ORDER
In this proceeding under 28 U.S.C. § 2254, petitioner Drew Terrell is seeking to persuade the court that he is not the person who in 1985 brutally murdered a 15-month-old little girl. Initially, he was convicted after a bench trial of felony murder and aggravated sexual assault and was sentenced to death. Many years later, former Governor George Ryan commuted the death sentence and reduced it to life imprisonment without parole. Terrell tried unsuccessfully to convince the state courts, and then the federal district court, that his attorney provided constitutionally ineffective assistance by conducting an inadequate investigation of the crime. Affidavits that Terrell has now collected show, he believes, that he falsely confessed to the crime in order to protect his mother, the true culprit. Presented with this theory, the Illinois courts concluded with confidence that the new information would not have made any difference to the outcome of the proceeding and that there was no point in holding an evidentiary hearing to delve further into the matter. The district court found that the decision of the state court was not unreasonable and denied Terrell’s § 2254 petition. Applying the deferential standard of review called for in these cases, we too conclude that Terrell has not shown enough to earn relief. We therefore affirm the judgment of the district court.
I
Because the governing law requires us to decide whether counsel’s alleged substandard performance is enough to undermine our confidence in the outcome of the proceedings in the state court, we must begin with a review of the crime and the proceedings that led to Terrell’s conviction. At the time of the offense in August 1985, Terrell was living with Elizabeth Terrell (his mother), Markeeter Hampton, and Hampton’s 15-month-old daughter, Laura. People v. Terrell (Terrell I), 132 Ill.2d 178, 138 Ill.Dec.176, 547 N.E.2d 145, 148 (1989). One morning Markeeter headed to work and left Laura in the care of Terrell and his mother. Id. Later that morning Terrell called Markeeter to tell her that Laura had been injured when she pulled a stereo down on top of herself and that she had been taken to the hospital. Id. Laura died a few hours later. Id.
Police questioned Terrell at the hospital, and he gave them the same story about the falling stereo that he had given Mar-keeter. Terrell I, 138 Ill.Dec. 176, 547 N.E.2d at 148. He explained that he was alone with Laura when the accident happened because his mother had stepped out to cash a check at a currency exchange. Id. The police confirmed that Elizabeth had indeed gone that morning to a nearby currency exchange. According to Terrell, his mother had returned a few minutes after the accident and brought Laura to the hospital. Terrell I, 138 IlLDee. 176, 547 N.E.2d at 148-49. But the doctors’ examinations of Laura revealed injuries inconsistent with the accident Terrell described. Id. at 149. Specifically, the doctors found evidence of sexual assault, including lacerations on Laura’s vagina and anus, significant vaginal tearing, and serious internal injuries, including a “huge tear” across her liver, collapsed lungs, and internal hemorrhaging. Id.
When the police brought Terrell into the station for questioning, he initially told the same story he had at the hospital, but he later changed it. In the presence of a court reporter, Terrell confessed — in detail. He said that after his mother had left *190for the currency exchange, Laura had woken up and started crying. He admitted that he hit her — both with an open hand and a fist — several times on her face, back, and stomach. He put the stereo equipment on the floor to create an alibi after he noticed bruises forming. Laura continued to cry, though, and after changing her diaper, Terrell said, he inserted a Q-tip and then his finger into her vagina all the way “up to the bone” because he was “looking for a pain response.” According to Terrell’s statement, his mother arrived home shortly after that, and he told her that Laura had pulled down the stereo on herself. Terrell later signed the transcribed statement, which was used against him at trial. Teirell I, 138 IlLDec. 176, 547 N.E.2d at 148-49.
At trial, the state also presented testimony from Laura’s mother, the medical examiner, and several detectives who had interviewed Terrell. Terrell I, 138 IlLDec. 176, 547 N.E.2d at 148^49. Terrell was the only witness for the defense, and this time he testified that after his mother left to cash her check, he “stepped outside” the apartment for approximately 40 minutes. Id. at 149. He said that he didn’t see anyone while he was gone, yet also that he spoke with “quite a few ... associates,” though he couldn’t remember any of their names. Id. Terrell initially testified that he noticed the fallen stereo and the injured child when he returned, but later during cross-examination, he changed his story and claimed that the accident did not happen until after he returned and that he heard the stereo fall while he was in a different room (returning to his story that the injuries had been caused by Laura’s knocking over the stereo). Id. He acknowledged that he confessed to police and that the signed statement accurately reflected what he had said to the court reporter at the station. Id. On redirect Terrell implied that police told him that he could not leave until he gave them a statement, but he also swore that the statement was not true. During closing arguments Terrell’s attorney proposed that someone else had entered the apartment while Terrell was out and attacked Laura.
