WOOD, Circuit Judge.

On June 20, 1997, Connie Wagner was found brutally murdered in her home in Palatine, Illinois. Wagner's wrist had been bound with a telephone cord and she had been stabbed more than 180 times. She appeared to have struggled with her assailant or assailants. Joseph Stock, Wagner's former boyfriend, became the prime suspect. Three months after the murder, Stock's friend Alfonso Najera told the police that four days after the murder Stock had confessed to killing Wagner. Inexplicably, the police left the ostensibly violent Stock on the streets for more than three years after learning of his purported confession, arresting him only in February 2001. Further complicating matters, none of the physical evidence found in Wagner's home pointed to Stock; the clothes he wore the day of the murder bore no traces of blood; and Stock voluntarily went to the police station to assist with the investigation on the day after the murder and, at that time, showed no indications of a struggle. It was undisputed that Wagner was involved in drugs and was in debt to drug dealers with gang affiliations, and her neighbors reported seeing a Hispanic man driving slowly down her street before the murder. Still, relying primarily on Najera's tip, Stock was charged and convicted in 2002 of first-degree murder.

Our task is not to pass judgment on the facts surrounding the crime and the investigation. We concede readily that some suggest Stock's innocence, while others seem quite consistent with his guilt. Rather, we must decide whether this is one of the cases in which a federal court may issue a writ of habeas corpus to someone convicted in state court, given the standards set forth in the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), 28 U.S.C. § 2254. AEDPA tightly constrains our review. Stock argues that his right to cross-examine the witnesses against him was unconstitutionally constrained; in particular, he believes that the trial court's evidentiary decisions prevented him from effectively challenging Najera's testimony. We conclude, however, that the Illinois court reviewing Stock's conviction did not unreasonably apply clearly established federal law, because the testimony he intended to elicit was inconclusive for the purpose of impeachment. We therefore affirm the decision of the district court to dismiss his petition.

I

On the evening before the murder, Wagner told Stock that she was moving to Texas. This marked the end of a dating relationship that had lasted for several months. The state's theory of the case was that Stock, angry with Wagner over the break-up, used a copy of her key to enter the house, killed her, changed into her brother's clothes, and drove off in her car. The last of those steps was supported by the fact that Stock's fingerprints were found in his ex-girlfriend's car. As noted above, the physical evidence discovered in Wagner's home — hair, fingerprints, and footprints — did not inculpate Stock.

Central to the state's case was the testimony of Najera. Najera's testimony is also the subject of this appeal, and so we review it in detail here. Najera testified that four days after the murder, Stock called him and said that he murdered Wagner because he was angry. After a few months, Najera went to the police and relayed this story. He signed a statement, written by a prosecutor, outlining the conversation. He also agreed to participate in a recorded telephone call with Stock in which he would try to elicit another confession. The recorded conversation did not go as the state had anticipated. Stock made a number of unsolicited, exculpatory statements during the call; Najera ignored some and affirmed others. Najera also failed to mention the confession explicitly. The closest that Najera came to confronting Stock was the following exchange:

Stock: I mean shit — you still believe me, don't you?

Najera: Yeah, I believe you, dude. I believe you, man. I just want to make sure that you didn't say something to anybody else and they come to court and then.

Stock: That what?

Najera: You didn't tell anybody else — you know what I'm saving? Cause they come to court and then I look like, you know.

Stock: Tell anybody what?

Najera: Anything. I mean did they subpoena anybody else?

Stock believes that his exclamation, "Tell anybody what?" shows that he never confessed to Najera and thus did not know what his friend cautioned against "tell[ing] anybody else." Najera's repeated failures to challenge Stock's denials, according to Stock, further undermine Najera's claim that Stock confessed to him before the phone call.

