OPINION
KAREN NELSON MOORE, Circuit Judge.Petitioner-Appellant Gregory Guyton Amunga (“Amunga”) was convicted by a Michigan jury of second-degree murder and sentenced to twenty-five-to-fifty years’ imprisonment. He now appeals the district court’s denial of his petition for a writ of habeas corpus, arguing that the trial court, the prosecutor, and defense counsel made various constitutional errors. Because his claims lack merit, we AFFIRM the district court’s decision.
I
On January 23, 1990, at approximately 5:30 a.m., Amunga arrived home by taxicab after a long night of celebrating a large buy-out payment from General Motors for thirteen years of employment. Having spent his ready cash, Amunga asked the driver to wait while he got money to pay his fare. Amunga soon discovered the body of his wife Wanda Anunga (“Wanda”), who had died as a result of multiple stab wounds. Amunga ran outside and told the cab driver to call the police; he then went back inside and called several family members before calling the police himself.
Once the police secured the murder scene, Amunga was taken to Edward R. Sparrow Hospital, where he was treated for a severe cut on his right hand.1 Shortly after 8:00 a.m., Robert W. Fisher (“Fisher”), a detective with the East Lansing Police Department who was designated as the chief investigator of Wanda’s murder, met the intoxicated and upset Amunga at the hospital and advised him of his Miranda rights, which Amunga affirmatively waived. Amunga was then transported to the police station, where he was questioned and fingerprinted and his bloody clothing was seized for evidence. Fisher and Kevin Patrick Daley (“Daley”), a fellow detective with the East Lansing Police Department, then took Amunga home.
On January 31, 1990, Fisher obtained information from Anthony Lewis Malone (“Malone”), who had been with Amunga for much of the evening of Wanda’s murder, that pointed to Amunga’s involvement in the homicide.2 At approximately 11:30 *535p.m., Fisher and Daley picked Amunga up for questioning. According to Fisher, Amunga had been drinking and smelled of alcohol but did not appear to be intoxicated. Fisher gave Amunga his Miranda warnings at 11:47 p.m., which Amunga acknowledged in writing. After Amunga agreed to submit to a polygraph test, Fisher drove Amunga to the Michigan State Police, where Amunga signed another waiver of his Miranda rights at 1:28 a.m.
On February 1, 1990, at approximately 2 a.m., Sergeant John Joseph Palmatier (“Palmatier”), a forensic specialist then studying for his doctorate, administered a polygraph test to Amunga, which took about forty minutes. Palmatier told Amunga that the test results pointed to him as Wanda’s murderer and examined him for the next four hours. At approximately 6:30 a.m., Fisher and Daley took over questioning; they obtained another written waiver and interviewed Amunga for another two hours. During this interrogation, Amunga stated that he and Malone had observed an individual coming out of his home in the early hours of January 23, 1990, when he went inside and argued with Wanda about getting more money. Amunga also related that after Malone left, Wanda took a knife from the kitchen and flicked it at him, but that he got the knife away. He then remembered Wanda “being on the floor kicking up at him and the knife being in his hand.” Joint Appendix (“J.A.”) at 882. However, Amunga did not state that he had stabbed Wanda. At 9:30 a.m., Amunga was placed under arrest.
Amunga was charged with first-degree murder. On October 3, 1990, Amunga filed a motion to suppress his statements to the police, which the trial court denied after holding a hearing under People v. Walker, 374 Mich. 331, 132 N.W.2d 87 (Mich.1965), on the question of voluntariness. After an eight-day jury trial, Amun-ga was convicted of second-degree murder; he was later sentenced to a prison term of twenty-five to fifty years. Amunga filed a timely appeal to the Michigan Court of Appeals, which remanded the case for an evidentiary hearing. On May 6, 1994, after holding the hearing, the trial court denied Amunga’s motion for a new trial. On August 18, 1995, the Michigan Court of Appeals affirmed the trial court’s judgment in a split decision. On March 25, 1997, the Michigan Supreme Court denied leave to appeal.