Terrell was convicted, and at his first sentencing three relatives testified on his behalf. Terrell I, 138 IlLDec. 176, 547 N.E.2d at 150. All three testified that Terrell’s mother was a bad influence and made Terrell feel responsible for her protection and welfare. Lottie Banks, Terrell’s cousin, said, “I may be wrong ... but I believe he is right here covering up for his mother.” The Illinois trial court sentenced Terrell to death, but his case was remanded for resentencing. Terrell I, 138 Ill.Dec. 176, 547 N.E.2d at 163-64. On resentencing, Terrell was appointed new counsel, who sought to introduce evidence that his mother had committed the murder. People v. Terrell (Terrell II), 185 Ill.2d 467, 236 Ill.Dec.723, 708 N.E.2d 309, 325-26 (1998). To support this theory, Terrell produced the affidavits from eight relatives that are now at issue in his § 2254 petition, describing the abusive relationship between Terrell and his mother, her control over him, and conversations in which both Terrell and his mother said that he was covering up for her because she believed that Terrell would not be punished as harshly for the crime because of his age. The trial court did not allow Terrell to present these affidavits, however, and the Supreme Court of Illinois affirmed this decision on appeal, holding that the evidence was “too remote and speculative” to be admissible. Terrell II, 236 Ill.Dec. 723, 708 N.E.2d at 325.
Terrell filed a postconviction petition in state court. His primary argument was that his trial attorney was ineffective for failing to investigate and present the theory that Elizabeth Terrell had committed *191the murder and that he had falsely confessed to cover up for her. To support his petition Terrell submitted the same affidavits that he had attempted to introduce at resentencing. Four of the affiants — Drew Terrell, Sr. (his father), Eloise Chambers (his cousin), Madeline Terrell (his grandmother), and Banks (the cousin who testified at his sentencing hearing) — all reported that Terrell told them he was taking the rap for his mother. Chambers also reported that she overheard Markeeter (Laura’s mother) telling Terrell during a prison visit that she did not believe that Terrell killed her daughter and that she knew Terrell’s mother was to blame. Terrell’s maternal uncle also stated that Elizabeth told him she asked Terrell to cover up for her because the police would go easy on him because he was young and could handle prison better. Moreover, at least four of the affiants stated that they heard from others that Elizabeth was very jealous of Markeeter and wanted her and her daughter out of the apartment. Relying on the affidavits of his father and Chambers, Terrell argued that his trial attorney was aware of the cover-up in time to present the defense. And because counsel’s trial strategy had been to show that the confession was a lie and to create doubt by showing that someone else could have killed Laura when Terrell left the apartment, Terrell argued that presenting evidence that his mother was that person and that there was a motive for the false confession was consistent with this strategy. Thus, Terrell concluded, it was unreasonable for counsel not to follow up with his relatives to determine if it was possible to present this additional information at trial.
Commenting that he could not conceive of how a jury could accept a “diametrically opposed statement by the defendant which contradicts everything that was said at trial,” the trial court dismissed Terrell’s petition and denied his request for an evi-dentiary hearing. The judge continued that “there’s no indication in any way, shape, or form, what would cause the mother to do such a thing if she were present,” and concluded that there was no “hope at all of there being a different verdict” if the new evidence were presented to a trier of fact, because the evidence would be offset by Terrell’s testimony under oath and his statement to police.
The Illinois Court of Appeals affirmed, focusing on the reasonableness of counsel’s actions. The appellate court did not cite Strickland, but it referred to Illinois state cases that did discuss the Strickland standard. Explaining that the Illinois courts require petitioners seeking postconviction relief to support their claims with “affidavits, records, or other evidence,” see 725 ILCS 5/122-2, the court focused on whether the affidavits from Terrell’s family showed that counsel never contacted them and thus was unaware of the possible defense. None did, the court concluded, because two of the affiants said that they talked to counsel about the cover-up and four said only that they were not asked to testify at Terrell’s trial, not that trial counsel never contacted them. As for the remaining two affiants, the court noted that Earline Wadlington said that counsel never contacted her but did not mention anything about a false confession or that Terrell’s mother was involved, and so her testimony would not have helped to establish a cover up. And although the last affiant, Lottie Banks, asserted that counsel never spoke to her, that statement was contradicted by the fact that she testified at both sentencing hearings. Citing Illinois cases holding that contact with potential witnesses constitutes adequate investigation and affidavits silent as to this contact will not support a failure-to-investigate *192claim, the appellate court concluded that Terrell had not met his burden of proof to show that his attorney’s performance was deficient. The appellate court, however, did not address the broader question whether counsel’s investigation was sufficient under the circumstances or whether it was reasonable for counsel not to pursue a defense based on the alleged cover up. Because Terrell did not make a substantial showing that his constitutional rights were violated, the appellate court also determined that he was not entitled to an evidentiary hearing.
