POOLER, Circuit Judge, filed an opinion concurring in the judgment.
JOSÉ A. CABRANES, Circuit Judge:Salih Sevencan appeals from an Opinion and Order of the District Court for the Eastern District of New York (Allyne R. Ross, Judge) entered on August 3, 2001, denying his petition for a writ of habeas corpus. The District Court granted a Certificate of Appealability on the issue of whether the trial court’s refusal to except Sevencan’s wife from a limited courtroom closure order violated Sevencan’s Sixth Amendment rights.
We hold that (1) the requirement set forth in Yung v. Walker, 296 F.3d 129, 136 (2d Cir.2002), that a “heightened showing” be made before a state trial court excludes a family member from a criminal trial as part of a limited closure order is satisfied where the record reflects that the state trial court considered the familial relationship at the time the family member was excluded; (2) where the record reflects that the state trial court was aware of the familial relationship, it necessarily includes an implicit or explicit finding that the court considered the familial relationship and found that the reasons justifying the Waller closure order extend to excluded family members; and (3) because the state trial court in the instant ease clearly considered the familial relationship in determining whether to exempt Sevencan’s wife from a properly entered limited closure order, its decision to exclude Sevencan’s wife was not “an unreasonable application of[ ] clearly established Federal law, as determined by the Supreme Court of the United States,” within the meaning of 28 U.S.C. § 2254(d).
I. Background
We assume familiarity with the background facts of this case as set forth in the District Court’s opinion, Sevencan v. Herbert, 152 F.Supp.2d 252 (E.D.N.Y.2001). *79We briefly set forth here only those facts necessary to our disposition.
Between June 3 and September 23, 1993, Sevencan and four co-defendants were tried in the Supreme Court for Kings County, New York, on various charges stemming from their participation in a conspiracy to import heroin from Turkey and sell it in the United States. Among the crimes that the defendants were charged with were weapons possession and conspiracy to commit murder.
The chief witness against Sevencan was an undercover police officer. Before the officer testified, the prosecution moved to seal the courtroom during the officer’s testimony. Defense counsel for Sevencan objected. The trial court held a hearing, after which it granted the motion to seal the courtroom during the officer’s testimony. In so ruling, the trial judge noted the importance of an open courtroom, but found the need to protect the identity of the undercover officer for his safety compelling, in light of the officer’s continuing undercover work. The judge made an exception for attorneys and law student interns working with defense counsel, stating:
a lawyer is a lawyer, and we’[re] sorry about spectators, family, I mean, another matter, something that [the prosecutor] can’t exclude from the courtroom is the two defendants on bail, they’re going to walk out, I mean, the family' — there’s always a certain amount of risk in everything we do and we try to do it.
152 F.Supp.2d at 255 (alterations in original).
Twenty days later, Sevencan’s wife attempted to attend the trial. Defense counsel sought an exception to the sealing order at sidebar, which the Court denied as follows:
[Defense Counsel]: Judge, the defendant’s wife is here and works all the time. This is practically the only day she can get here and would like to come in. I understand-
The Court: The courtroom is sealed.
[Defense Counsel]: Yes, it is. That’s why I’m applying to you [so that] it be allowed-
The Court: The reason.we seal it is to protect the undercover. I don’t think she falls within the exceptions I’ve created. What’s the district attorney’s position?
[The Prosecutor]: I would object.
The Court: Your application is denied.
Id. at 255-56.
After Sevencan was convicted, he argued on appeal, inter alia, that closures of the courtroom, including the exclusion of his wife, deprived him of this Sixth Amendment rights. The Appellate Division of the Supreme Court rejected his arguments as follows:
The defendant contends that he was denied his right to a public trial when the trial court closed the courtroom during the testimony of two undercover police officers. However, his present claim was waived by his failure to object to the closures at trial, and, in any event, is without merit.
People v. Sevencan, 258 A.D.2d 485, 685 N.Y.S.2d 735, 736 (2d Dep’t 1999) (citing People v. Akaydin, 258 A.D.2d 466, 685 N.Y.S.2d 737 (2d Dep’t 1999) (companion case)). Notably, although the Appellate Division appeared to hold that Sevencan had not objected to the closures at trial, it did not similarly hold that his co-defendant, Akaydin, had also waived his objection to those closures. See Akaydin, 685 N.Y.S.2d at 738. Yet it appears from the record that counsel for Sevencan objected more vocally than counsel for Akaydin. *80Sevencan, 152 F.Supp.2d at 260. See generally N.Y.Crim. Proc. Law § 470.05(2).1 The New York State Court of Appeals denied leave to appeal further. See People v. Sevencan, 93 N.Y.2d 1027, 697 N.Y.S.2d 586, 719 N.E.2d 947 (1999).
