LUCERO, Circuit Judge.
Lori Lynn McLuckie, a Colorado state prisoner convicted of first-degree murder and sentenced to life imprisonment, appeals the district court’s denial of her petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254. This court granted McLuckie a certificate of appealability (“COA”) pursuant to 28 U.S.C. § 2253(c) with respect to her sole claim of legal error: that trial counsel’s failure to investigate and present psychological evidence deprived her of effective assistance of counsel under Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Thus, exercising jurisdiction under 28 U.S.C. §§ 1291 and 2253, we are presented with two questions: (1) whether McLuckie’s constitutional right to effective assistance of counsel was violated; and (2) whether the judgment of the Colorado Court of Appeals denying post conviction relief under Strickland “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States, within the meaning of 28 U.S.C. § 2254(d)(1).” Williams v. Taylor, 529 U.S. 362, 367, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (quotation omitted). Because we answer the second question in the negative, we affirm the denial of habeas relief.
I
The objective facts relating to the conviction are undisputed. On May 27, 1988, Denver Police executed a search warrant at McLuckie’s apartment, revealing a grisly scene. Once inside, they found the head and torso of the dismembered body of Andrew Vigil, with whom McLuckie had been romantically involved. McLuckie was asleep in the bedroom. A search of the premises revealed a saw in the kitchen, a bloody sheet in the bathtub, and rubber gloves in McLuckie’s bedroom. In trash dumpsters outside the apartment, they found grocery bags containing body parts wrapped in aluminum foil.
Due to the bizarre and macabre nature of the case, the two public defenders who were assigned to represent McLuckie immediately enlisted the aid of a mental-health expert, Dr. Susan Bernhard. After an examination, including the administration of several clinical tests, Dr. Bernhard concluded that McLuckie may have had a “meritorious mental state defense.” (1 R. Doc 19, para. 2, 3.) Dr. Bernhard noted that McLuckie was suffering from severe emotional problems, that test data supported an impaired mental condition defense, that she may have had an insanity defense, and that the matter called for further investigation. However, Dr. Bern-hard did not conclude that McLuckie met the standards for legal insanity or diminished mental capacity in Colorado.
An expert in Battered Woman Syndrome, Dr. Lenore Walker, was then contacted. After examining McLuckie, Dr. Walker prepared a report in which she concluded that McLuckie suffered from Battered Woman Syndrome as a sub-category of Post-Traumatic Stress Disorder. She found that McLuckie was a former rape victim, that she had been physically and sexually abused in her relationship with Vigil, and that the homicide arose out of McLuckie’s “psychological condition from being battered and from being sexually abused.” (3 id. at 56.) Dr. Walker noted that McLuckie’s “serious mental health problems” presented a “complex case” and “were not diagnosable in the ususal way.” (3 id. at 57.) She explained that McLuckie’s actions were “consistent with a dissociative state and other inability to perceive reality.” (1 id. Doc. 2, Ex. C, para. 5.) Dr. Walker suggested that [1195]*1195McLuekie’s perception of reality was impaired sufficiently to negate the deliberation required for first-degree murder under C.R.S. § 18-3-102(a). She stated that, in her professional opinion, “McLuckie did have a mental health disorder that was often seen in battered women and other abuse victims who have a psychotic break with reality because of the extreme levels of fear that they will be killed by the abuse.” (1 id. Doc. 2, Ex. C, para. 3.) Like Dr. Bernhard, Dr. Walker did not definitively conclude that McLuckie met the legal definition of insanity.
Based on the information from the two psychological experts, the public defenders intended to attempt to negotiate a plea of guilty to second-degree murder. Were the case to proceed to trial, the public defenders intended to call both Walker and Bern-hard as expert witnesses. Before their investigation could proceed further, however, McLuckie filed a pro se motion on October 12, 1988, to dismiss her public defenders and appoint new counsel. Her father retained Donald Lozow as her defense attorney. While Lozow had some months to prepare, with the trial scheduled to begin on January 30,1989, he made few preparations for trial because he anticipated that the State would offer a plea bargain. For example, though he came to believe that his client was insane, Lozow never attempted to reach Dr. Bernhard, despite having her contact information. Lozow testified at a Colorado state post-conviction Rule 35(c) hearing that he never hired an investigator, and did not recall interviewing witnesses other than the landlord, including the next-door neighbor who had heard sounds of an argument.
