
610 F.3d 404 (2010)
John EBERT, Petitioner-Appellant,
v.
Donald GAETZ, Warden,[*] Respondent-Appellee.
No. 09-1627.
United States Court of Appeals, Seventh Circuit.
Argued March 30, 2010.
Decided June 23, 2010.
*405 Carl P. Clavelli, Attorney (argued), Chicago, IL, for Petitioner-Appellant.
Michael R. Blankenheim, Attorney (argued), Office of the Attorney General, Chicago, IL, for Respondent-Appellee.
Before POSNER, ROVNER, and TINDER, Circuit Judges.
TINDER, Circuit Judge.
A jury in Cook County, Illinois, convicted John Ebert of murder and armed robbery. On direct appeal, the Illinois Appellate Court overturned his convictions after concluding that he was denied the effective assistance of counsel. Ebert was tried again, and the second jury also convicted him. Ebert again challenged his conviction on ineffective assistance grounds, this time alleging that his counsel erred in failing to refile a previously unsuccessful motion to quash his arrest and suppress an inculpatory statement he gave. The appellate court rejected Ebert's ineffective assistance of counsel argument and affirmed his convictions; the Illinois Supreme Court denied leave to appeal. After exhausting his state court postconviction remedies, Ebert sought a writ of habeas corpus from the federal courts. The district court denied his petition but granted a certificate of appealability on the issue of ineffective assistance of counsel with respect to the Fourth Amendment motions. We now affirm.

I. Background

A. Factual Background
On February 29, 1992, an elderly Chicago man, Frank Svec, attended a neighborhood Mardi Gras festival. Off-duty policemen saw him there with his downstairs neighbor, Sharon Brasher; Sharon's twelve-year-old daughter, Michelle; Sharon's live-in boyfriend, James Maynard; and Robert English, a friend of Sharon and Maynard's who had recently moved into an extra bedroom in the apartment Svec shared with another elderly man, Albert Jevorutsky. At the festival, Svec paid *406 for everyone's food and drinks with money from his recently cashed retirement check.
The group left the festival sometime between 10:30 p.m. and 11:30 p.m. Sharon's fourteen-year-old son, Michael, observed that Sharon was "kind of drunk" when she and Michelle returned to the converted tavern below Svec and Jevorutsky's apartment that the Brasher family was temporarily calling home. Around 2:00 a.m., by Michael's estimation, he and Michelle were awakened when Maynard and English knocked on the front door of the tavern/residence. Michelle let them in, and Michael saw them attempting to open a door to some stairs that led from the tavern to the upstairs apartment shared by Svec, Jevorutsky, and English. (English, who had moved in just a few days earlier and had not yet paid his first month's rent in full, did not have his own key to the upstairs apartment.) Michael testified that he did not see whether English and Maynard got the door open, though when the police later examined the door they found it unlocked.
Sometime between 2:30 a.m. and 3:00 a.m., according to Sharon, who reportedly looked at a large illuminated clock when she awoke, Maynard reentered the downstairs tavern. Maynard was covered with blood and told Sharon that he had killed two people and "liked it." He changed out of his bloody jean jacket and cowboy boots, threw about $300 on the floor, and, after arguing with Sharon, left the tavern with her. When Sharon and Maynard got outside, they saw petitioner Ebert standing there yelling "Franco," a name he used to refer to Svec. This was not unusual; Ebert often yelled for Svec to let him in so he could watch television. Ebert and Maynard decided to go get some drinks elsewhere, and Sharon went back inside the tavern to go to sleep.
In the morning, Sharon gave Michael $50 from the $300 Maynard had brought home so he could buy some shoes. She told Michael not to ask where the money had come from, and instructed him to throw away a bag of garbage that contained Maynard's bloody boots. She also washed Maynard's bloody clothes. (Sharon later pleaded guilty to concealing a homicide, and told the jury as much at Ebert's second trial.)
Later that day, March 1, 1992, during the afternoon, the police found Svec and his roommate Jevorutsky dead in their apartment. Both had been repeatedly stabbed and beaten, and Jevorutsky's throat had been slit. The men's rooms were ransacked and there was blood all over the floors and walls. The police found two knives beneath Jevorutsky's body and one near the foot of his bed. They did not find any knives or weapons near Svec's body, nor were they able to recover any fingerprints from his bedroom. The medical examiner concluded that Svec and Jevorutsky had died from their stab wounds, but she did not determine the precise time of death. The bedroom and belongings of the apartment's newest inhabitant, English, were undisturbed.
