
525 F.3d 500 (2008)
Elijah JONES, Petitioner-Appellant,
v.
Pamela WALLACE, Respondent-Appellee.
No. 07-1470.
United States Court of Appeals, Seventh Circuit.
Argued March 4, 2008.
Decided April 29, 2008.
*501 Thomas L. Shriner, Jr., Brian K. Hagedorn (argued), Foley & Lardner, Milwaukee, WI, for Petitioner-Appellant.
Katherine L. Tripp (argued), Office of the Attorney General Wisconsin, Department of Justice, Madison, WI, for Respondent-Appellee.
Before CUDAHY, KANNE, and EVANS, Circuit Judges.
PER CURIAM.
Elijah Jones was convicted in Wisconsin state court of first degree sexual assault of a child. After exhausting state post-conviction remedies, Jones sought federal habeas corpus relief under 28 U.S.C. § 2254. He argues that his counsel was ineffective at trial for failing to discover and introduce evidence that would have impeached the testimony of the victimthe only evidence offered by the prosecution. The district court denied Jones's petition without holding an evidentiary hearing. Jones now asks us to remand for a hearing so that he might further develop his claims. But Jones does not allege facts that, if proven, would warrant relief. Therefore we affirm.
Jones's conviction was based exclusively on the testimony of his victim, "K.J." According to K.J.'s trial testimony, she was 12 years old when Jones assaulted her. At the time, Jones was dating her mother. K.J.'s family did not have a clothes washer and dryer, so K.J. went to Jones's apartment to do the family's laundry. Jones picked her up at home and drove her to his apartment. During the drive, Jones asked whether she had boyfriends or was sexually active.
While at the apartment, K.J. watched television on the couch. Jones sat down next to her and covered them both with a blanket. Under the blanket, he began to rub her thigh and then her vagina, over her clothes. She asked him to stop, and he did. He then took a shower and emerged naked. He asked her to look at his body and asked if she had pubic hair like he did. After K.J. had been at Jones's apartment for about two hours, he took her home. He told her not to tell anyone what had happened or they would both get in trouble. Within two days, however, she told her cousin, and her mother eventually found out and questioned her, resulting in a report to the police.
There were four discrepancies between K.J.'s testimony at trial and her previous statements to officers and at a preliminary hearing: (1) whether the security guard at Jones's apartment building momentarily came to the door to talk to Jones around the time of the assault; (2) whether K.J.'s mother had warned her to be careful around Jones because he "might try something;" (3) whether Jones was naked when he touched her; and, most important for this appeal, (4) whether K.J.'s mother called Jones's apartment while K.J. was there and, if she did, whether K.J. spoke to her. Counsel's failure to fully exploit *502 the fourth discrepancy is the basis for Jones's collateral attack.
At trial, defense counsel emphasized three of these discrepancies: whether the security guard came to the door, whether Jones was naked during the assault, and whether K.J. spoke with her mother when she called. Counsel argued that the inconsistencies collectively undermined K.J.'s credibility. What counsel failed to do, however, was to investigate Jones's cell phone and land line records to determine if the call from K.J.'s mother actually occurred. Jones now produces call records for his cell phone that do not show an incoming call from K.J.'s mother, as well as a letter from one phone company stating that its records show that Jones did not have a land line at the time of the offense. Jones argues that counsel could have used these records to impeach K.J. more effectively, changing the question whether she talked to her mother to whether her mother even called. Jones claims this change would have more persuasively undermined K.J.'s account and may even have suggested she fabricated her testimony. Depending on its nature, additional impeachment in this case could be of great importance because Jones was convicted based only on K.J.'s testimony.
Though the trial judge was without the benefit of the phone records, she considered the other three discrepancies argued by counsel when determining Jones's guilt. She determined, however, that they did not impair K.J.'s credibility as to the actual assault. Instead, the judge focused on K.J.'s demeanor and the fact that her testimony regarding the assault itself was vivid and consistent at all times. The judge noted that any discrepancies between K.J.'s trial testimony and earlier statements during her initial report to police were of little consequence because the officer who interviewed K.J. did not have a clear recollection of his conversation with her and because he merely conducted a brief screening interview before directing her to the appropriate officers for a complete investigation. The judge also pointed to numerous other specific details that K.J. testified to, such as the layout of the room, that Jones had offered her a Klondike bar, the timing of the event, where he was in the room, what he wore, and other like details that were undisputed and bespoke her powers of observation. The judge determined that K.J.'s testimony contained far more consistencies than inconsistencies and that the consistencies outweighed any discrepancies in minor details that were extraneous to the assault. The judge also found that K.J. was credible because she did not embellish her story. After finding Jones guilty, the judge sentenced him to 28 years in prison.