Although Lozow did meet with Dr. Walker before trial to discuss Battered Woman Syndrome, Dr. Walker later testified that these meetings gave her the impression that Lozow did not understand the defense. Lozow reserved the right to call Dr. Walker as a witness, but told her that he planned to defend McLuckie by putting on a self-defense theory. Dr. Walker told Lozow that she disagreed with Lozow’s sequence of events, but that she remained willing to testify as to her psychological findings.
Despite Lozow’s assumption that the case would settle, it eventually became clear that the case would go to trial. It was only at this point, shortly before trial was scheduled to commence, that Lozow and McLuckie “started talking about the offense itself,” (4 Supp. R. at 11) and Lo-zow “started to really prepare for trial,” (4 id. at 9). After meetings with McLuckie and a discussion with Dr. Walker, Lozow began to have “serious doubts as to the state of [McLuckie’s] sanity.” (4 id. at 9-12.) Accordingly, Lozow sought leave to enter a plea of not guilty by reason of insanity on behalf of McLuckie on January 26, four days before the beginning of trial, explaining to the court that he had “confirmed [his] doubts with Lenore Walker” and that he had good cause to enter the new plea. (4 id. at 11.) His primary explanation for his failure to enter the plea earlier was that he had anticipated a plea bargain. He stated “maybe I was incompetent not to have brought it up” earlier. (4 id. at 17.) The court rejected the plea as untimely, but ordered, at Lozow’s request, that McLuckie be examined once again by Dr. Walker and a different mental-health expert, Dr. Gutterman. Neither Dr. Walker nor Dr. Gutterman was willing to state that McLuckie met the standards for insanity and/or diminished mental capacity in Colorado.
A jury trial began on January 30, 1989. Calling McLuckie to the stand, Lozow proceeded to present self defense as the theory of his ease. According to McLuckie, Vigil came to the house uninvited. She thought he had been drinking and she was [1196]*1196frightened because she was pregnant with another man’s child. Vigil began making threats to both her and her unborn child. McLuckie testified that Vigil raped her, threw one of her cats into the kitchen, and punched the television screen before approaching McLuckie in the kitchen. She testified that she hit him with a hammer, grabbed a knife, and “was just stabbing.” (5 id. at 920.) McLuckie further testified that, once he fell to the ground, she put handcuffs on Vigil because he was making noises. McLuckie explained that she did not tell the police because she was afraid they would not believe her, as she had previously been a victim in a rape case in which the defendant was acquitted.
A pathologist testified that there were approximately forty-nine stab wounds to Vigil’s head, back, and neck, that a stomach wound was inflicted post-mortem, and that Vigil had bled to death. Lozow had not interviewed the pathologist prior to trial. Two police officers testified that they did not observe any injuries, scratches, or bruises on McLuckie when she was placed under arrest. After deliberation, the jury returned a verdict of first-degree murder and abuse of a corpse. McLuckie was sentenced to life imprisonment on June 9, 1989. The Colorado Court of Appeals affirmed the conviction; one dissenter would have remanded for a trial on the issue of insanity, concluding that the trial court should have accepted the plea of not guilty by reason of insanity that was tendered four days before trial. People v. McLuckie, No. 89CA1195, slip op. at 13-14 (Colo.Ct.App. Dec. 12, 1991).