Sevencan subsequently timely filed the instant petition in the United States District Court for the Eastern District of New York. He sought relief on various grounds, including the closures of the courtroom and exclusion of his wife. The proceedings subsequently focused on the exclusion of Sevencan’s wife.
Inasmuch as the state trial court had made no findings specific to Sevencan’s wife, the District Court held a hearing pursuant to Nieblas v. Smith, 204 F.3d 29 (2d Cir.1999) (holding that district courts have the discretion to conduct evidentiary hearings to determine whether a courtroom closure was justified where the record of proceedings before the trial court was not sufficient to determine whether the closure was proper). See 152 F.Supp.2d at 263-64. Based upon the evidence adduced at the hearing, the District Court held that the closure with respect to Sevencan’s wife was justified. Id. at 264-68. It then rejected Sevencan’s remaining claims, and denied the petition. Id. at 269-70. The District Court granted a Certificate of Appealability limited to the issue of whether the exclusion of Seven-can’s wife deprived him of his Sixth Amendment rights. See id. at 270.
On appeal, Sevencan argues that (1) hearings pursuant to Nieblas v. Smith are not appropriate in cases governed by the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”), Pub.L. No. 104-132, 110 Stat. 1214, and that, accordingly, the writ should have been granted based on the lack of findings by the state trial court; and (2) even if the evidence adduced at the Nieblas hearing in the District Court was properly considered, that Court erred in holding that the evidence and record here were sufficient to support the decision to exclude Sevencan’s wife from the courtroom.
The State opposes Sevencan’s claims, and also argues that, as a preliminary matter, the District Court erred in holding that the Appellate Division’s holding that Sevencan “waived” his closure claims was not an independent and adequate state-law ground for the denial of Sevencan’s claim. See generally Coleman v. Thompson, 501 U.S. 722, 749-50, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991); Fama v. Comm’r of Corr. Servs., 235 F.3d 804, 809 (2d Cir.2000) (“Federal courts may not review state court decisions that rest on an adequate and independent state procedural default unless petitioner can show both cause and prejudice or a fundamental miscarriage of justice.”).
We do not reach the issues of the propriety of the Nieblas hearing and the alleged independent and adequate state-law ground for the denial of Sevencan’s claim because we conclude that the petition should be denied on the basis of the record of the state trial court proceedings. Cf. *81Nieblas, 204 F.3d at 31 (“Because we ultimately find that the courtroom closure was proper, however, we need not consider these procedural arguments.”); Brown v. Kuhlmann, 142 F.3d 529, 534 (2d Cir.1998) (similar).
We hold that (1) the requirement we set forth in Yung v. Walker, 296 F.3d 129, 136 (2d Cir.2002), that a “heightened showing” be made before a state trial court excludes a family member from a criminal trial as part of a limited closure order is satisfied where the record reflects that the state trial court was aware of the familial relationship; and (2) because the state trial court in this case clearly considered the familial relationship in considering whether to exempt Sevenean’s wife from a properly entered limited closure order, the state trial court’s decision to exclude Sev-encan’s wife was not “an unreasonable application of[ ] clearly established Federal law, as determined by the Supreme Court of the United States,” within the meaning of 28 U.S.C. § 2254(d).
Accordingly, we affirm the judgment of the District Court.
II. DISCUSSION
The habeas statute, as amended by AEDPA, provides, in relevant part:
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. § 2254(d). In Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), the Supreme Court authoritatively interpreted the phrase “clearly established Federal law, as determined by the Supreme Court of the'United States” to mean “the holdings, as opposed to the dicta, of [the Supreme Court’s] decisions as of the time of the relevant state-court decision.” 529 U.S. at 412, 120 S.Ct. 1495. “[A]s the statutory language makes clear, ... 2254(d)(1) restricts the source of clearly established law to [the Supreme Court’s] jurisprudence.” Id.
