WALKER, Circuit Judge:

Petitioner-appellant Pedro Nieblas appeals from the October 22, 1998 judgment of the district court denying his petition for a writ of habeas corpus. The petition, filed pursuant to 28 U.S.C. § 2241(c)(3) and former 28 U.S.C. § 2254, alleged, inter alia, that Nieblas had been denied his Sixth Amendment right to a public trial when the courtroom was closed for the testimony of one witness, an undercover officer, during his drug trial in state court. On appeal, Nieblas contends that the district court erred in hearing additional evidence on the propriety of the courtroom closure and, largely on the basis of this evidence, denying the petition. We find these arguments unavailing and thus affirm.

BACKGROUND

On May 12, 1992, during Nieblas’s state-court trial on drug charges, the prosecution asked the court to close the courtroom for the testimony of the undercover officer who had purchased drugs from Nieblas. Defense counsel objected and a brief hearing was held. At the hearing, the officer testified that he continued to do undercover work with Brooklyn South Narcotics, that his identity was unknown to the public for “[sjafety reasons,” and that the courtroom had always been sealed when he testified in other cases. The judge agreed to seal the courtroom “in the interest of the safety of this police officer.” Defense counsel registered no further objection to the closure. Ultimately, Nieblas was convicted of criminal sale and possession of a controlled substance and sentenced to concurrent prison terms of nine to eighteen years for the two major counts.

Nieblas subsequently appealed his conviction through the state court system. He argued, among other things, that his Sixth Amendment right to a public trial had been denied on account of the courtroom closure. The Appellate Division of the New York Supreme Court found this claim unpreserved for appeal because defense counsel did not object to the closure following the hearing. See People v. Nieblas, 213 A.D.2d 498, 624 N.Y.S.2d 900, 900 (2d Dep’t 1995). With a minor exception, the court then affirmed his conviction and sentence. See id. at 901. Nieblas’s application to the New York Court of Appeals for leave to appeal was denied.

On August 12, 1995, Nieblas filed a petition for a writ of habeas corpus in federal district court and included the Sixth Amendment claim among the grounds for relief. The district court requested supplemental memoranda from the parties after concluding that the state had failed to present facts sufficient under Second Circuit law to justify the courtroom closure. He ordered the state to submit an affidavit from the undercover officer to address “the principal deficiencies in the justification of the courtroom closure in the record”:

Specifically, the affidavit should identify the location of the ... drug sale by neighborhood and state whether — at the time the undercover officer testified — he was still doing undercover work in the neighborhood where the defendant’s drug use took place.

On May 28, 1998, the state submitted an affidavit from the officer, Detective Joseph Ramirez. On October 16, 1998, the court gave Nieblas’s counsel the opportunity to cross-examine the detective on his affidavit. The affidavit and testimony established that (1) the operation involving Nieblas occurred in Boro Park in the 66th precinct, and (2) at the time of Nieblas’s trial, Ramirez had been transferred to the *31 adjacent 72nd precinct, but could have been assigned to further undercover work in the vicinity of his transaction with Nieb-las.

On October 22, 1998, the district judge denied the habeas petition. He “assume[d] ... that the general objection voiced by counsel was sufficient to preserve the record and that the issue has not been procedurally forfeited.” He explained that he decided to exercise his discretion to hear additional evidence because

it was my view that if ... a further evidentiary hearing developed a record that was sufficient to justify the courtroom closure, then the defendant’s right to a public trial was not violated by the partial closure merely because the factual finding made by the trial judge was not properly supported by the record.

According to the district judge, at least where the issue does not pertain to the guilt or innocence of the defendant, a federal habeas court should not reverse a conviction for denial of the right to a public trial without affording the state “the opportunity of showing that [it] has sufficient evidence to meet a specific objection to closure that ... was not raised at the time that the closure application was made.” Based in large part on evidence gathered from the detective’s affidavit and testimony before the district court, the judge determined that the partial courtroom closure was justified and thus denied the petition. This appeal followed.