In September 1994, McLuckie was represented by new counsel in her state post-conviction proceedings brought pursuant to Colorado Rule of Criminal Procedure 35(c). A two-day evidentiary hearing was held before the same judge who had presided at trial. At the hearing, the public defenders who had initially worked on the case testified that a claim of self defense was inappropriate in light of the facts of the homicide and that expert assistance was necessary to help the jury understand a mental-state defense. A criminal-defense expert testified that the case clearly called for a mental-state defense and that a theory of self defense was completely inconsistent with the facts of the case. Lozow acknowledged that he failed to pursue any kind of mental-state defense (be it insanity, diminished mental capacity, or Battered Woman Syndrome) despite his belief that McLuckie was insane, but now claimed that he chose not use Dr. Walker at trial because she had told him about “devastating information” in her notes that he feared would inevitably be produced should he call her as a witness. (3 R. at 140.) The “devastating information” was alleged to consist of a statement written by McLuckie that she planned to kill the victim in the way she did. Although Dr. Walker testified on the first day of the two-day evidentiary hearing, she was not present on the second day when Lozow testified, and was unable to rebut this statement. However, in an affidavit later submitted to the federal district court in connection with McLuckie’s habeas petition, Dr. Walker explained that by “devastating information,” Lozow may have been referring to a note in Dr. Walker’s files indicating that months before the murder, McLuckie had done some research in the library on toxic substances. (1 id. Doe. 2, Ex. C at 6.) According to Dr. Walker, the note contained nothing-about planning the murder and, in any event, the eventual homicide had nothing to do with poisonous substances.
The trial court denied McLuckie’s Rule 35(c) motion, and the Colorado Court of Appeals affirmed, holding that “even if ... an effective attorney would have presented [Dr. Walker’s] expert testimony, we cannot conclude that there is a reasonable proba[1197]*1197bility of a different result.” People v. McLuckie, No. 95CA2212, slip op. at 11 (Colo.Ct.App. Jan. 22, 1998). The court reasoned that the possibility of potentially devastating information coming to light if Dr. Walker were called to testify precluded a determination that Lozow’s failure to call Dr. Walker resulted in prejudice. Id. at 8, 11. Certiorari was denied by the Colorado Supreme Court, with Justice Bender dissenting, who noted that he would grant certiorari as to whether “defense counsel’s indolent and haphazard representation fell well below constitutional standards of effective assistance of counsel.” McLuckie v. People, No. 98SC167, slip op. at 1 (Colo. Aug. 24, 1998). Having exhausted her state remedies, McLuckie filed an application in federal district court for a writ of habeas corpus under 28 U.S.C. § 2254. In denying McLuckie’s ha-beas petition, the district court concluded that while McLuckie’s counsel was indeed ineffective, she did not meet the prejudice prong of Strickland because “it is too much to say that Dr. Walker’s testimony based solely on Ms. McLuckie’s statements to her would have probably altered the outcome by a return of a verdict of less than first degree murder.” McLuckie v. Abbott, No. 99-M-1575, slip op. at 8 (D.Colo. Dec. 28, 2001).
II
Because McLuckie filed her § 2254 petition in the district court after the effective date of the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”), AEDPA’s provisions apply to this appeal. See Hooks v. Ward, 184 F.3d 1206, 1213 (10th Cir.1999). Under AEDPA, the appropriate standard of review depends on whether a claim was decided on the merits in state court. “If the claim was not heard on the merits by the state courts, and the federal district court made its own determination in the first instance, we review the district court’s conclusions of law de novo and its findings of fact, if any, for clear error.” LaFevers v. Gibson, 182 F.3d 705, 711 (10th Cir.1999) (interpreting § 2254(d)). If a petitioner’s claims were adjudicated on their merits by the state courts, she will be entitled to federal habe-as relief only if she can establish that the state court decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States,” 28 U.S.C. § 2254(d)(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). When reviewing a state court’s application of federal law, we are precluded from issuing the writ simply because we conclude in our independent judgment that the state court applied the law erroneously or incorrectly. Rather, we must be convinced that the application was also objectively unreasonable. Williams, 529 U.S. at 412, 120 S.Ct. 1495. In reviewing McLuckie’s petition, we are also mindful that “[a] determination of factual issues made by a State court shall be presumed to be correct” and that “[t]he applicant shall have the burden of rebutting the presumption of correctness by clear and convincing evidence.” § 2254(e)(2).