In Waller v. Georgia, 467 U.S. 39, 104 S.Ct. 2210, 81 L.Ed.2d 31 (1984), the Supreme Court held that, before public access to a courtroom in a criminal case may be restricted, “[1] the party seeking to close the hearing must advance an overriding interest that is likely to be prejudiced, [2] the closure must be no broader than necessary to protect that interest, [3] the trial court must consider reasonable alternatives to closing the proceeding, and [4] [the court] must make findings adequate to support the closure.” Id. at 48, 104 S.Ct. 2210. The violation of the constitutional right to a public trial is a “structural error”2 warranting remediation regardless of prejudice. See Id. at 50 & n. 9, 104 S.Ct. 2210.
In Vidal v. Williams, 31 F.3d 67 (2d Cir.1994), we reversed a District Court’s denial of a habeas petition on the ground that the closure of a courtroom to a defendant’s parents was improper. In that case, the defendant’s parents were in the courtroom at the time the prosecutor sought closure, and defense counsel re*82quested that they be allowed to remain. Id. at 68. The state trial court had rejected that request based on the fact that the parents lived within three miles of the area in which the officer .conducted undercover operations, and closed the courtroom. Id. We held that the proximity of the parents’ residence to the officer’s area of operation was insufficient to justify their exclusion, relying in part on the Supreme Court’s “specific[ ] notation of] a special concern for assuring the attendance of family members of the accused” in In re Oliver, 333 U.S. 257, 271-72 & n. 29, 68 S.Ct. 499, 92 L.Ed. 682 (1948). Vidal, 31 F.3d at 69.
Since Vidal, we have often noted in pre-AEDPA or pre-Williams v. Taylor cases that particular attention must be paid to the exclusion of family members. See English v. Artuz, 164 F.3d 105, 108 (2d Cir.1998) (granting a habeas petition in a pre-AEDPA case where the prosecutor sought closure of the courtroom, the defendant asked that his family be allowed to remain, and the state trial court denied the defendant’s request and closed the courtroom); Guzman v. Scully, 80 F.3d 772, 775-76 (2d Cir.1996) (similar, citing Oliver); see also Bowden v. Keane, 237 F.3d 125, 130 n. 1 (2d Cir.2001) (dicta, “Special concerns may apply when the spectators selectively barred from the courtroom are the defendant’s family members.” (citing Vidal)); Brown, 142 F.3d at 538 (similar, citing Vidal and Oliver); Ayala v. Speckard, 131 F.3d 62, 72 (2d Cir.1997) (in banc) (similar, citing Vidal and Guzman).
In Yung v. Walker, 296 F.3d 129, 136 (2d Cir.2002) — the first and only decision of our Court on the exclusion of family members applying the AEDPA standard (as informed by Williams v. Taylor) — -we recently held that the showing articulated in Vidal was not required by “clearly established” Supreme Court law. Because the District Court had relied on Vidal, we vacated the judgment and remanded for application of “the more general teachings of Waller and In re Oliver." Id.
In the case now before us, the District Court likewise followed Vidal and analyzed the issue as if “clearly established” law includes our (Second Circuit) pre-AEDPA jurisprudence regarding the consideration due to family members in such circumstances. See Sevencan, 152 F.Supp.2d at 262-63. This was error. As we recognized in Yung, no Supreme Court decision has ever expressly held that family members must be given special consideration by trial courts deciding whether to close a courtroom, and Vidal is not “clearly established” law within the meaning of 28 U.S.C. § 2254(d)(1) and Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389. See Yung, 296 F.3d at 136. Accordingly, Yung requires that we consider Sevencan’s claim in light of “the more general teachings of Waller and In re Oliver.” See id.3
*83Oliver, which we (properly) cited in Vidal, 31 F.3d at 69, in support of our holding there that the exclusion of family members requires a heightened showing, involved a trial in total secrecy by a state judge who, pursuant to Michigan law, simultaneously acted as grand jury and trial court. See Oliver, 333 U.S. at 261-66, 68 S.Ct. 499. In using the language on which we later relied in Vidal, the Supreme Court in Oliver was making the point that no court had ever permitted a totally secret trial; at the very least family and friends were permitted to attend. Id. at 271-72 & n. 29, 68 S.Ct. 499. The holding of the Supreme Court in Oliver did not rest on the failure to admit a family member. Rather, the Court held that a trial in total secrecy, in the highly unusual circumstances presented there, was unconstitutional. Id. at 272-73, 68 S.Ct. 499.