Knowing that Najera would testify about the confession, Stock planned to use the recordings to impeach Najera, by showing that Najera neither challenged Stock's exculpatory statements nor followed through on his promise to obtain confirmation of Stock's confession. Before trial, the state filed a motion in limine to bar the introduction of the recorded conversation as hearsay. It argued that the out-of-court conversation was nothing but "self-serving statements by an accused" and thus inadmissible hearsay, citing People v. Patterson, 154 Ill.2d 414, 182 Ill.Dec. 592, 610 N.E.2d 16 (1992). Stock argued that he did not intend to use the statements to prove the truth of the matter asserted, i.e. his innocence, but to impeach Najera by omission. The trial court concluded that the recorded conversations were inadmissible hearsay. At the same time, however, the judge said that if Najera denied that he failed to confront Stock. about the confession during the call, then the defense could question Najera about the substance of the call, although it could not introduce the actual recorded conversation. At the state's request, the trial court later clarified its ruling, permitting the introduction of Najera's "tell anybody else" statement to rebut the defense's contention that he did not raise the issue with Stock, but still prohibiting the defense from introducing Stock's "Tell anybody what?" response. In short, the court decided that the defense could confront Najera about his failure to raise the confession during the recorded call, but in that case, the state could introduce Najera's allusion to the supposed confession, and the defense could not respond with Stock's potentially exculpatory response. At trial, the defense cross-examined Najera extensively about a range of issues, but stayed away from the recorded conversation.

As noted earlier, Stock was convicted of first-degree murder. He was sentenced to 90 years' imprisonment. Stock appealed his conviction to the Illinois Court of Appeals, raising five issues including the Confrontation Clause claim that forms the basis of his § 2254 petition. Stock argued that the restrictions placed on the cross-examination of Najera by the trial court violated his right guaranteed by the Sixth and Fourteenth Amendments to confront his accuser. The appellate court quoted Delaware v. Fensterer, 474 U.S. 15, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985), for the proposition that "the Confrontation Clause guarantees an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish." Id. at 20, 106 S.Ct. 292. (In this connection, the appellate court appeared to ignore a series of Supreme Court cases, discussed in further detail below, holding that certain limitations on cross-examination are unconstitutional.) The court also discussed the propriety of the evidentiary decision under Illinois law, noted the discretion given to trial courts under state law to reach evidentiary decisions, and commented that, even if the decision was in error, any error would have been harmless. The appellate court affirmed Stock's conviction and sentence, and the Illinois Supreme Court denied his petition for leave to appeal.

Finding no remedy in the state courts, Stock turned to the federal courts and to the writ of habeas corpus. The United States District Court for the Northern District of Illinois concluded that Stock satisfied the threshold procedural requirements for the § 2254 petition, but concluded that the merits of Stock's claim did not clear the high bar for relief — Stock did not establish that the Illinois appellate court unreasonably applied clearly established federal law when it rejected his Confrontation Clause claim. On this basis, the district court denied Stock's petition for a writ of habeas corpus. At Stock's request, the district court certified his request for a certificate of appealability.

II

Our review of Stock's petition is governed by AEDPA, 28 U.S.C. § 2254, which permits a federal court to issue a writ of habeas corpus only if the state court reached a decision on the merits of a claim, and that decision was either "contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States," id. § 2254(d)(1), or "was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding," id. § 2254(d)(2). Stock brings his petition under § 2254(d)(1). Whether the state court's decision was contrary to or an un-reasonable application of clearly established federal law "is a mixed question of law and fact that we traditionally also review de novo but with a grant of deference to any reasonable state court decision." Jackson v. Frank, 348 F.3d 658, 662 (7th Cir. 2003) (quoting Schaff v. Snyder, 190 F.3d 513, 522 (7th Cir. 1999) (emphasis in original)). In this case, as in all cases that come to us under AEDPA, we emphasize that our decision expresses no independent opinion about the correctness of the state court's judgment.

Section 2254(d)(1) has two branches — the so-called "contrary to" and "unreasonable application of theories. The Illinois appellate court's decision will be "contrary to" clearly established federal law "if the state court arrive[d] at a conclusion opposite to that reached by [the Supreme] Court on a question of law" or "if the state court confront[ed] facts that [were] materially indistinguishable from a relevant Supreme Court precedent and arrive[d] at a result opposite to [the Supreme Court]." Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). Our review is of the state court's decision, not the cases it cited (or failed to cite) along the way. See Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002) ("[Section 2254(d)(1)] does not even require awareness of [Supreme Court] cases, so long as neither the reasoning nor the result of the state-court decision contradicts them.") (emphasis in original). In this court, Stock argues that the Illinois appellate court's holding was contrary to the Supreme Court's decisions in Delaware v. Van Arsdall, 475 U.S. 673, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986), and Davis v. Alaska, 415 U.S. 308, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). Stock did not present this argument to the district court, however, and so it is not properly before us. Even if he had, we believe that Stock's case is better understood as an assertion that the state court unreasonably applied the applicable law; the facts of Stock's case are distinguishable from the Supreme Court precedents, but they do call to mind the central holdings of those cases. Stock tries valiantly to show that the Illinois court failed to apply those principles to his case, and it is to this argument that we now turn.