On March 19, 1998, Amunga filed, pro se, a petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254, raising seven grounds for relief. The matter was referred to a magistrate judge, who recommended after holding a hearing that the district court deny Amunga’s petition. On September 11, 2000, the district court adopted the magistrate judge’s report and recommendation, except for its reliance on the “reasonable jurist” standard that had been abrogated by [Terry] Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), and dismissed the case. On October 25, 2000, the district court denied Amunga’s motion for a certifi*536cate of appealability (“COA”). Amunga appealed. On March 28, 2001, we granted Amunga’s motion for a COA as to these claims: “1) whether the trial court should have suppressed involuntary statements he made to the police; 2) whether the trial court improperly refused to admit into evidence the videotape of his interrogation; 3) whether the prosecutor committed misconduct by introducing negative character evidence; 4) whether the prosecutor committed misconduct by eliciting false testimony from a witness that no promises were made concerning potential charges; and 5) whether his trial counsel rendered ineffective assistance by failing to present expert testimony regarding the psychological effect of Amunga’s lengthy interrogation.”
II
In a habeas corpus proceeding, we review a district court’s legal conclusions de novo and factual findings for clear error. Ford v. Curtis, 277 F.3d 806, 808 (6th Cir.), cert, denied, 2002 WL 1224957 (Oct. 7, 2002). Because Amunga filed his habe-as petition after the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”) became effective, this case is governed by AEDPA. Under those provisions, we may not grant a writ of habe-as corpus for any claim that was adjudicated on the merits in state court unless the adjudication:
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or
(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d)(l)-(2). In addition, the findings of fact made by a state court are presumed to be correct and can be contravened only if the habeas petitioner can show by clear and convincing evidence that the state court’s factual findings were erroneous. Id. § 2254(e)(1).
In Williams, the Supreme Court interpreted § 2254(d)(1) as requiring a distinction between decisions that are “contrary to” and those that are an “unreasonable application of’ clearly established Supreme Court precedent. Williams, 529 U.S. at 405. A state court decision is “contrary to” Supreme Court precedent “if the state court arrives at a conclusion opposite to that reached by [the Supreme] Court on a question of law,” or “ if the state court confronts facts that are materially indistinguishable from a relevant Supreme Court precedent” and arrives at a different result. Id. A state court decision is also “contrary to” Supreme Court precedent if the state court “applies a rule that contradicts the governing law set forth” in those precedents. Id.
A state court decision involves an “unreasonable application of’ clearly established Supreme Court precedent “if the state court identifies the correct governing legal principle from [the] Court’s decisions but unreasonably applies that principle to the facts of the ... case.” Id. at 413. We may not overturn a state court decision simply because we conclude that the state court incorrectly applied Supreme Court precedent — the state court must have applied the relevant Supreme Court precedent in an objectively unreasonable manner. Id. at 411.
In reviewing a state court decision under AEDPA, we must look only to the Supreme Court holdings that existed at the time of the state court’s decision. Id. at 412. We may not base our decision on Supreme Court dicta or the decisions of the courts of appeals. See id.
*537A
Amunga argues that the trial court deprived him of his due process rights by allowing the use at trial of his statements to the police, which Palmatier allegedly coerced.3 Under clearly established Supreme Court precedent, “certain interrogation techniques, either in isolation or as applied to the unique characteristics of a particular suspect, are so offensive to a civilized system of justice that they must be condemned under the Due Process Clause of the Fourteenth Amendment.” Miller v. Fenton, 474 U.S. 104, 109, 106 S.Ct. 445, 88 L.Ed.2d 405 (1985). The totality of the circumstances determines the voluntariness of a confession. See Withrow v. Williams, 507 U.S. 680, 693, 113 S.Ct. 1745, 123 L.Ed.2d 407 (1993) (listing as “potential circumstances ... the crucial element of police coercion, the length of the interrogation, its location, its continuity, the defendant’s maturity, education, physical condition, and mental health,” as well as a failure to comply with the requirements of Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966) (internal citations omitted)).