Jones pursued a direct appeal as well as collateral relief in the Wisconsin courts, arguing the ineffectiveness of his trial counsel. See State of Wisconsin v. Jones, No. 02-0554-CR (Wis.Ct.App. Sept. 30, 2003). At his post-conviction proceeding, Jones first produced his cell phone records showing that no call was placed to his phone during the time that K.J. was at his apartment on the day of the incident (though he did not yet produce the land line records he now contends counsel should have investigated). Jones argued that his attorney should have investigated his cell phone records and used them to impeach K.J. regarding her testimony that her mother had called the apartment.
The Wisconsin Court of Appeals rejected Jones's claims without an evidentiary hearing. It found that the evidence would not have sufficiently undermined K.J.'s credibility to change the outcome of Jones's trial and thus counsel's failure to discover it was not prejudicial. The court noted that counsel had already mounted an *503 unsuccessful attack on K.J.'s credibility based on similar discrepancies, and that even if counsel had discovered and admitted Jones's cell phone records, the records did not preclude the possibility that the call from K.J.'s mother was placed on a land line.
Jones next sought relief in the district court under § 2254. He again produced the cell phone records, but added a letter from a telephone company stating that he did not have a land line at the time of the incident. He reiterated his argument that, had counsel investigated and examined K.J. on this discrepancy, especially when combined with other inconsistencies in her testimony, there is a reasonable probability that the outcome of trial would have been different. The district court determined that the evidence did not show that counsel's failure to procure the phone records was prejudicial. It also denied an evidentiary hearing because Jones did not allege facts that would entitle him to relief, and thus he was not entitled to a hearing.
On appeal, Jones argues that he was entitled to an evidentiary hearing in the district court to prove counsel's ineffectiveness, and he asks us to remand for a hearing. The state courts refused Jones's request for a hearing. Accordingly, he is not at fault for failing to develop the factual record, and we look only to whether, if proven, his proposed facts would entitle him to relief. See Richardson v. Briley, 401 F.3d 794, 800 (7th Cir.2006); Davis v. Lambert, 388 F.3d 1052, 1059-62 (7th Cir. 2004); Matheney v. Anderson, 253 F.3d 1025, 1038-39 (7th Cir.2001).
To obtain relief, Jones must demonstrate that the Wisconsin Court of Appeals' decision was either contrary to, or an unreasonable application of, Supreme Court precedent. See Davis, 388 F.3d at 1058-59; Harris v. Cotton, 365 F.3d 552, 555 (7th Cir.2004). Jones proceeds under the theory that the state court's conclusion was an unreasonable application of the correct precedent. To be unreasonable, the decision must not only be incorrect, but so incorrect that it lies outside of the range of reasonable conclusions. Dixon v. Snyder, 266 F.3d 693, 700, 703 (7th Cir.2001); Matheney, 253 F.3d at 1041; Washington v. Smith, 219 F.3d 620, 628 (7th Cir.2000).
Because Jones must show facts that would warrant relief if proven, the reasonableness inquiry folds into his request for a hearing, leaving us to ask: if Jones successfully proved all he claims he would prove at a hearing, would his evidence establish that the Wisconsin Court of Appeals' decision that counsel performed effectively was unreasonable? If so, then we must remand for a hearing.
Jones's telephone records do not undermine the reasonableness of the Wisconsin Court of Appeals' decision. Though counsel's failure to investigate impeaching evidence can constitute deficient performance, see Harris, 365 F.3d at 556; Washington, 219 F.3d at 628, Jones cannot show that he was prejudiced, that is, he cannot show that the existence of his phone records undermines confidence in his conviction, see Davis, 388 F.3d at 1064; Harris, 365 F.3d at 555. The question of the phone call is too far afield from the central facts of the assault. Moreover, the evidence he presents is not actually impeaching.