The police questioned various people throughout the neighborhood about the murders but did not immediately make any arrests. On April 23, 1992, Delores Esparza, the owner of a building down the street that Maynard and the Brashers moved into in mid-March, came forward and told the police that she had overheard a conversation between English, Maynard, Sharon Brasher, and petitioner Ebert. She reported that she had seen the foursome enter the Brashers' basement apartment and then heard three male voices talking and laughing about how they had robbed and murdered two old men, whom *407 they said "bled like stuffed pigs." After obtaining this information from Esparza, the police re-questioned Michael and Michelle Brasher. On the afternoon of May 1, 1992, Michael told them about the mysterious $50 he received, and about Sharon's instructions to dispose of Maynard's bloody boots. Michael also reported that Maynardhis mother's boyfriendhad told him in confidence that Ebert was one of the three people involved in the stabbings of Svec and Jevorutsky. Armed with this information, the police went looking for Ebert.
Ebert learned from the owner of a local bar he frequented, Jeannette's Place, that the police were looking for him that same evening. He called the police, and when they came to Jeannette's Place, he went with them voluntarily. The trial court nonetheless concluded that Ebert was "in custody" because he was not free to leave after he agreed to accompany the officers to a nearby police station. After Ebert spent about an hour alone in an interview room at the station, some officers drove him to a different station to get his palm print, returned him to the original station, and placed him in another interview room after explaining that he needed to wait for his palm print to "clear." Ebert spent the night and a good part of the next day in the interview room alone. On May 2, 1992, an assistant state's attorney and a detective came in to interview him, and at 5:45 p.m. he gave a statement implicating himself, English, and Maynard in the robbery and murders.
In his statement, Ebert explained that on March 1, 1992, he had been outside Svec's apartment at about 5:00 a.m. He said that he had yelled upstairs and English let him in to watch television; Svec and Jevorutsky were asleep in their rooms. A short while later, Maynard yelled upstairs. Ebert and English let him in, at which point Maynard said he needed some money and proposed that the men rob Svec. Ebert agreed that they should rob Svec and went into Svec's bedroom to start looking for money. Svec woke up and ran into the apartment's common living room. Maynard was waiting there and began to hit, punch, and kick Svec, while Ebert, accompanied by English, returned to Svec's room to continue the search for money. English found some coins, and Ebert found a drawer full of knives. Ebert showed Maynard the knives, and Maynard took one and went to Jevorutsky's room with English. Ebert continued searching Svec's room and eventually found $900 in cash, which the trio divided evenly. Ebert then suggested that they should break the lock on the front door so that the robbery would look like a forced entry. English instructed Ebert to dispose of a white plastic bag containing knives, a task he carried out on his way to reconvene with the others at White Castle later that morning. The police reported that the lock on Jevorutsky's bedroom door was broken, and Sharon testified that English retrieved a pillowcase full of coins from a nearby Taco Bell a few days after the murders.

B. Procedural Background
The state charged Ebert, English, and Maynard with armed robbery and murder. Before his trial, Ebert moved to quash his arrest on the grounds that the police lacked probable cause to arrest him, and to suppress his confession as fruit of the poisonous tree. See United States v. Swift, 220 F.3d 502, 507 (7th Cir.2000) ("Evidence which is obtained was the result of an illegal arrest is fruit of the poisonous tree and it must be excluded unless the government can show that it was obtained as a result not of the illegality, but rather by means sufficiently distinguishable to be purged of the primary taint."). English *408 made a similar motion, and the trial court held a joint hearing at which both Ebert and English testified. (Ebert and English were tried separately. English was acquitted after a bench trial.) The trial court also heard testimony from two police detectives who had worked on the case. The first detective provided hearsay testimony about Esparza's statementhe relayed that another officer told him what Esparza had said. This testimony was largely corroborated by the nonhearsay testimony of the second detective, who had actually interviewed Esparza. The second detective also testified about Michael's statements. He admitted on cross-examination that Michael's statements had not been completely consistent throughout the investigation, but Ebert's attorney did not pursue the matter beyond eliciting that admission.