Confessions are involuntary only if the defendant can establish “the crucial element of police overreaching.” Colorado v. Connelly, 479 U.S. 157, 163, 107 S.Ct. 515, 93 L.Ed.2d 473 (1986). On occasion, the Supreme Court has deemed certain methods and situations to be “inherently coercive.” See, e.g., Oregon v. Elstad, 470 U.S. 298, 312 n. 3, 105 S.Ct. 1285, 84 L.Ed.2d 222 (1985) (collecting cases); Ashcraft v. Tennessee, 322 U.S. 143, 153-54, 64 S.Ct. 921, 88 L.Ed. 1192 (1944) (defendant “held incommunicado, without sleep or rest” for thirty-six hours while questioned by relays of officers “without respite”). The use of a confession that is “not the product of a rational intellect and a free will” also constitutes a denial of due process. Mincey v. Arizona, 437 U.S. 385, 398, 98 S.Ct. 2408, 57 L.Ed.2d 290 (1978) (quotation omitted).
In this case, Amunga contends that Pal-matier’s interrogation techniques coerced him into making certain admissions. At the suppression hearing, the trial court admitted that it was “not trained in psychology ... [or] psychological methods” before concluding that Palmatier’s interrogation did not coerce Amunga’s statements. J.A. at 722.4 On remand, the trial court heard from Dr. Michael F. Abram-sky (“Abramsky”), who testified (1) that Amunga at the time of interrogation “was in a vulnerable, psychological state, due to recent sleeplessness, alcohol and drug use and the loss of his wife,”5 and (2) that *538Palmatier used “coercive and persuasive [interrogation] techniques,” which consisted of(a) building up his own credibility, (b) characterizing polygraph tests as infallible, and (c) telling Amunga that the polygraph test showed that he was lying, thus (d) creating cognitive dissonance that forced Amunga to make compromises between his belief that he did not murder Wanda and the polygraph test result that he was not innocent. J.A. at 1318-29. Dr. Abramsky also suggested that Amunga became “exceedingly dependent and needy of pleasing” Palmatier because Palmatier “presented] hisself [sic] as having life or death control over [Amunga]” and that Palmatier’s questions could have created false memories in Amunga. J.A. at 1330.
Under AEDPA, the scope of our review is limited to the question whether a state court decision “was contrary to, or involved an unreasonable application of, clearly established Federal law.” 28 U.S.C. § 2254(d)(1). Dr. Abramsky’s report and testimony were in the record before the Michigan Court of Appeals, which seems to have relied instead on its own review of the videotapes and the transcript of the suppression hearing in finding that, under the totality of the circumstances, Amunga’s statements were voluntarily made. It is arguable that this decision was contrary to Leyra v. Denno, 347 U.S. 556, 74 S.Ct. 716, 98 L.Ed. 948 (1954), where the Supreme Court granted habeas relief to a defendant who at the time of his confession was “already physically and emotionally exhausted” and whose “ability to resist interrogation was broken to almost trance-like submission by use of the arts of a highly skilled psychiatrist.” Id. at 561. It is also arguable that the apparent failure of the Michigan Court of Appeals to consider Dr. Abramsky’s expert testimony was an unreasonable application of the totality-of-the-circumstances test, assuming that the coercive force of Palma-tier’s interrogation techniques could not be properly evaluated without understanding their psychological underpinnings. See Mincey, 437 U.S. at 401 (“Determination of whether a statement is involuntary ... requires careful evaluation of all the circumstances of the interrogation.”).
However, the limited scope of habeas review under AEDPA precludes us from granting relief on this claim. First, the facts of this case are materially distinguishable from those of Leyra, where the confession came “as the climax of days and nights of intermittent, intensive police questioning.” Leyra, 347 U.S. at 561. Second, although the Michigan courts may not have considered the psychological effects of Palmatier’s interrogation techniques, they did look at the length, location, and conditions of the interrogation, the nature of Amunga’s answers, and Amunga’s mental capacity. The expert testimony that Dr. Abramsky provided certainly could have added to the Michigan courts’ understanding of the totality of the circumstances, but it was not inherently necessary. We thus conclude that the totality-of-the-eircumstances test was not unreasonably applied.