The only “clearly established” law within the meaning of 28 U.S.C. § 2254(d)(1) relevant to this case, then, is Waller’s four-factor test for closures generally. See Williams v. Taylor, 529 U.S. at 412, 120 S.Ct. 1495 (holding that “clearly established Federal law, as determined by the Supreme Court of the United States” means “the holdings, as opposed to the dicta, of [the Supreme Court’s] decisions as of the time of the relevant state-court decision” (emphasis added)).
Accordingly, Sevencan is. entitled to relief only if he can demonstrate that the state court’s decision “resulted in. a decision that was contrary to, or involved an unreasonable application of,” Waller. See 28 U.S.C. § 2254(d)(1).
A state court’s decision is “contrary to” clearly established law, within the meaning of § 2254(d)(1), if “the state court applies a rule that contradicts” governing Supreme Court law, or if it “confronts a set of facts that are materially indistinguishable from a decision of [the Supreme] Court and nevertheless arrives at a result different from [Supreme Court] precedent.” Williams, 529 U.S. at 405, 406, 120 S.Ct. 1495. Ordinarily, a “run-of-the-mill state-court decision applying the correct legal rule from our cases to the facts of a prisoner’s case would not fit comfortably within § 2254(d)(1)’s ‘contrary to’ clause,” even if a federal court believes that the state-court reached the wrong result. Id. at 406, 120 S.Ct. 1495. This is just such a “run-of-the-mill” case — indeed, petitioner does not contend that the result is “contrary to” federal law, but, rather, that the state appellate court “failfed] to [properly] apply” federal law. See Pet’r’s Br. at 29. This claim is properly analyzed pursuant to the “unreasonable application” clause of 28 U.S.C. § 2254(d). See Williams v. Taylor, 529 U.S. at 407, 120 S.Ct. 1495.
*84A decision is an “unreasonable application” of clearly established Supreme Court law if a. state court “identifies the correct governing legal principle from [the Supreme Court’s] decisions but unreasonably applies that principle to the facts of [a] prisoner’s case.” Id. at 413, 120 S.Ct. 1495. Under this standard, “a federal habeas court may not issue the writ simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly. Rather, that application must also be unreasonable.” Id. at 411, 120 S.Ct. 1495. In order to grant the writ there must be “[s]ome increment of incorrectness beyond error,” although “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.” Francis S. v. Stone, 221 F.3d 100, 111 (2d Cir.2000) (internal quotation marks omitted).
In this case, the trial court’s initial decision to close the courtroom clearly comported with Waller: [1] the prosecutor advanced an “overriding interest” that was “likely to be prejudiced” by a public hearing — the safety of the undercover officer; [2] the closure was “no broader than necessary to protect that interest,” as it was solely for the officer’s testimony; [3] the trial court considered reasonable alternatives proposed by the defense — the admission of other lawyers and legal interns— and [4] the trial court made “findings adequate to support the closure,” in that it found that the undercover officer would indeed be in danger if he was publicly identified. See Waller, 467 U.S. at 48, 104 S.Ct. 2210. Accordingly, Sevencan is entitled to relief only if the trial court’s refusal to make an exception to its general closure order for his wife was an “unreasonable” application of Waller.
In discussing Waller, the Yung panel noted that “it would be an unreasonable interpretation of Waller or, at a minimum, an unreasonable failure to extend Waller, not to require a heightened showing before excluding family members,” 296 F.3d at 136.4 Yet, because the Yung panel remanded to the District Court for reconsideration of the issue, it never had the opportunity in Yung to articulate exactly what the “heightened showing” standard requires a defendant to show. Rather, the opinion in Yung indicated that the “heightened showing” could be satisfied in cir*85cumstances where there was no likelihood that the family members would encounter an undercover officer in the future, and, accordingly, remanded the cause to the District Court “for a reassessment of the reasonableness of the state court’s adjudication in light only of the relevant Supreme Court precedent.” Id. at 136 & n. 1.
In this case, unlike in Yung, the District Court denied the writ, although it employed the wrong legal standard. Accordingly, we will apply Yung’s “heightened showing” standard to determine whether we can affirm the District Court’s judgment on a ground upon which it did not rely. Cf. Shumway v. United Parcel Serv., Inc., 118 F.3d 60, 63 (2d Cir.1997).