After Terrell’s PLA was denied, Terrell filed his § 2254 petition in the district court. He argued that the Illinois courts erred by denying him a hearing, unreasonably determining the facts and mischarac-terizing the affidavits, and misapplying Strickland. The district court first determined that it could not review the state court’s decision to dismiss Terrell’s post-conviction petition without a hearing because that raised only a state-law issue. On the merits, the court concluded that the Illinois Appellate Court’s determination was not an unreasonable application of Strickland. As the district court saw it, if Terrell was claiming that his attorney failed to conduct an adequate investigation, the threshold question was whether counsel had contacted the identified witnesses, and it was not unreasonable for the appellate court to evaluate Terrell’s claim by asking whether his affidavits supported that assertion. Although the state court did not cite Strickland, the district court continued, that was not required so long as the holding did not contradict Supreme Court precedent.
II
We granted Terrell a certificate of appealability and appointed counsel. On appeal Terrell argues that the state courts misapplied Strickland and that his trial attorney was ineffective for not adequately investigating and pursuing a defense that Terrell had falsely confessed to cover up for his mother. Terrell insists that this theory is consistent with counsel’s trial strategy that someone else abused and murdered Laura. He also contends that the district court erred in determining that his request for an evidentiary hearing was a noncognizable, state-law claim because his hearing request in federal court had been based on federal law. At oral argument, it became clear that there is really no dispute about the evidentiary hearing. Both parties recognize that the question whether Terrell was entitled to a hearing in the district court is one of federal law, and that the federal court has nothing to say about the state court’s procedures. On this point, our only comment is that Terrell’s right to a federal hearing is governed by Cullen v. Pinholster, — U.S. —, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011), and, because Terrell’s claims were adjudicated on the merits by the state courts, he must proceed on the basis of the record those courts created.
Under the Antiterrorism and Effective Death Penalty Act (AEDPA), 28 U.S.C. § 2254, we may issue a writ of habeas corpus if the state court’s merits decision on Terrell’s claim 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); see Smith v. McKee, 598 F.3d 374, 382 (7th Cir.2010). To constitute an “unreasonable application” of clearly established federal law, the state court’s decision must correctly identify the correct governing legal rule for Terrell’s ineffective-assistance claim, and unreasonably apply it to the facts of his case. Muth v. Frank, 412 F.3d 808, 813-14 (7th Cir.2005). Put another way, Terrell *193must show that the Illinois Appellate Court’s decision falls “well outside the boundaries of permissible differences of opinion.” Raygoza v. Hulick, 474 F.3d 958, 963 (7th Cir.2007) (quoting Hardaway v. Young, 302 F.3d 757, 762 (7th Cir.2002)).
To prevail on a claim of ineffective assistance, Terrell must establish that (1) his attorney’s representation “fell below an objective standard of reasonableness” and (2) he was prejudiced by counsel’s deficient performance. Strickland, 466 U.S. at 687, 104 S.Ct. 2052. Great deference is given to counsel in recognition of the fact that there is a wide range of reasonable defense strategies, and the reasonableness of counsel’s conduct must be assessed as a whole. Id. at 689, 104 S.Ct. 2052; United States v. Recendiz, 557 F.3d 511, 531 (7th Cir.2009). To show prejudice, Terrell must establish that there is a reasonable probability that, absent counsel’s errors, the outcome of the trial would have been different. Adams v. Bertrand, 453 F.3d 428, 435 (7th Cir.2006). State petitioners like Terrell face an additional burden because on top of the deference that we give counsel’s strategic litigation choices, AED-PA adds another layer of deference to the state court’s application of the legal standard. Harrington v. Richter, — U.S. —, 131 S.Ct. 770, 788, 178 L.Ed.2d 624 (2011); Toliver v. McCaughtry, 539 F.3d 766, 774 (7th Cir.2008).