Amunga also claims that Palmatier violated his Miranda rights by continuing to question him after he “requested the interrogation be stopped and he be taken to his grandmother’s house.” Appellant’s Br. at 17. In Michigan v. Mosley, 423 U.S. 96, 96 S.Ct. 321, 46 L.Ed.2d 313 (1975), the Supreme Court held “that the admissibility of statements obtained after the person in custody has decided to remain silent depends under Miranda on *539whether his ‘right to cut off questioning’ was ‘scrupulously honored.’” Id. at 104. Thus the first, factual question is whether Amunga decided to remain silent. In denying the suppression motion, the trial court made the following finding: “Now, the Court finds that, despite being given numerous opportunities to conclude the exam, [] the Defendant apparently either desiring to find out what happened, or to, if you will, persuade the examiners of his version of the events, continued to respond and participate in this inquiry.” J.A. at 722.
In the absence of clear and convincing evidence to the contrary, we must presume this factual finding to be correct. Our review of the videotapes bears out the trial court’s finding. For example, after Amun-ga asks to see his grandmother or to be taken to her house, Amunga comments that his mind is a total blank, but he continues to talk about how he is feeling. About thirty minutes later, Amunga tells Palmatier to stop, which Palmatier does, but then Amunga starts talking again about how he cannot remember, even though he keeps going over his memories. Because these statements do not indicate that Amunga decided to remain silent, we do not grant habeas relief on this claim.
B
Next, Amunga argues that the trial court deprived him of his rights to present a defense and to confront the witnesses against him by “refus[ing] to admit into evidence the entire videotape of [his] interrogation.” Appellant’s Br. at 27. It appears from the record that the jury did hear Fisher and Daley’s interrogation of Amunga. This videotape was played during the prosecutor’s direct examination of Fisher. Defense counsel then moved that the trial court order the prosecution to play the videotape of Palmatier’s interrogation, which preceded Fisher and Daley’s interrogation, on the ground “that right now the Jury is seeing what appears to be a very antiseptic admission.” J.A. at 900. The trial court denied the motion, finding that the videotape of Palmatier’s interrogation contained “four hours of discussion of polygraph,” which was “simply inadmissible testimony.” J.A. at 898, 901.6
In Crane v. Kentucky, 476 U.S. 683, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986), the Supreme Court held that the trial court’s “blanket exclusion of the proffered testimony about the circumstances of [the defendant’s confession deprived him of a fair trial.” Id. at 690. This case does not involve such an absolute exclusion. Defense counsel closely questioned Palmatier about the interrogation, essentially summarizing the contents of the videotape “time frame by time frame.” J.A. at 1282 (Bennett Test.). He also reminded the jury of the circumstances of Amunga’s statements in his closing argument.
Amunga now argues that his defense was hampered because the jury could not “view the interrogation [he] experienced.” Appellant’s Br. at 30. Under clearly established Supreme Court precedent, state evidentiary rules do not abridge a defendant’s right to present evidence as “long as they are not arbitrary or disproportionate to the purposes they are designed to serve.” United States v. Scheffer, 523 U.S. 303, 308, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998) (quotation omitted). *540“[T]he exclusion of evidence [is] unconstitutionally arbitrary or disproportionate only where it has infringed upon a weighty interest of the accused.” Id.; see also id. at 315 (stating that the exclusion of evidence would be unconstitutional if it “significantly undermined fundamental elements of the defendant’s defense”). In Wong v. Money, 142 F.3d 313 (6th Cir.1998), we held that an Ohio rule against the use of expert psychiatric testimony to show diminished capacity did not abridge the defendant’s right to present a defense because it neither “preclude[d her] from introducing any factual evidence” nor “prohibit[ed her] from testifying in her own behalf.” Id. at 323, 325. The same analysis applies in this case. The trial court apparently excluded the videotape of Palmatier’s interrogation based on Michigan law that references to polygraph tests are inadmissible. See People v. Ray, 431 Mich. 260, 430 N.W.2d 626, 628 (Mich.1988); People v. Nash, 244 Mich.App. 93, 625 N.W.2d 87, 91 (Mich. Ct.App.2000) (per curiam).7 It cannot be said that the rule against polygraph testimony is arbitrary or disproportionate to the purpose of excluding unreliable evidence.8 Moreover, Amunga was able to introduce the facts of Palmatier’s interrogation and testify in his own behalf.