Ill
The clearly established federal law controlling the issues raised in this case is Strickland v. Washington, under which a defendant is denied her constitutional right to effective assistance of counsel when: (1) counsel’s performance was deficient; and (2) the deficient performance prejudiced the defendant. 466 U.S. at 687, 104 S.Ct. 2052. Under the first prong, we look to whether “counsel’s representation fell below an objective standard of reasonableness,” meaning “reasonableness under prevailing professional norms.” Id. at 688, [1198]*1198104 S.Ct. 2052. “Judicial scrutiny of counsel’s performance must be highly deferential,” and courts are instructed to “indulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance.” Id. at 689, 104 S.Ct. 2052.
Under the second prong of Strickland, the defendant must demonstrate a “reasonable probability” that counsel’s performance prejudiced the defendant, meaning a probability “sufficient to undermine confidence in the outcome.” Id. at 694, 104 S.Ct. 2052. This is less than' a preponderance of the evidence, for “a defendant need not show that counsel’s deficient performance more likely than not altered the outcome of the trial.” Fisher v. Gibson, 282 F.3d 1283, 1307 (10th Cir.2002) (emphasis added) (quotation omitted).
A
We first address the deficient-performance prong of Strickland. The Colorado Court of Appeals denied McLuckie’s motion for post-conviction relief based on a conclusion that McLuckie was not prejudiced by Lozow’s performance. It did not expressly determine that Lozow’s performance was adequate under Strickland. Nevertheless, it is arguable that the Colorado Court of Appeals did decide this question in light of its determination that Lozow’s decision not to call Dr. Walker was an appropriate tactical one. Thus, we assume that the Colorado Court of Appeals determined that Lozow’s performance was constitutionally adequate and we consider whether this determination was an unreasonable application of Strickland.
Maintaining that Lozow’s performance did not fall below a reasonable standard, the state argues that, given Lozow’s testimony at the Rule 35(c) hearing that he did not call Dr. Walker to testify because he feared that damaging information contained in her notes would come into evidence, his decision not to pursue a Battered-Woman-Syndrome defense was a reasonable tactical trial decision. While the record is somewhat ambiguous as to whether the trial court had, in fact, required production of Dr. Walker’s notes,1 the possibility remained that the information contained in the notes could come to light through cross-examination had Lo-zow called Dr. Walker to testify.
Nevertheless, however legitimate Lo-zow’s fear of putting Dr. Walker on the stand may have been, Lozow made no attempt whatsoever to follow up with Dr. Bernhard, who had concluded that McLuckie was suffering from “severe emotional problems” and may have a “meritorious mental-state defense.” (1 R. Doc. 19 at 2.) Moreover, Lozow’s performance calls into question far more than a failure to call particular witnesses. Lozow’s attempt to enter a plea of not guilty by reason of insanity four days before trial suggests that it was clear, even to Lozow, that the case called for some kind of mental-state defense and that it was largely Lozow’s initial failure to prepare and investigate that led to a situation where it was too late to put on a proper mental-state defense. See Kimmelman v. Morrison, 477 U.S. [1199]*1199365, 384, 106 S.Ct. 2574, 91 L.Ed.2d 305 (1986) (“Because [the adversarial] testing process generally will not function properly unless defense counsel has done some investigation into the prosecution’s case and into various defense strategies, [the Supreme Court has] noted that counsel has a duty to make reasonable investigations or to make a reasonable decision that makes particular investigations unnecessary.” (quotation omitted)); Battenfield v. Gibson, 236 F.3d 1215, 1228-29 (10th Cir.2001) (holding that defense counsel’s failure to investigate rendered resulting strategy unreasonable); Seidel v. Merkle, 146 F.3d 750, 756 (9th Cir.1998) (indicating that where counsel has actual or constructive notice of a client’s mental problems, he has a duty to conduct an investigation in order to be able to make an informed decision regarding the possibility of a mental-state defense). Lozow certainly had actual and constructive notice of his client’s mental problems. However, by the time Lozow realized that a mental-state defense was appropriate, his erratic and belated efforts to prepare only days before trial were too little, too late.
