possession of a weapon. The prosecutor stated at Beatty’s trial that Elliot was not receiving any consideration in return for his testimony, which Elliot substantiated during cross-examination. At some point after Beatty was convicted, the case against Elliot was dropped. In addition, Flournoy had been charged in a drug prosecution, but that case was dismissed and sealed about three months before Beatty’s trial. Beatty’s motions speculated that the timing of these two favorable dismissals indicated that the prosecution misrepresented the absence of promised favorable treatment to Elliot and Flournoy in exchange for testifying. In a decision dated December 1, 1993, these motions were denied because the circumstances necessary for unsealing a record of criminal proceedings, as enumerated in CPL § 160.50[l][d], were not satisfied. On March 3, 1994, the New York Appellate Division, First Department, denied Beatty’s application for leave to appeal this order.

In September 1995, Beatty brought another CPL § 440.10 motion to vacate his conviction. This motion was denied on July 2; 1996, and leave to appeal was denied on October 24,1996. In August 1996, Beatty filed a writ of error coram nobis in the Appellate Division, which was denied by order dated April 2,1998.

On March 25,1998, Beatty petitioned for federal habeas relief on multiple grounds, including the allegedly improper denial of his motion to unseal records of Elliot and Flournoy’s criminal proceedings. On July 9, 1998, Beatty’s petition was transferred to then-Magistrate Judge Naomi Reice Buchwald. On August 16, 1998, while this federal petition was pending, Beatty moved for discovery seeking various documents pertaining to his state court trial and Elliot and Flournoy’s criminal pro*496eeedings. By order entered September 30, 1998, Judge Buchwald denied Beatty’s discovery application. In a report and recommendation dated September 1, 1999, Judge Buchwald recommended denial of each of Beatty’s challenges to his conviction. By order entered December 20, 1999, the District Court adopted these recommendations in their entirety.

On December 29, 2000, this Court granted a certificate of appealability on two issues: 1) whether Beatty has presented a cognizable claim under the Due Process Clause of the Fourteenth Amendment, the Confrontation Clause of the Sixth Amendment, or Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and, if so, whether this claim was properly exhausted in state court; and 2) whether the district court erred either in refusing to grant petitioner’s request for discovery pursuant to Rule 6 of the Rules Governing § 2254 Proceedings or in refusing to grant an evidentiary hearing on this matter.

We review a district court’s denial of a petition for a writ of habeas corpus de novo. Pavel v. Hollins, 261 F.3d 210, 215 (2d Cir. 2001); Fama v. Comm’r of Corr. Servs., 235 F.3d 804, 808 (2d Cir. 2000).

A state prisoner is eligible for federal habeas relief only upon exhausting state court remedies, unless there is an absence of an available state corrective process or circumstances are such that the state court process would be ineffective to protect the prisoner’s rights. 28 U.S.C. § 2254(b)(1). A petitioner exhausts state remedies by “(i) presenting] the federal constitutional claim asserted in the petition to the highest state court (after preserving it as required by state law in lower courts); and (ii) informing] that court (and lower courts) about both the factual and legal bases for the federal claim.” Ramirez v. Attorney Gen., 280 F.3d 87, 94 (2d Cir. 2001). As we explained in Daye v. Attorney General, 696 F.2d 186, 192 (2d Cir. 1982) (en banc), the exhaustion requirement entails “that in state court the nature or presentation of the claim must have been likely to alert the court of the claim’s federal nature.” Accord Cox v. Miller, 296 F.3d 89, 99 (2d Cir. 2002).

Although Beatty moved to unseal the records in state court, he never moved to vacate his conviction on the ground that the state denied him access to those records. Rather, Beatty’s only mention of this claim came in efforts to unseal the records in the criminal proceedings pertaining to Elliot and Flournoy, which was not a challenge to the validity of his conviction under federal law but a motion based on state rules. See Hodge v. Greiner, 269 F.3d 104, 107 (2d Cir. 2001) (holding that a state court proceeding seeking material for purposes of a CPL § 440.10 motion did not toll the federal habeas statute because the “proceeding did not challenge [the petitioner’s] conviction”). If Beatty prevailed on these motions, the remedy would not have been vacatur of his conviction. Therefore, even if the refusal to unseal these records could provide Beatty with a valid basis for federal habeas relief, Beatty never alerted a New York state court to this claim’s federal nature. See Daye, 696 F.2d at 192.

Because Beatty has failed to exhaust his claim in state court, the District Court did not abuse its discretion in denying him discovery or an evidentiary hearing. “A habeas petitioner, unlike the usual civil litigant in federal court, is not entitled to discovery as a matter of ordinary course.” Bracy v. Gramley, 520 U.S. 899, 904, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997). Rather, discovery is only allowed if the district court, acting in its discretion, finds “good cause” to allow it. Rule 6(a) of the Rules Governing Section 2254 Cases; see Bracy, 520 U.S. at 904. This “good cause” standard is satisfied “ ‘where specific allegations before the court show reason to be*497lieve that the petitioner may, if the facts are fully developed, be able to demonstrate that he is ... entitled to relief.’ ” Bracy, 520 U.S. at 908-09 (quoting Hams v. Nelson, 394 U.S. 286, 299, 89 S.Ct. 1082, 22 L.Ed.2d 281 (1969)); accord Wallace v. Ward, 191 F.3d 1235, 1245 (10th Cir. 1999); Quesinberry v. Taylor, 162 F.3d 273, 279 (4th Cir. 1998).

We review a district court’s denial of a habeas petitioner’s request for discovery for abuse of discretion. Bracy, 520 U.S. at 909; see Romano v. Gibson, 278 F.3d 1145, 1150 (10th Cir. 2002). A district court’s refusal to hold an evidentiary hearing for a state prisoner is also reviewed for abuse of discretion, Maggio v. Williams, 464 U.S. 46, 50, 104 S.Ct. 311, 78 L.Ed.2d 43 (1983), and the court enjoys “broad discretion to hear further evidence in habeas cases,” Nieblas v. Smith, 204 F.3d 29, 31 (2d Cir. 1999).

Because Beatty has failed to exhaust his claim in state court, he lacked a valid basis for federal habeas relief when he moved for discovery and an evidentiary hearing. Accordingly, the District Court did not abuse its discretion in denying discovery or an evidentiary hearing because, regardless of the fruits of those procedures, Beatty would not be entitled to relief. See Clark v. Johnson, 202 F.3d 760, 766 (5th Cir. 2000) (“In evaluating whether the District Court abused its discretion in denying [the petitioner] discovery and an evidentiary hearing, we next consider whether there is a factual dispute which, if resolved in [the petitioner’s] favor, would entitle him to relief.”).

We have reviewed all of the petitioner’s other arguments and find them to be without merit. We affirm the judgment of the district court.