In determining the “heightened showing” required by Yung, we begin with an examination of Waller, the primary “relevant Supreme Court precedent.” See Yung, 296 F.3d at 136. The four prongs of Waller are principally animated by two concerns. The first and second prongs — the requirement that the party seeking closure “advance an overriding interest” and that the closure be “no broader than necessary,” Waller, 467 U.S. at 48, 104 S.Ct. 2210 — together operate to insure that a defendant’s right to a public trial is curtailed only to the extent necessary to protect an overriding interest. Accordingly, the “no broader than necessary” requirement is typically satisfied where the overriding interest is the safety of a witness and the courtroom is closed only during that witness’s testimony. See, e.g., Brown v. Artuz, 283 F.3d 492, 501 (2d Cir.2002).
The third and fourth prongs of Waller — the requirements that the trial court “consider reasonable alternatives to closing the proceeding, and ... make findings adequate to support the closure,” 467 U.S. at 48, 104 S.Ct. 2210 (emphasis added) — are procedural instructions designed in part to insure that a record exists upon which the closure order can be reviewed. Accordingly, Waller’s third prong is satisfied where the record establishes that the trial court explicitly considered alternatives to complete closure, see Ayala, 131 F.3d at 70-71, and the fourth prong is satisfied where a reviewing court “can glean competent evidence from the record that justifies closure,” Bowden v. Keane, 237 F.3d 125, 133 (2d Cir.2001).
We next consider the observation in Oliver that “without exception all courts [in the United States] have held that an accused is at the very least entitled to have his friends, relatives and counsel present, no matter with what offense he may be charged.” 333 U.S. at 271-72, 68 S.Ct. 499. Although in Vidal we held that this statement evinced “a special concern for assuring the attendance of family members of the accused,” 31 F.3d at 69, it would not be an “unreasonable application” of Oliver, see 28 U.S.C. § 2254(d)(1), to regard that statement as merely noting that, in some situations, the reasons justifying the closure of a courtroom to the general public would not necessarily justify the exclusion of “friends, relatives and counsel.” Oliver, 333 U.S. at 272, 68 S.Ct. 499.
The panel in Yung held that “[although the portion of In re Oliver that specifically refers to family members is dicta, we believe that Waller’s second mandate — that the closure be no broader than required to protect the overriding interest at stake — envisions an examination not just of the length of the closure but also of the portion of the public excluded.” 296 F.3d at 136. For this reason, the Yung panel held that it would be an unreasonable application of Waller not to require a “heightened showing” before excluding family members. Id. To the extent we are now required to define this “heightened *86showing,” we hold that a state trial court’s decision to exclude a family member from a criminal trial as part of a properly-entered limited closure order will not be an “unreasonable interpretation” of Supreme Court law so long as the trial court (1) reasonably applies the general requirements of Waller and (2) is made aware of the familial relationship before conducting its Waller analysis. No further showing is necessary because, where the record reflects that the state trial court was aware of the familial relationship, it necessarily contains an implicit or explicit finding that the reasons justifying the limited closure order under Waller also apply to the excluded family member and, therefore, that the closure was not overly broad in its application to the defendant’s relatives.
In her concurring opinion, Judge Pooler maintains that “Yung ... requires the prosecution to make a heightened showing to justify the exclusion of family members” and that the standard we articulate in the instant case “does not constitute a showing” and therefore “does not satisfy Yung.” But the Supreme Court has not articulated a standard requiring heightened protection for a defendant’s family members from courtroom exclusion. And if, as Judge Pooler urges, we construe Yung as placing an additional burden on the prosecution whenever a family member is excluded from the courtroom in order to meet the requirements for courtroom closure set forth in Waller, then Yung’s “heightened showing” requirement clearly would violate Congress’ express mandate in AEDPA that “[a]n application for a writ ... shall not be granted ... unless the adjudication of the claim ... resulted in a decision that was contrary to, or involved an unreasonable application of, clearly Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1) (emphasis added).5
We recently held in Kennaugh v. Miller, 289 F.3d 36, 45 (2d Cir.2002), an opinion by Judge Calabresi, that “a state court determination is reviewable under AEDPA if the state decision unreasonably failed to extend a clearly established, Supreme Court defined, legal principle to situations which that principle should have, in reason, governed” (emphasis added). But an interpretation of “heightened showing” that places an additional burden on the prosecution does not extend the Supreme Court’s holding in Waller to a new situation. Rather, it alters the Waller standard whenever a family member is involved. If we were to hold that state court decisions to exclude family members constitute an “unreasonable interpretation” of Waller unless they are based upon “stronger proof’ than Waller generally mandates, we would be requiring state courts to comply with the federal law “as determined by” this Circuit, even though “the statutory language makes clear ... that § 2254(d)(1) restricts the source of clearly established law to [the Supreme] Court’s jurisprudence.” Williams, 529 U.S. at 412, 120 S.Ct. 1495.