After careful review of the record, we have little difficulty agreeing with the district court that Lozow’s performance fell below an objective standard of reasonableness. The record reflects a complete lack of preparation and investigation, resulting in a defense that was clearly inconsistent with the facts of the case, and little investigation even for the defense that was presented. As noted, the objective facts of the case were undisputed, and the only question to be resolved at trial was whether McLuckie would be convicted of first-degree murder, second-degree murder, or manslaughter. Given these circumstances, and considering the bizarre and disturbing nature of the case, as well as indications from two psychological experts that McLuckie suffered from severe mental problems, a failure to timely investigate a client’s mental state, let alone a failure to assert a mental-state defense at trial, falls well below an objective standard of reasonableness. See Seidel, 146 F.3d at 755-56 (noting that counsel has' a duty to make adequate investigations into a mental-state defense where there are abundant signs that a client suffers from mental illness).
In a case where there was no issue beyond that of McLuckie’s mental state, Lozow’s performance deprived her of any chance of convincing the jury that she did not have the requisite mental state for a first-degree murder conviction. We agree with the district court that Lozow’s performance clearly fell short of the constitutional minimum under Strickland. To the extent that the Colorado Court of Appeals held to the contrary, that conclusion was an unreasonable application of Strickland to the facts of this case.
B
We next address the prejudice prong of Strickland. The Colorado Court of Appeals concluded that McLuckie was not prejudiced by Lozow’s performance within the meaning of Strickland. Because this is an issue the Colorado Court of Appeals adjudicated, we must determine whether the Colorado courts made an objectively unreasonable application of the prejudice prong of Strickland to the facts of this ease.
At the heart of the Colorado Court of Appeals’ conclusion that McLuckie suffered no prejudice from Lozow’s failure to put Dr. Walker on the stand is Lozow’s testimony at the Rule 35(c) hearing, at which he claimed that he did not call Dr. Walker because Dr. Walker allegedly had notes indicating that McLuckie had planned the killing in the manner in which it was eventually carried out. People v. McLuckie, No. 95CA2212, slip op. at 8-9 (Colo.Ct.App. Jan. 22, 1998). This fact, [1200]*1200reasoned the state court, makes it impossible to “conclude that there is a reasonable probability that presentation of the expert’s testimony would have changed the outcome of the case.”2 Id. at 11.
Our review of the record suggests that the possible negative repercussions of calling Dr. Walker to testify are less clear-cut.3 Even if Dr. Walker’s notes were introduced and they did contain information suggesting that McLuckie planned to commit murder, Dr. Walker later explained to the district court that any information in her notes did not change her opinion of the case and that she was prepared to explain that to a jury. In her affidavit, Dr. Walker explained that McLuckie had researched the use of poisons at the library some months before the murder, but that it was normal for battered women to contemplate killing their abusers. In any event, Dr. Walker observes that this does not demonstrate that McLuckie planned the killing because the use of poison did not- feature in the homicide.
Dr. Walker’s testimony could have been helpful to the defense. For'example, the primary evidence presented in McLucMe’s defense was her own trial testimony, rendering her credibility a central issue. In its closing argument, the state attacked McLuckie’s credibility on the grounds of inconsistency and memory loss, arguing that “credibility is crucial in this case,” (1 Supp. R. at 1312), and telling the jury that “people who conveniently claim a lack of memory are not to be believed,” (1 id. at 1317). Dr. Walker’s testimony could have been useful to help explain gaps and inconsistencies in McLuckie’s story to the jury as being typical of people suffering from [1201]*1201Battered Woman Syndrome and Post-Traumatic Stress Disorder, and would have helped to show that the degree of McLuckie’s fear was reasonable. In addition, the prosecution made references during the trial to McLuckie’s communications with a mental-health expert, possibly further calling her credibility into question, but the jury was never able to hear from a mental-health expert who could have explained the nature of those communications and resultant findings.
In response, the state argues that even if Dr. Walker had offered testimony on Battered Woman Syndrome at trial, it is unlikely that it would have changed the result because: (1) Battered Woman Syndrome was not an established defense in Colorado at the time; and (2) there was no predicate evidence to form a proper foundation for a Battered Woman Syndrome defense (police reports, documented history of abuse, etc.), rendering Dr. Walker’s testimony potentially inadmissible. Assuming that an expert in Battered Woman Syndrome can be essential to a jury’s understanding of the defendant’s testimony,4 the state nevertheless argues that, in the instant case, the lack of such testimony resulted in no prejudice.