Terrell tries to pick apart the appellate court’s decision, arguing that the court never cited Strickland and thus misapplied its standard. But the appellate court’s failure to cite Strickland is neither here nor there. See Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002). All that is required is that neither the reasoning nor the result of the state court’s decision contradicts Supreme Court precedent. Id. Here, although the appellate court narrowly construed Terrell’s claim, the court’s assessment of counsel’s performance is consistent with the standards set forth in Strickland. Attorneys have a duty “to make reasonable investigations or to make a reasonable decision that makes a particular investigation unnecessary.” Strickland, 466 U.S. at 691, 104 S.Ct. 2052. But trial counsel is not obligated to chase down every lead or “engage in a scavenger hunt for potentially exculpatory information” without direction from a client, and counsel’s decision to avoid pursuing investigations that would be fruitless cannot be considered unreasonable. United States v. Farr, 297 F.3d 651, 658 (7th Cir.2002); see Strickland, 466 U.S. at 691, 104 S.Ct. 2052; Brown v. Sternes, 304 F.3d 677, 691-92 (7th Cir.2002). Even if Terrell’s relatives told his attorney about the possibility that Terrell had falsely confessed to cover for his mother, it was reasonable for counsel not to pursue this line of defense. Although Terrell changed his story several times, in each account he consistently said that his mother had left him alone in the apartment and did not return until after the incident happened. Moreover, counsel knew that the police had confirmed at least a partial alibi for his mother, having spoken with the manager of the currency exchange who said that she had been in two or three times that morning to cash her check.
Terrell also contends that the appellate court evaluated his affidavits too narrowly, considering them only to see if they showed whether counsel contacted each person without assessing their exculpatory significance or asking if it was reasonable for counsel not to pursue the cover-up defense based on this information. But the significance of the affidavits is questionable, and Terrell’s argument is based on the faulty assumption that the cover-up defense was plausible and consistent with the strategy counsel used at trial. All the *194statements Terrell produced were from family members who clearly disliked his mother and blamed her for his problems and misconduct. It is unlikely that such testimony would have been persuasive, see Woods v. Schwartz, 589 F.3d 368, 377 (7th Cir.2009), even considering the cumulative impact of multiple relatives telling essentially the same story, see Raygoza, 474 F.3d at 964. Moreover, on the key points relating to the allegedly false confession— ie., the way Terrell’s mother controlled him, any motive she had to harm Laura or Markeeter, and acknowledgments of the cover-up by Terrell, Elizabeth, and Mar-keeter — the weight of the affidavits was diminished by the fact that they were based on hearsay, or double hearsay, and would likely be inadmissible in the form they presently had. Even though hearsay theoretically might help counsel to find admissible evidence, the Illinois courts were entitled to take the position that Terrell had plenty of time to find better evidence during the postconviction period, and that he had failed to do so. Notably, the Supreme Court of Illinois characterized Terrell’s affidavits as “too speculative and remote” to support a contention that his mother was the real perpetrator. Terrell II, 236 Ill.Dec. 907, 708 N.E.2d at 325. Although it is true that admissibility issues alone do not excuse an attorney from pursuing potentially exculpatory information, it was not beyond the pale for the Illinois courts to infer that counsel had permissible strategic reasons not to spend time investigating this defense.
Even if we were to accept Terrell’s argument that the Illinois Appellate Court’s application of Strickland was too narrowly focused on a supposed failure to investigate and that this was enough to show substandard performance, Terrell would not be entitled to prevail. He would still have to show that he was prejudiced by counsel’s failure to pursue this alternate theory. But the Illinois courts squarely rejected any possibility of prejudice, concluding to the contrary that the outcome of the case would not have been affected at all if the possibility that Terrell was taking the rap for his mother had been explored. Put in Strickland’s terms, the state judge made it clear that his confidence in the result was not shaken in the least by this new line of inquiry. The most damning evidence against Terrell was his signed confession to police, which described in detail abuse that was consistent with the medical examiner’s findings of Laura’s injuries. Although Terrell implied that the statement had been coerced, there was little, if any, evidence to support this theory, and his own divergent accounts of what happened undermined his credibility.
We conclude, for these reasons, that the district court correctly found that Terrell is not entitled to relief. The judgment of the district court is Affirmed.