The trial court denied Ebert's motion. (It also denied English's.) It found that by the time Ebert was under arrest on May 1, 1992, the police had Esparza's, Michael's, and Michelle's statements, which it concluded provided adequate probable cause to support the arrest. It had no need to make a finding as to Ebert's poisonous tree claim.
Ebert proceeded to a jury trial. At Ebert's trial, the assistant state's attorney who obtained his inculpatory statement read it to the jury, and Sharon Brasher testified for the state. The jury convicted Ebert of armed robbery and murder, but Ebert got the convictions reversed on ineffective assistance of counsel grounds. His counsel had asked the judge in open court, on the second day of trial, for permission to amend Ebert's answer to include an alibi defense. The defense that Ebert's counsel had already begun presenting to the jury, compulsion, was wholly inconsistent with an alibi defense (in addition to being legally unavailable to refute murder charges). Indeed, when counsel asked to add the alibi defense, he had already told the jury that Ebert had been present at the crime scene and was "compelled" to participate in the criminal acts because he was afraid Maynard would kill him if he didn't. The trial court allowed the amendment over the state's objection, and Ebert's counsel thereafter presented a single-witness alibi defense.
The appellate court determined that Ebert's counsel's trial preparation was "questionable" and found the mid-trial change of tactics, precipitated by Sharon Brasher's testimony that the murders happened sometime before 3:00 a.m., "objectively unreasonable." It explicitly criticized counsel's apparent failure to question the Brashers about the timeline of the crime. The appellate court also concluded that Ebert had been prejudiced by his counsel's actions. It stated that the "evidence against defendant at trial was not so overwhelming as to render counsel's deficient performance innocuous," and noted specifically that "no evidence of Michael's statements regarding Maynard's implication of the defendant or Esparza's statements concerning the conversation in the basement apartment were introduced at trial."
Ebert also argued to the appellate court that his motion to quash and suppress should have been granted. The appellate court articulated the familiar "totality of the circumstances" probable cause standard, see Illinois v. Gates, 462 U.S. 213, 231, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983), and proceeded to scrutinize the "essentially two pieces of information which the state argued established probable cause to arrest" Ebert: the statements from Michael Brasher and Delores Esparza. The appellate court noted that probable cause to arrest can rest upon information that would not be admissible at trial, such as *409 hearsay, if the information is supported by some indicia of reliability. The appellate court found such indicia of reliability in Michael's statements, and noted that the police also had Esparza's statement when they arrested Ebert. The court concluded that Esparza's statement, "when viewed in combination with the other information known to police, supports, at least minimally, a reasonable belief that the defendant was involved in the murder," and further concluded that the trial court's probable cause finding was not "manifestly erroneous." The Illinois Supreme Court declined to grant Ebert leave to appeal the probable cause issue.
Ebert went to trial again in 1998. His new counsel did not refile or otherwise seek to relitigate Ebert's motion to quash and suppress. He did, however, present a better-developed alibi defense: he found three unrelated witnesses who all testified that Ebert had been at Jeannette's Place from about 10:00 p.m. until about 3:45 a.m. on the night of the murders. The exculpatory timeline posited by Ebert's witnesses dovetailed with that proposed by Sharon Brasher, who again testified that Maynard returned home covered in blood sometime between 2:30 and 3:00 a.m., and that of Michael Brasher, who testified that Maynard and English tried to get upstairs at around 2:00 a.m. (It was also consistent with Ebert's inculpatory statement, however, which was again read to the jury.) Ebert's counsel highlighted the dearth of physical evidence against Ebertthe police had been unable to match Ebert's finger or palmprints to the few prints found at the crime sceneand drew the jury's attention to discrepancies between Ebert's statement and the other evidence. He also called Ebert's sister to testify that she frequently gave him money in an apparent attempt to undermine any motive Ebert might have had to commit robbery. The jury nevertheless found Ebert guilty of armed robbery and murder, and the court, as required by statute, sentenced him to natural life imprisonment, to be served concurrently with a thirty-year term for the robbery.