In order for a state court's decision to reflect an "unreasonable application" of governing Supreme Court jurisprudence, the state court must have done something worse than merely "appl[ying] clearly established federal law erroneously or incorrectly." The application of federal law must be "objectively unreasonable" before relief is possible under this branch of AEDPA. See Williams, 529 U.S. at 409-10, 120 S.Ct. 1495. We have observed that a state court may act unreasonably by failing to apply established federal law to facts that are materially indistinguishable to those examined by the Supreme Court. See Williams v. Bartow, 481 F.3d 492, 498 (7th Cir. 2007). Even in this instance, AEDPA tightly constrains the availability of the writ, particularly where a state court has engaged in a careful inquiry into the relevant question — here, whether the right of confrontation was infringed. Compare Lindh v. Murphy, 96 F.3d 856 (7th Cir. 1996) ( en banc), rev'd, 521 U.S. 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997) (finding no violation of the Confrontation Clause under the AEDPA standards of review), with Lindh v. Murphy, 124 F.3d 899 (7th Cir. 1997) (issuing the writ on the same facts applying the pre-AEDPA standards on remand).

Turning to the law that Stock asserts was applied unreasonably, we begin by recalling that the Supreme Court has characterized the right of confrontation as "paramount." Davis, 415 U.S. at 319, 94 S.Ct. 1105. It has also warned that "where constitutional rights directly affecting the ascertainment of guilt are implicated, the hearsay rule may not be applied mechanistically to defeat the ends of justice." Chambers v. Mississippi 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973). Furthermore, the Court has made clear that the limitations on impeachment may constitute violations of the Confrontation Clause. In Davis, the Court reversed the decision of the trial court to enforce a protective order that prevented the defense from confronting a key prosecution witness with his juvenile criminal record. And in Chambers, the Court rejected a trial court's application of state evidentiary rules that precluded the defense from examining a witness in a manner that would implicate that witness in the criminal conduct.

Stock asserts that clearly established federal law provides that "the Confrontation Clause is violated when a trial court unreasonably restricts or completely prohibits a defendant from asking questions necessary to impeach the credibility of witness testimony." We accept this formulation for purposes of the argument. Indeed, we too have noted that state interests, including those reflected in the state's evidentiary rules, may need to bend in order to ensure that defendants have the right to confront the witnesses against them. See, e.g., Dunlap v. Hepp, 436 F.3d 739, 742 (7th Cir. 2006). But it is equally well established that the law calls for a case-specific inquiry into a number of competing priorities. See id. As the Supreme Court said in Van Arsdall, "[T]rial judges retain wide latitude insofar as the Confrontation Clause is concerned to impose reasonable limits on such cross-examination based on concerns about, among other things, harassment, prejudice, confusion of the issues, the witness' safety, or interrogation that is repetitive or only marginally relevant." 475 U.S. at 679, 106 S.Ct. 1431. Even Stock's formulation of the law acknowledges that it is only unreasonable limits that create Confrontation Clause problems. Before any later court can decide whether a limitation imposed by the trial court was reasonable or unreasonable, it must look at the potential testimony and the bases for exclusion.

The trial court in Stock's case was aware of the fine lines that it was asked to draw. The court endeavored to balance Stock's ability to challenge Najera's testimony against the basic evidentiary principle that self-serving, out-of-court statements are inadmissible for the purpose of exculpating the declarant. See, e.g., United States v. Haddad, 10 F.3d 1252, 1258 (7th Cir. 1993) ("Ordinarily a defendant's self-serving, exculpatory, out of court statements would not be admissible."). The trial court initially excluded Stock's statements as inadmissible hearsay. In response to the motion for clarification, the defense asked the court to admit Stock's statement, "Tell anybody what?" for the purpose of impeaching Najera's claim that he confronted Stock with the confession during the recorded phone call. Defense counsel urged that this was a permissible use, and that the exchange was not being offered for the truth of the matter asserted, see FED.R.EVID. 801(C). But the trial court worried that the jury would take this statement as Stock's denial of his guilt, and the court concluded that it could not countenance the prejudice that would come along with admitting the evidence. The Illinois appellate court affirmed this conclusion, relying on People v. Hosty, 146 III.App.3d 876, 100 III.Dec. 356, 497 N.E.2d 334 (1986). Despite these limitations, Stock was permitted to cross-examine Najera extensively, including on issues of potential bias and on his failure directly to confront Stock with his purported confession during the recorded conversation. It may be troubling that Stock was barred from providing the jury with the context surrounding Najera's statements and omissions. But it was up to the trial court to draw the line, and we are not prepared to say that its actions lacked support.