As to the claim that a Battered-Woman-Syndrome defense was not generally accepted in Colorado until after the time of McLuckie’s trial, even without such terminology to describe McLuckie’s situation, presentation of the psychological evidence regarding McLuckie’s severe mental problems might have had a significant influence on the jury’s verdict. See Turner, 158 F.3d at 458 (explaining that, even in the absence of terminology such as Battered Spouse Syndrome to describe the defendant’s situation, presentation of psychiatric evidence could have had a strong influence on the jury’s verdict). However, the claim that there was no predicate evidence to form a proper foundation for a Battered-Woman-Syndrome defense is more troubling. While trial courts certainly have broad discretion to admit or prohibit expert witness testimony, foundational evidence is a factor in determining admissibility. See Lanari v. People, 827 P.2d 495, 504 (Colo.1992) (en banc) (explaining that, in exercising its discretion under Colorado Rule of Evidence 702 to admit-or prohibit testimony by expert witnesses in criminal cases, the trial court should consider, inter alia, “the. sufficiency and extent of the foundational- evidence upon which the expert witness’ ultimate conclusion is to be based”). So far as the record indicates, the only evidence of McLuckie’s Battered Woman Syndrome was Dr. Walker’s testimony based on her interviews with McLuckie. McLuckie has not argued that such evidence, in fact, exists. She has not, for example, argued that evidence of Vigil’s abuse would have been discovered had Lozow conducted a proper investigation. Thus, Dr. Walker’s testimony alone might not have persuaded the jury that McLuck-ie had been abused by Vigil, and may not have been admissible without proper foundation.
McLuckie argues that we should not limit our prejudice review to the possible effects of Battered Woman Syndrome and Dr. Walker’s testimony on the outcome of the trial. She notes that Dr. Bernhard, the first expert to examine McLuckie, (1) found symptoms more severe than did Dr. Walker, ’(2) suggested an impaired mental-condition defense was warranted, and (3) recommended further evaluation. However, the results of Dr. Bernhard’s examination were given to Dr. Walker, who, after [1202]*1202conducting further evaluation, was unable to state that McLuckie suffered from any mental disease or defect, a predicate for a plea of diminished mental capacity. Like Dr. Walker and Dr. Gutterman, Dr. Bern-hard did not conclude that McLuckie met the insanity standards in Colorado. Thus, it is far from clear whether Dr. Bernhard’s testimony would have made any difference at trial.
Given that proper investigation and preparation of a mental-state defense, followed by the presentation of a mental-state defense at trial, could have- proyided the jury with an alternative explanation for McLuckie’s actions, we have concerns about the negative effects of trial counsel’s performance on the outcome of the case. However, even were we to conclude that the weight of these factors is “sufficient to undermine confidence in the outcome,” Osborn v. Shillinger, 861 F.2d 612, 626 (10th Cir.1988), we may not issue the writ simply because we conclude in our independent judgment that the state court applied federal law erroneously or incorrectly. Williams, 529 U.S. at 411, 120 S.Ct. 1495. Rather, we must be convinced that the application was also “objectively unreasonable.,”5 Id, at 409, 120 S.Ct. 1495. To “substitute[ ][our] own judgment for that of the state court” would be to contravene AEDPA’s statutory mandate. Woodford v. Visciotti, 537 U.S. 19, 123 S.Ct. 357, 360, 154 L.Ed.2d 279 (2002).
Recognizing the ambiguities surrounding Dr. Walker’s testimony, including the lack of evidence, beyond McLuckie’s statements to Dr. Walker, to support a Battered-Woman-Syndrome defense, and the fact that no mental-health expert who examined McLuckie was able to state that she met the standards of either insanity or diminished mental capacity under Colorado law, it is simply too much to say that the Colorado Court of Appeals’ determination that the second prong of Strickland was not met is “objectively unreasonable.” We therefore conclude that, under AED-PA, McLuckie has not demonstrated that we are empowered to grant the relief that she seeks.
IV
For the foregoing reasons, the judgment of the district court denying habeas relief is AFFIRMED. Appellant’s motion to supplement the record on appeal is granted.