Ebert's counsel filed a post-trial motion for a new trial in which he accused himself of providing ineffective assistance because he failed to relitigate Ebert's motion to quash and suppress. Counsel alleged that he had in his possession but did not take any action with respect to two statements purportedly made by Delores Esparza soon after the hearing on Ebert's motion to quash and suppress.[1] In the first statement, which was handwritten but signed by Esparza and an assistant public defender, Esparza claimed that the conversation she had overheard involved Ebert, Maynard, Sharon Brasher, and, instead of English, Michael Brasher. She noted that she had confirmed the participants' identities with Sharon. Esparza also changed the time at which she heard the conversation, from the afternoon to about 4:00 a.m., but she maintained that the conversation contained a statement about pigs bleeding when their throats are cut. The second statement Ebert's counsel attributed to Esparza was an unsigned typed memorial of an unidentified person's "interview with Delores Esparza on Monday, March 23, 1993." In this statement, which was riddled with typographical errors and mis-spellings, *410 Esparza again placed the conversation around 4:00 or 4:30 a.m., and again stated that the four participants were Ebert, Maynard, and Sharon and Michael Brasher. She further stated that she heard discussion about pigs' throats bleeding when they are slit, but, according to the statement's final line, "[s]he did not hear or tell the police that she heard any conversation regarding robbery or murder."
The trial court denied Ebert's post-trial motion. Ebert then pursued an ineffective assistance of counsel claim on direct appeal. Echoing the claims his counsel made in the post-trial motion, Ebert contended that counsel's failure to seek to quash his arrest and suppress his statement before the second trial constituted ineffective assistance. Ebert further argued that his counsel should have more fully investigated the new statements allegedly made by Esparza. The appellate court considered the two new Esparza statements, and, applying the familiar test articulated in Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), speculated that Ebert's counsel "may well have made a tactical decision that further investigation would be fruitless, given the other evidence of probable cause." The appellate court much more explicitly concluded that Ebert could not satisfy the prejudice prong of Strickland. It found that there was no "reasonable probability that the final result in this case would have been different had defense counsel investigated further and made a motion to suppress." It noted that it was applying the probable cause conclusions it had announced when it heard Ebert's case previously, because the facts had not substantially changed. (This is the "law of the case" doctrine, the purposes of which are "to further consistency, to avoid constantly revisiting rulings, and to conserve judicial resources." Sharp Elecs. Corp. v. Metro. Life Ins. Co., 578 F.3d 505, 510 (7th Cir. 2009).) The appellate court found that Esparza's new statements did not negate the detectives' testimony that she originally told them she overheard a conversation about a murder. It also found that there were no new developments with respect to Michael's statements, and reiterated that Michael's and Esparza's statements provided an adequate basis for probable cause. The Illinois Supreme Court denied leave to appeal the ruling.
After exhausting his direct appeals, Ebert sought and was denied postconviction relief from the Illinois courts. He then turned to the federal courts, where he filed a multi-ground petition for a writ of habeas corpus. The district court denied Ebert's petition on all grounds. With respect to his ineffective assistance claim, it rested its conclusion on our holding in Holman v. Page, 95 F.3d 481, 492 (7th Cir.1996): that, under the Strickland standard for ineffective assistance, "no prejudice exists when evidence gathered in violation of the Fourth Amendment is erroneously admitted at trial." After we granted Ebert a certificate of appealability, we overruled Holman, see Owens v. United States, 387 F.3d 607 (7th Cir.2004), and remanded Ebert's case to the district court for reconsideration of his ineffective assistance of counsel claim.
The district court dutifully reexamined the claim. It concluded that "it is far from clear that Ebert's motion to suppress would have been granted had trial counsel interviewed Esparza and renewed the motion to suppress his confession." The district court considered the information the police had at the time they arrested Ebert, and determined that "[e]ven if Esparza had repudiated her statement to the police, the totality of the circumstances at the time of Ebert's arrest" was sufficient to establish probable cause. The district *411 court ultimately found "little reason to believe that a renewed Fourth Amendment challenge would have been meritorious such that the Illinois Appellate Court's conclusion to the contrary could be considered erroneous, or beyond that, `well outside the boundaries of permissible differences of opinion.'" (quoting Hardaway v. Young, 302 F.3d 757, 762 (7th Cir.2002)). Ebert disagreed and sought a certificate of appealability on the ineffective assistance issue. The district court granted his request, and we now consider his arguments.