Beyond these countervailing interests, we think that there is a more fundamental problem with Stock's argument. The Confrontation Clause permits the defendant "to expose to the jury the facts from which jurors, as the sole triers of fact and credibility, could appropriately draw inferences relating to the reliability of the witness." Davis, 415 U.S. at 318, 94 S.Ct. 1105. In this connection, we are not concerned with immaterial limitations on cross-examination. See Van Arsdall, 475 U.S. at 679-SO, 106 S.Ct. 1431 (calling for deference to the trial court when excluding "marginally relevant" evidence and asking whether the jury would have had a "significantly different impression" of the witness's credibility had the testimony been admitted). Once again, the only question before us is whether the state court's conclusion was an objectively unreasonable application of the Supreme Court's Confrontation Clause decisions. In specific terms, we must ask whether the state court acted unreasonably when it concluded that the excluded testimony was not relevant enough.

To begin with, we note that this was impeachment testimony. We can assume that Stock would have benefitted from being able to introduce out-of-court denials without subjecting himself to cross-examination, but excluding this obvious hearsay does not implicate the Confrontation Clause. Stock tries to work around the hearsay problem by arguing that the episode shows that Najera was lying: Najera did not directly confront Stock about the confession (as he promised the police he would do), and Najera's affirmations of Stock's professions of innocence might have cast doubt in the jury's mind on whether Stock really did make an earlier confession to Najera. Impeachment is certainly a proper purpose, but the purported value of these statements is undercut by their ambiguity. For whatever reason, Najera and Stock spoke elliptically throughout their conversation, exemplified by the "tell anybody else" — "Tell anybody what?" exchange. We have reread these statements many times, and we can find nothing in them that establishes that the two men were talking about a confession. Even Najera's affirmations of Stock's denials — e.g., "I believe you, dude" — are inconclusive. For all we know, Najera was playing his part in a charade Stock was creating or affirming Stock's cover story (rather than the truth).

Further, bearing in mind the narrow permissible purpose of the evidence, the trial court reasonably could have concluded that there was little value added for the defense in these statements. Despite Stock's arguments to the contrary, we cannot say with any degree of confidence that this evidence if admitted would show that Najera was not to be trusted. The fact that Najera did not contradict Stock (who might have really been his friend) could mean that he was loyal, scared, unaware, or any number of other things. And Stock would have gained little through the use of the ambiguous "Tell anybody what?" line, especially since the court permitted the defense to cross-examine Najera on his failure directly to raise the confession. Although the trial court may have given the state a slight advantage when it permitted the state to introduce the "tell anybody else" statement without including Stock's response, these distinctions are subtle at best. In Davis, the Supreme Court worried about the exclusion of a witness's prior offense that would have explained the police's suspicion of his involvement, and in Chambers, the trial court improperly excluded the testimony of several witnesses that strongly suggested that another witness had committed the crime and confessed to it soon thereafter. The Najera-Stock exchange is nothing like these examples.

Like our Lindh decisions, this is a case where the AEDPA standards have bite. As we have emphasized throughout, the only question before us is whether the state appellate court's application of clearly established federal law lies "well outside the boundaries of permissible differences of opinion." Hardaway v. Young, 302 F.3d 757, 762 (7th Cir. 2002). Given the vagueness of the conversation, we answer that question in the negative — reasonable minds could differ on whether the trial court unconstitutionally infringed Stock's right to confront Najera, and thus the state appellate court did not act unreasonably in upholding Stock's conviction.

It follows therefore that the district court was correct to dismiss Stock's § 2254 petition. We therefore AFFIRM the judgment of the district court.