First, Jones's proposed impeachment evidence is peripheral to the central facts of the crime and does not rise to the level of other cases in which this court found ineffective assistance for failure to investigate and impeach. For instance, in Davis, the defendant's attorney failed to investigate or present any eyewitnesses to support the defendant's theory of self-defense, including *504 the only sober eyewitness to the altercation in question. Davis, 388 F.3d at 1056, 1062-64. Similarly, in Harris, the defendant's attorney did not investigate a toxicology report which showed that the victim was under the influence of cocaine and alcohol, evidence that would have significantly strengthened the defendant's claim of self-defense. Harris, 365 F.3d at 554, 556-57. In Washington, counsel did not investigate or present several eyewitnesses who corroborated the defendant's alibi as well as his argument that the murder weapon did not belong to him. Washington, 219 F.3d at 629-31. Lastly, in Dixon, the defendant was charged with murder, but the only eyewitness recanted his statement to police that incriminated the defendant. Dixon, 266 F.3d at 696, 704. Counsel did not impeach the earlier statement by cross-examining the witness with the later recantations. Id. at 704. The unifying theme in these cases is that the overlooked evidence or impeachment involved facts central to the actual crime.
Unlike these cases, Jones's counsel failed to investigate phone records that did not dispute the central facts of Jones's assault on K.J. Their use to impeach K.J. could undermine only her recollection of the phone call, which itself is only loosely related by temporal proximity to the assault. It is the type of peripheral fact about which a witness could understandably be mistaken without undermining the credibility of her testimony about the assault. Next to her clear and consistent accounts of the assault, any mistaken recollection about the phone call is of minor importance.
Instead, this case more closely resembles Murrell, in which the defendant argued that his counsel was ineffective for failing to impeach a night club security guard with prior testimony. Murrell v. Frank, 332 F.3d 1102, 1107-08, 1112-13, 1115. But the inconsistency was slight (whether the guard saw the defendant before he dropped a gun or saw him next to the gun immediately after he dropped it) such that it would not have undermined the guard's credibility on the central issue of whether the defendant was the shooter. Id. Similarly, in Lowery, counsel's failure to impeach a prosecution witness was inconsequential because the witness's credibility had already been damaged by his admission that he was receiving prosecutorial leniency in exchange for his testimony. Lowery v. Anderson, 225 F.3d 833, 843-44 (7th Cir.2000). Moreover, his testimony on the critical points was consistent and was corroborated by the defendant's own admissions to police and to his cell mate. Id.
Like these cases, the details of the phone call and even the question of its existence are of little importance to the central facts of the case. Moreover, the Judge did consider impeachment already in the record regarding K.J.'s recollection of the call, and found her arguable inconsistency overshadowed by her confident demeanor and consistent recollection about the specific details of how, when, and where Jones actually touched her. While we are mindful that K.J.'s testimony was uncorroborated, a fact that adds appreciable weight and urgency to Jones's arguments, we require a more effective attack on her credibility before we will deem the Wisconsin Court of Appeals' decision unreasonable.
Second, the evidence on which Jones relies would not show prejudice because it is not in fact impeaching. The evidence does not show conclusively that K.J. lied or was mistaken because the phone records do not preclude the existence of another phone in the apartmenteither another cell phone that Jones possessed or borrowed for which he did not produce call *505 records, or a land line from a company other than the one whose letter he submits. Jones could have deposed K.J.'s mother and asked if she called, or presented additional evidence that no other phones were present, but he did not. At argument, Jones opined that such additional supporting evidence could possibly be produced if we granted a hearing. But this argument puts the cart before the horse. It is Jones's burden to show that the facts he alleges would warrant relief before we can remand for a hearing. Now, not later, is the time to produce the evidence that the Wisconsin Court of Appeals' decision was unreasonable. At best, Jones's records rule out some ways that the call may have occurred, but they do not disprove, or even necessarily oppose, K.J.'s testimony that her mother called.
Jones's phone record evidence, even if true, does not sufficiently undermine the reliability of his trial and, thus, the Wisconsin Court of Appeals' ruling on counsel's adequacy was reasonable. Therefore, Jones is not entitled to a hearing, and the judgment of the district court is AFFIRMED.