II. Discussion
We review the district court's denial of a petition for habeas corpus de novo. Smith v. McKee, 598 F.3d 374, 381 (7th Cir.2010). Under the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), we conduct our review with a great deal of deference to the Illinois courts that previously evaluated Ebert's claim. Ben-Yisrayl v. Buss, 540 F.3d 542, 546 (7th Cir.2008) ("[U]nder post-AEDPA habeas law, we defer to a great extent to the decisions of the state courts, and review these decisions for reasonableness only."). We may grant habeas relief only if the Illinois courts' adjudication of Ebert's claim "was contrary to, or involved an unreasonable application of clearly established Federal law as determined by the Supreme Court of the United States," or "was based on an unreasonable determination of the facts in light of the evidence presented." 28 U.S.C. § 2254(d). Unreasonableness is a high bar in this context: "[a] state court's decision is `unreasonable' within the meaning of § 2254(d)(1) only if it is `so erroneous as to be objectively unreasonable' and `well outside the boundaries of permissible differences of opinion.'" Bennett v. Gaetz, 592 F.3d 786, 790 (7th Cir.2010) (quoting Emerson v. Shaw, 575 F.3d 680, 684 (7th Cir.2009)). We review the decision of the last Illinois court that substantively considered Ebert's claim, Gonzales v. Mize, 565 F.3d 373, 379 (7th Cir.2009), and we will presume that court's factual findings to be correct unless Ebert rebuts that presumption with clear and convincing evidence, Ben-Yisrayl, 540 F.3d at 546 (citing 28 U.S.C. § 2254(e)(1) and Miller-El v. Dretke, 545 U.S. 231, 240, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005)).
The Supreme Court set forth the legal principles that govern claims of ineffective assistance of counsel in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Under Strickland, a defendant must demonstrate both that his counsel's performance was deficient when measured against prevailing standards of professional reasonableness, and that the deficient performance prejudiced his defense. Strickland, 466 U.S. at 689-92, 104 S.Ct. 2052; Brown v. Finnan, 598 F.3d 416, 422 (7th Cir.2010) (citing Wiggins v. Smith, 539 U.S. 510, 521, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003)). When the ineffective assistance claim is based on counsel's failure to file a motion to suppress, as it is here, the defendant must also prove "that his Fourth Amendment claim is meritorious and that there is a reasonable probability that the verdict would have been different absent the excludable evidence in order to demonstrate actual prejudice." Kimmelman v. Morrison, 477 U.S. 365, 375, 106 S.Ct. 2574, 91 L.Ed.2d 305 (1986); see also United States v. Cieslowski, 410 F.3d 353, 360 (7th Cir. 2005). These are at best difficult showings to make, particularly since Strickland requires that we presume counsel "rendered adequate assistance and made all significant decisions in the exercise of reasonable professional judgment," Strickland, 466 U.S. at 690, 104 S.Ct. 2052, and evaluate his performance as a whole rather than focus on a single failing or oversight, Peoples v. United States, 403 F.3d 844, 848 *412 (7th Cir.2005). Ebert's uphill slope is even steeper under AEDPA, which adds an extra layer of deference to our review. See Ellison v. Acevedo, 593 F.3d 625, 633 (7th Cir.2010); Ben-Yisrayl, 540 F.3d at 546; Conner v. McBride, 375 F.3d 643, 657 (7th Cir.2004) ("[W]e do not apply the Strickland standards directly, but instead ask whether the post-conviction court's factual findings and conclusions pass AEDPA muster.").
Ebert argues, as he has consistently, that his counsel's performance was deficient because he did not sufficiently investigate the new statements from Esparza and relitigate the motion that was raised before Ebert's first trial.[2] In evaluating counsel's decision not to investigate the new statements, the second appellate court concluded the decision was a tactical one that it saw no reason to second-guess. See Eckstein v. Kingston, 460 F.3d 844, 849 (7th Cir.2006). The court came to this conclusion after accurately recognizing Strickland as the governing precedent. We therefore examine only whether the state court applied Strickland unreasonably, which occurs only when the state court's application of "clearly established Federal law" is wholly outside the boundaries of permissible differences of opinion. Bennett, 592 F.3d at 790.