Our interpretation of Yung’s “heightened showing” requirement saves this requirement from constituting a violation of AEDPA because it interprets it in a *87way that does not alter the standard articulated by the Supreme Court in Waller. In order for a court to evaluate whether a courtroom closure is overly broad (as required by Waller) insofar as it is being applied to family members, it must independently consider whether the exclusion of family members is necessary. See Oliver, 333 U.S. at 272, 68 S.Ct. 499 (arguably suggesting that, in some situations, the reasons justifying the closure of a courtroom would not also justify the exclusion of “friends, relatives and counsel”).
In the instant case, the record demonstrates that the state trial court was aware of the familial relationship between Sevencan and his wife. See Sevencan, 152 F.Supp.2d at 255-56. The court explicitly found a sufficient basis for the exclusion of family members generally at the conclusion of the closure hearing, and implicitly found a sufficient basis for the specific exclusion of Sevencan’s wife when the later application for admission to the courtroom was made on her behalf. Because the trial court was clearly aware of the familial relationship between Sevencan and his wife, and bécause its decision to close the courtroom otherwise comported with Waller, see supra at 85, ante, the court’s exclusion of Mrs. Sevencan from the courtroom during the undercover officer’s testimony does not amount to an unreasonable application of clearly established federal law as determined by the Supreme Court. Accordingly, the defendant’s constitutional claim based on the courtroom closure must fail.
III. Conclusion
In sum:
1.The Supreme Court’s decision in Waller v. Georgia, 467 U.S. 39, 48, 104 S.Ct. 2210, 81 L.Ed.2d 31 (1984), requires that, before public access to a courtroom in a criminal case may be restricted, “[1] the party seeking to close the hearing must advance an overriding interest that is likely to be prejudiced, [2] the closure must be no broader than necessary to protect that interest, [3] the trial court must consider reasonable alternatives to closing the proceeding, and [4] [the court] must make findings adequate to support the closure.”
2. Prior to the enactment of AEDPA and the Supreme Court’s decision in Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), we held in a habeas case that, in deciding whether to close a courtroom to the public, a trial court must pay particular attention to the exclusion of family members. See, e.g., Vidal v. Williams, 31 F.3d 67 (2d Cir.1994).
3. Pursuant to AEDPA and the Supreme Court’s decision in Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389, we may only consider the four-factor test set forth by the Supreme Court in Waller — and not our own pre-AEDPA case law concerning the exclusion of family members from the courtroom — in deciding whether the trial court unreasonably applied clearly established federal law by closing the courtroom to family members.
4. Following the enactment of AEDPA and the Supreme Court’s decision in Williams v. Taylor, a panel of this Court held in Yung v. Walker, 296 F.3d 129, 136 (2d Cir.2002), that a state trial court’s exclusion of a family member from a criminal trial as part of a limited closure order amounts to an unreasonable application of Waller unless there has been a “heightened showing” that the exclusion is necessary.
Based upon the above, we hold that:
1. The requirement set forth in Yung v. Walker, 296 F.3d 129, 136 (2d Cir.2002), that a “heightened showing” be made be*88fore a state trial court excludes a family member from a criminal trial as part of a limited closure order is satisfied where the record reflects that the state trial court considered the familial relationship at the time the family member was excluded;
2. Where the record reflects that the state trial court was aware of the familial relationship, it necessarily includes an implicit or explicit finding that the court considered the familial relationship and found that the reasons justifying the Waller closure order extend to excluded family members; and
3. Because the state trial court in the instant ease clearly considered the familial relationship in determining whether to exempt Sevencan’s wife from a properly entered limited closure order, its decision to exclude Sevencan’s wife was not “an unreasonable application of[ ] clearly established Federal law, as determined by the Supreme Court of the United States,” within the meaning of 28 U.S.C. § 2254(d).
Accordingly, we affirm the judgment of the District Court.