DISCUSSION

We review a district court’s decision to grant or deny a writ of habeas corpus de novo. See Reyes v. Keane, 118 F.3d 136, 138 (2d Cir.1997). Here, we are primarily concerned with whether the district judge erred in holding a hearing on the propriety of courtroom closure and subsequently, on the basis of evidence adduced at this hearing, denying Nieblas’s petition. As a preliminary matter, the state urges us not even to reach the merits of this Sixth Amendment claim because it was neither exhausted in state court nor preserved for appellate or collateral review. Because we ultimately find that the courtroom closure was proper, however, we need not consider these procedural arguments. See, e.g., Brown v. Kuhlmann, 142 F.3d 529, 534 (2d Cir.1998).

Nieblas contends that the district court abused its discretion by affording the state a second chance to make the showing necessary to justify the courtroom closure and then denying the petition based on the evidence the state presented. According to Nieblas, since the state had ample opportunity to justify the closure at trial and failed to meet the strict standards articulated by the Supreme Court, see Waller v. Georgia, 467 U.S. 39, 48, 104 S.Ct. 2210, 81 L.Ed.2d 31 (1984), and this court, see Ayala v. Speckard, 131 F.3d 62, 70 (2d Cir.1997) (en banc), cert. denied, 524 U.S. 958, 118 S.Ct. 2380, 141 L.Ed.2d 747 (1998), and since the state would not have been given a second chance under state-court rules, see People v. Havelka, 45 N.Y.2d 636, 643-44, 412 N.Y.S.2d 345, 384 N.E.2d 1269 (1978), it was error for a federal court to allow the state to present additional evidence on collateral review. We disagree.

A district court has broad discretion to hear further evidence in habeas cases. See Townsend v. Sain, 372 U.S. 293, 318, 83 S.Ct. 745, 9 L.Ed.2d 770 (1963) (“In every case [the district judge] has the power, constrained only by his sound discretion, to receive evidence bearing upon the applicant’s constitutional claim.”); Jones v. Vacco, 126 F.3d 408, 417 n. 2 (2d Cir.1997) (“In habeas cases, the district court is not limited to the state court record, and has discretion to conduct an evidentiary hearing.”). In recent years, the Supreme Court and Congress have severely limited the situations in which a habeas court is required or even permitted to hold an evidentiary hearing to consider factual claims by a habeas petitioner. See *32 Keeney v. Tamayo-Reyes, 504 U.S. 1, 5-6, 112 S.Ct. 1715, 118 L.Ed.2d 318 (1992) (requiring a hearing only when the petitioner can establish cause for his failure to develop an adequate factual record below and prejudice resulting from that failure); 28 U.S.C. § 2254(e)(2) (prohibiting a district court from holding an evidentiary hearing where the habeas applicant “failed to develop the factual basis of a claim in State court proceedings” unless the applicant meets several stringent requirements). However, where the district court chooses to hear additional evidence on behalf of the state—or a petitioner who meets the requirements of 28 U.S.C. § 2254(e)(2)—its discretion remains broad. See McDonald v. Johnson, 139 F.3d 1056, 1060 (5th Cir.1998) (noting that a petitioner who meets the requirements of § 2254(e)(2) may be entitled to an eviden-tiary hearing at the district court’s discretion); Pagan v. Keane, 984 F.2d 61, 64 (2d Cir.1993) (noting, that Keeney did not deprive district courts of their “power to hold a hearing even though one was not required”).

We find the district court’s decision to gather additional evidence here to be a reasonable exercise of its discretion under the circumstances. First, a district court should readily hold a hearing where the defendant may have sandbagged the state or otherwise engaged in strategic manipulation during the state-court proceeding. See Kuhlmann, 142 F.3d at 543; see also Brown v. Andrews, 180 F.3d 403, 409 n. 4 (2d Cir.1999). In this case, for example, defense counsel objected in a perfunctory way to the prosecution’s request to close the courtroom, thereby increasing the likelihood that the court would close the proceedings erroneously without a fully developed justification on the record. The result was the creation of an appealable issue at virtually no cost to the defendant. See Kuhlmann, 142 F.3d at 542. Under these circumstances, the defendant himself shares the responsibility for the error because the record at trial might have been more fully developed had the defendant raised more specific objections to the closure and the state’s proffered justifications.