Here, this inquiry requires us to delve deeper than is ordinarily required. The second appellate court rested its finding that counsel's decision was a legitimate strategic one on its concomitant conclusion that the other evidence of probable cause was adequate to support Ebert's arrest and would remain so even if Esparza's new statements had been pitted against it. That finding, in turn, rested on the first appellate court's determination that probable cause supported the arrest and that the motion to quash was not denied erroneously. This recursion runs us right into Ebert's other primary contention: that a motion to quash his arrest and suppress his confession would have been meritorious because the courts relied on unreliable evidence to find probable cause.
Police have probable cause to make an arrest when "the facts and circumstances within their knowledge and of which they had reasonably trustworthy information were sufficient to warrant a prudent man in believing that the petitioner had committed or was committing an offense." Beck v. Ohio, 379 U.S. 89, 91, 85 S.Ct. 223, 13 L.Ed.2d 142 (1964). Probable cause "is a practical, nontechnical conception," id. (quoting Brinegar v. United States, 338 U.S. 160, 176, 69 S.Ct. 1302, 93 L.Ed. 1879 (1949)), and its existence is determined using a "totality-of-the-circumstances approach," Illinois v. Gates, 462 U.S. 213, 230-31, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983). The police must consider the "`veracity' and `basis of knowledge' of persons supplying hearsay information," id. at 238, 103 S.Ct. 2317, but those two considerations are complementary: "a deficiency in one may be compensated for, ... by a *413 strong showing as to the other," id. at 233, 103 S.Ct. 2317. In short, "it does not take much to establish probable cause. The officers must have more than a bare suspicion that they have the right guy, but they need not have enough evidence to support a conviction or even to show that their belief is more likely true than false." Fox v. Hayes, 600 F.3d 819, 833 (7th Cir.2010).
The first appellate court accurately laid out the applicable law governing probable cause even though it did so largely in terms of state rather than federal law. See Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002). It then stated that there were "essentially two pieces of information which the state argued established probable cause to arrest" Ebert: the statement from Michael Brasher and the statement from Delores Esparza. Ebert challenged both statements, but the court found the statements sufficiently reliable to support a finding of probable cause.
The court addressed Ebert's concerns about the reliability of Michael's statements first. It reasoned that Michael was not a police-paid confidential informant, and noted that Ebert failed to provide evidence showing that Michael's connections to Sharon and Maynard undermined the heightened reliability that citizen informants are often accorded. It went on to note that Michael's statements "implicated those that [Ebert] suggests Michael would fabricate to protect and therefore bolstered his reliability." It recognized that the police's admission that Michael's statements had not been entirely consistent could call Michael's credibility and reliability into doubt, but found that Ebert's failure to develop the extent or even the character of the alleged inconsistencies left it without a basis to conclude that Michael's statements were unreliable. See Spiegel v. Cortese, 196 F.3d 717, 725 (7th Cir.1999) (noting that witnesses do not have to be "unfailingly consistent to provide probable cause"). These conclusions were not unreasonable determinations of the facts in light of the evidence presented, nor did they involve a contravention or unreasonable application of federal law.
The court also addressed the reliability of Maynard's statement to Michael. (Michael relayed to the police that Maynard told him in confidence that Ebert was one of the three people involved in the murders.) It found no reason to doubt the reliability of the statement made in confidence to Michael. Ebert claims, however, that the court erred in giving any weight to the Maynard-via-Michael statement because "there was simply no `range of details' provided by Michael Brasher's alleged statement sufficient to justify the level of trustworthiness necessary to a finding of probable cause particularly when the source was James Maynard." Appellant's Br. 20. Ebert is correct inasmuch as he contends that the Supreme Court has recognized that a source whose information contains a range of details is more reliable than one whose does not. See Gates, 462 U.S. at 245-46, 103 S.Ct. 2317. But he misses the mark when he claims that Michael's statement was wholly devoid of reliability-enhancing detail. Michael, whose identity was fully disclosed, told the police that he saw Maynard and English try to get upstairs on the night of the murders. Michelle independently corroborated that detail. He also told the police that he personally disposed of Maynard's bloody boots. Both of these details tend to place Maynard at the crime scene and thus corroborate his statement to Michael about who else was there, especially when Maynard's statement did not exculpate himself. The fact that Maynard had testified to a grand jury that English told him that he was the only perpetrator does not undermine these details; Maynard *414 made those statements to divert police attention from himself, a step he would not have needed to take when speaking in confidence to his live-in girlfriend's son. And when considered in conjunction with the other information from Michaelas the appellate court properly considered itthe statement contributes something relevant, not determinative, to the totality of the circumstances analysis.