. Section 470.05(2) of New York’s Criminal Procedure Law provides, in relevant part:
For purposes of appeal, a question of law with respect to a ruling or instruction of a criminal court during a trial or proceeding is presented when a protest thereto was registered, by the party claiming error, at the time of such ruling or instruction or at any subsequent time when the court had an opportunity of effectively changing the same. Such protest need not be in the form of an "exception" but is sufficient if the party made his position with respect to the ruling or instruction known to the court, or if in [response] to a protest by a party, the court expressly decided the question raised on appeal.
. See Johnson v. United States, 520 U.S. 461, 468-69, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997) ("A 'structural' error, we explained in Arizona v. Fulminante, is a 'defect affecting the framework within which the trial proceeds, rather than simply an error in the trial process itself.’ ”) (citing Waller).
. Our concurring colleague, Judge Pooler, finds no error in the District Court’s reliance upon Vidal. She reasons: “Once the [District] [C]ourt found that the state court-acted properly even under Vidal, which arguably is more protective of the ability of family members to attend a trial than is Waller, it had no need to determine whether the closure would survive using a Waller analysis. A fortiori it would.” While this may be true, it does not change the fact that, under AEDPA, district courts may look only to Supreme Court precedent in deciding whether a state court decision amounts to “an unreasonable application of[ ] clearly established federal law.” 28 U.S.C. § 2254(d)(1).
Further, Judge Pooler expresses her view that we too should have decided this case on the "narrower” ground that ”th[e] evidence was more than sufficient to justify the closure under Vidal.” But "[w]e review a district court's denial of a habeas petition de novo,” Aparicio v. Artuz, 269 F.3d 78, 89 (2d Cir.2001), and we see no reason to repeat the mistake made by the District Court in relying *83upon pre-AEDPA case law decided by our Circuit, rather than following AEDPA's mandate to consider only "clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1). In any event, as noted in the text, Yung makes clear that Vidal is not "clearly established” Supreme Court law. 296 F.3d at 136.
Judge Pooler cites our decision in Leslie v. Artuz, 230 F.3d 25, 32-33 (2d Cir.2000), for the proposition that "we have not hesitated to rely on our precedent to establish that a state court did not unreasonably apply Supreme Court precedent.” But the Second Circuit opinions we cited in Leslie were relied upon because they pertained to similar factual circumstances as those before us in Leslie and they reached the same result as the state court decision being reviewed. Accordingly, we cited our own case law in Leslie to establish that Supreme Court precedent could not possibly mandate an outcome contrary to that reached by the state court — we did not impose a standard upon the state court that, while established in our Circuit, had never been articulated or even addressed by the Supreme Court.
. This "heightened showing" requirement articulated in Yung may appear to be dictum. The Yung panel held:
It is the district court's implicit assumption that the Vidal analysis is the only way to measure the propriety of excluding family members that causes us to remand. Because we cannot determine with confidence whether the district court would have reached the same result if it had applied the more general teaching of Waller and In re Oliver rather than the specific language of Vidal, we vacate the district court's judgment and remand for a reassessment of the reasonableness of the state court’s adjudication in light only of the relevant Supreme Court precedent.
296 F.3d at 136 (emphasis added). Because Yung neither applied, nor expressly instructed the district court to apply, the "heightened showing” standard, its articulation of this standard may be regarded as non-essential to the court’s holding. See Black's Law Dictionary 408 (5th Ed.1979) (defining 'dictum' as "an observation or remark made by a judge in pronouncing an opinion upon a cause, concerning some rule, principle, or application of law, or the solution of a question suggested by the case at bar, but not necessarily ... essential to its determination ... ”). Nevertheless, because the Yung court seems to have implicitly incorporated the idea of a "heightened showing" into its instruction to the District Court regarding further proceedings on remand, we appear to be bound by it. Accordingly, we defer to the Yung panel and apply the "heightened showing” requirement set forth in Yung.
. Judge Pooler laments that our interpretation of Yung's “heightened showing” requirement "will lead ineluctably to the exclusion of an accused’s closest family members, those who are most likely to offer the accused support at trial.” But this ominous conclusion ignores the relatively stringent requirements of Waller and presupposes that state courts and legislatures are entirely unable and unwilling to protect the rights of their defendants. And even if Judge Pooler's concerns were valid, AEDPA simply does not allow us to consider them in reviewing a state court decision pursuant to a petition for habeas corpus.