Second, a district court is particularly justified in conducting an ex post hearing where the state’s failure to present adequate evidence below is excusable—for example, due to a change in the governing law. In this case, the state trial court’s hearing on closure was held in 1992, prior to significant clarifications in the law by both the New York Court of Appeals, see People v. Martinez, 82 N.Y.2d 436, 443, 604 N.Y.S.2d 932, 624 N.E.2d 1027 (1993), and this court, see Ayala, 131 F.3d at 72; Kuhlmann, 142 F.3d at 537, which required more particularized showings of geographical proximity between the area where the undercover officer was continuing his work and the place where defendant was arrested or where trial audience members might reside. In applying these decisions retroactively, it was entirely reasonable for the district court to allow the state to supplement its evidence in support of closure.

Third, where either of the above two reasons or any other similar reason exists, it is particularly appropriate for a habeas court to gather additional evidence—rather than granting the defendant the “windfall” of a new trial—where the alleged constitutional violation does not affect the fairness of the outcome at trial, as in courtroom closure cases like this one. Waller, 467 U.S. at 50, 104 S.Ct. 2210. The improper exclusion of the public from the courtroom during the testimony of a single witness, even a witness crucial to the case against the defendant, generally does not “ ‘risk[ ] an unreliable trial outcome and the consequent conviction of an innocent person.’ ” Kuhlmann, 142 F.3d at 539 (quoting O’Neal v. McAninch, 513 U.S. 432, 442, 115 S.Ct. 992, 130 L.Ed.2d 947 (1995)).

We reject petitioner’s contention that the district court is or should be pro *33 hibited from holding a hearing if a state court would not do so on direct review. “The whole history of the writ ... refutes a construction of the federal courts’ habeas corpus powers that would assimilate their task to that of courts of appellate review.” Townsend, 372 U.S. at 311, 83 S.Ct. 745.

Having concluded that the district court’s decision to hear further evidence was a proper exercise of its discretion under the circumstances, we turn to whether the courtroom closure in this case violated Nieblas’s Sixth Amendment rights. In this regard, we find no constitutional error; the additional evidence produced by the state plainly satisfies the constitutional requirements for courtroom closure. The Supreme Court has articulated a four-factor test for evaluating the propriety of courtroom closure. See Waller, 467 U.S. at 48, 104 S.Ct. 2210. The only factor in serious dispute here is the first one: “[T]he party seeking to close the hearing must advance an overriding interest that is likely to be prejudiced.” Id. We have interpreted this requirement to mean that a trial should be closed to the public only based on “persuasive evidence of serious risk to an important interest,” Ayala, 131 F.3d at 70, including the need to protect an undercover officer’s anonymity and safety, see Brown, 180 F.3d at 406 (citing Kuhlmann, 142 F.3d at 537). In Ayala, we found closure warranted where an undercover officer specifically identified the area where the defendant was arrested and testified that the officer would soon be returning to that very area as part of his work. See Ayala, 131 F.3d at 72.

Similarly, the affidavit and testimony received by the district court in this case established that (1) the operation involving Nieblas occurred in the Boro Park neighborhood of Brooklyn, and (2) although at the time of Nieblas’s trial the officer had been transferred to an adjacent precinct, he still could have been assigned to further undercover work in the vicinity where Nieblas trafficked in drugs. This evidence is sufficient to justify the closure.

CONCLUSION

For the foregoing reasons, we find no fault with the district court’s decisions (1) to hear additional evidence on the propriety of courtroom closure and (2) to deny the petition for a writ of habeas corpus. The judgment of the district court is affirmed.