Ebert nonetheless challenges the appellate court's mere consideration of the Maynard-via-Michael statement, on Confrontation Clause grounds. He cites Lee v. Illinois, 476 U.S. 530, 539-42, 106 S.Ct. 2056, 90 L.Ed.2d 514 (1986), and Lilly v. Virginia, 527 U.S. 116, 131, 119 S.Ct. 1887, 144 L.Ed.2d 117 (1999), for the proposition that the confession of an accomplice is presumptively unreliable. This argument doesn't get Ebert very far, however, because the court considered the statement at a suppression hearing, not Ebert's trial; the Confrontation Clause was not implicated. See United States v. Harris, 403 U.S. 573, 584, 91 S.Ct. 2075, 29 L.Ed.2d 723 (1971) (noting that Confrontation Clause precedent "seems inapposite to ... proceedings under the Fourth Amendment"). Additionally, Maynard's statement to Michael did not necessarily implicate himself; it was not a "confession" like the ones in Lee and Lilly.
We are similarly unpersuaded by Ebert's unsupported claim that the first appellate court erred in its consideration of Delores Esparza's statement. The court accurately characterized the police's testimony about the statement. It highlighted the "bled like stuffed pigs" language, and it mentioned that the overheard conversation had revolved around the murders of two old men. The court did not appear to place great weight on Esparza's statement, however, concluding only that it "supports, at least minimally, a reasonable belief that [Ebert] was involved in the murders." This was not an unreasonable conclusion for the appellate court to draw, particularly in light of a different officer's corroborating description of the bloody crime scene and the unfortunate state of the victims, one of whom had his throat slit like the "pigs" that were discussed in the conversation Esparza overheard. Nor was it the result of an unreasonable application or dereliction of federal law. Probable cause "does not require evidence sufficient to support a conviction, nor even evidence that it is more likely than not that the suspect committed a crime," United States v. Carrillo, 269 F.3d 761, 766 (7th Cir. 2001) (quotation omitted), and "the amount of information the police are required to gather before establishing probable cause for an arrest is in inverse proportion to the gravity of the crime and the threat of its imminent repetition," Mason v. Godinez, 47 F.3d 852, 856 (7th Cir.1995). Given the gravity of the crimes here, the probable cause bar was low; the first appellate court did not err in concluding it had been cleared.
The second appellate court's harkening back to this objectively reasonable conclusion was also objectively reasonable. It was not absolutely required to adhere to its earlier holding, see Castro v. United States, 540 U.S. 375, 384, 124 S.Ct. 786, 157 L.Ed.2d 778 (2003); White v. United States, 371 F.3d 900, 902 (7th Cir.2004) ("And it's not as if the law of the case doctrine were a straitjacket that might cause a miscarriage of justice."), but it was certainly permitted to, see People v. Sutton, 233 Ill.2d 89, 330 Ill.Dec. 198, 908 N.E.2d 50, 58 (2009) ("[T]he determination of a question of law by an appellate court in the first appeal may be binding on the court in a second appeal."). As the second appellate court cogently explained, none of the well-established exceptions to the law *415 of the case doctrine applied. It pointed out that the facts underlying the first appellate court's probable cause evaluation were not "so substantially different as to require a different interpretation." The court also took the crucial next step: it considered whether the facts would have substantially changed if defense counsel had further investigated Esparza. It concluded that the new Esparza statements, even if fully credited by the trial court, would not have necessarily negated her earlier testimony or in any way undermined Michael's.
This conclusion is not unreasonable. Key portions of the statements, namely the "pigs" language and the presence of Ebert, are consistent across all three versions. Moreover, the appellate court considered Esparza's initial statement minimally supportive of probable cause only "when viewed in combination with the other information known to police." It would therefore be highly unlikely that changes to the statement, or even a retraction thereof, would result in a significant reweighing of the totality of the circumstances. Even if Esparza took the stand at a new suppression hearing and recanted her first statement to the policethe best-case scenario in Ebert's viewher testimony and dubious third "statement" would be competing with testimony from police officers the trial court already found credible. See Hinton v. Uchtman, 395 F.3d 810, 820 (7th Cir.2005). And the court would still have the statements from Michael and Michelle, as well as any other fruits of the investigation preceding Ebert's arrest, on which to reasonably rest probable cause. Ebert thus cannot demonstrate that a motion to suppress would have been meritorious, a requisite for a successful ineffective assistance of counsel claim in this situation regardless of the deficiency of counsel's performance. See Kimmelman, 477 U.S. at 382, 106 S.Ct. 2574.
It is of no moment that the court neglected to give weight to Ebert's attorney's assessment of his performance as constitutionally ineffective. See McAfee v. Thurmer, 589 F.3d 353, 356 (7th Cir.2009) (noting that attorney "reflection after the fact is irrelevant to the question of ineffective assistance of counsel"); Chandler v. United States, 218 F.3d 1305, 1315 n. 16 (11th Cir.2000) (en banc) ("Because the standard is an objective one, that trial counsel ... admits that his performance was deficient matters little."). No more helpful are the cases to which Ebert attempts to analogize his own. This is not a case in which counsel failed to interview potential alibi witnesses because he thought an alibi defense would be futile, see Raygoza v. Hulick, 474 F.3d 958, 964-65 (7th Cir.2007); to the contrary, Ebert's second counsel presented three alibi witnesses on his behalf. Nor is it one in which counsel failed to order a potentially critical toxicology report, see Harris v. Cotton, 365 F.3d 552, 555-56 (7th Cir. 2004), or neglected to order a competency hearing, see Burt v. Uchtman, 422 F.3d 557, 566-69 (7th Cir.2005). The Esparza statements that Ebert's attorney allegedlythere is nothing in the record one way or the otherfailed to investigate would not have afforded Ebert a reasonable probability of a different result at trial. Contra Toliver v. McCaughtry, 539 F.3d 766, 776 (7th Cir.2008). Ebert simply cannot satisfy the prejudice element of Strickland, and the state courts were not acting contrary to or unreasonably applying federal law when they reached that conclusion.

III. Conclusion
The state court's conclusion that the new statements from Esparza did not negate *416 its earlier finding of probable cause to arrest Ebert was not "so erroneous as to be objectively unreasonable," and Ebert's counsel was not constitutionally remiss in failing to file what would have been an unmeritorious motion to quash his arrest and suppress his inculpatory statement. We therefore AFFIRM the district court's denial of Ebert's petition for a writ of habeas corpus.
NOTES
[*]  Pursuant to Federal Rule of Appellate Procedure 43(c)(2), Donald Gaetz, the current warden of the Menard Correctional Center, is automatically substituted for former warden Donald A. Hulick.
[1]  It is not clear how or when counsel procured these statements, which were purportedly taken by two other assistant public defenders and were the subject of a motion in limine at James Maynard's trial. (The motion was denied, and the state did not call Esparza to testify at that trial, either.) All we know is that counsel got them sometime before Ebert's second trial because he indicated in the post-trial motion that he had shared them with the state in advance of trial.
[2]  Ebert also contends that his counsel should have interviewed Sharon and Michael Brasher before the second trial. He points out that the first appellate court admonished his first counsel for not interviewing Sharon, and leaps from there to the conclusion that his second counsel therefore could not have made a reasonable strategic decision not to interview and call as witnesses Sharon and Michael. This particular factual basis for the ineffective assistance claim is procedurally defaulted, however, because Ebert did not fully present it to the state courts, see Pole v. Randolph, 570 F.3d 922, 935 (7th Cir.2009) (citing Stevens v. McBride, 489 F.3d 883, 894 (7th Cir.2007)). And because this claim is defaulted, there is no need for us to consider at length Ebert's post-argument Fed. R.App. P. 28(j) letter addressing it in the context of Bynum v. Lemmon, 560 F.3d 678, 684-85 (7th Cir.2009).