Amunga also contends that he “was unable [to] confront, [to] impeach and to cross-examine Sgt. Palmatier fully” because defense counsel was limited to “verbally challenging] Sgt. Palmatier’s inaccurate and misleading testimony.” Appellant’s Br. at 28-29. As discussed above, defense counsel was afforded and took advantage of the opportunity to cross-examine Palmatier. Amunga essentially argues that this opportunity was inadequate because defense counsel could not effectively rebut Palmatier’s evasiveness, if not actual perjury, on cross-examination. However, the Supreme Court has held that the Confrontation Clause generally “guarantees an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish.” Delaware v. Fensterer, 474 U.S. 15, 20, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985) (per curiam). The Fensterer Court specifically noted that cross-examination contains the following “assurances of reliability”: “the factfinder can observe the witnesses] demeanor under cross-examination, and the witness is testifying under oath and in the presence of the accused.” Id. Therefore, we hold that the Michigan Court of Appeals did not apply Supreme Court precedent in an objectively unreasonable way when it concluded that Amunga was sufficiently able to challenge the reliability of his statements to the police through defense counsel’s “extensive[] cross-examin[ation]” of Palmatier. J.A. at 172.
*541c
The relevant question in cases of alleged prosecutorial misconduct “is whether the prosecutors’ comments ‘so infected the trial with unfairness as to make the resulting conviction a denial of due process.’ ” Dar-den v. Wainwright, 477 U.S. 168, 181, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986) (quoting Donnelly v. DeChristoforo, 416 U.S. 637, 643, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974)).
1
Amunga first argues that the prosecutor committed misconduct by introducing negative character evidence, which violated “[a] fundamental rule” against the use of propensity evidence. Appellant’s Br. at 34. Evidentiary rules, however, are a matter of state law, and the Michigan Court of Appeals found no error. Because “it is not the province of a federal habeas court to reexamine state-court determinations on state-law questions,” Gall v. Parker, 231 F.3d 265, 307 (6th Cir.2000) (quoting Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991)), cert, denied, 533 U.S. 941, 121 S.Ct. 2577, 150 L.Ed.2d 739 (2001), we cannot grant habeas relief on this claim.
2
Amunga also claims that the prosecutor committed misconduct by eliciting false testimony from Malone that no promises were made concerning potential charges for Wanda’s murder. At trial, Malone testified on direct examination that he had not been “promised anything by the prosecution or the police to testify here today” or “granted immunity to testify here today.” J.A. at 773. Malone testified on cross-examination that he had not been promised immunity “[f]or getting rid of evidence [or] for lying to the authorities” and that he had not yet been charged “for any of this wrongdoing.” J.A. at 778.
In denying Amunga’s motion for a new trial, the trial court made the following factual finding:
The alleged promise made to Tony Malone can best be summarized by Tony Malone himself when he stated “I am saying I wasn’t promised, you know. The promise [that] was made to me was saying they wouldn’t charge me with murder if I did not commit the murder .... ” The Court finds that this was not much of a “promise”, because the converse would be true that if Tony Malone committed the murder, he would have been charged with the murder. Therefore, the Court finds Defendant’s averments to be without merit.
J.A. at 167 (internal citation omitted). Absent clear and convincing evidence to the contrary, we must presume the trial court’s finding to be correct. Amunga simply describes Malone’s explanation as “ridiculous” and questions why Malone was not prosecuted for his actions in this case. Appellant’s Br. at 38.9 Because this *542argument does not constitute clear and convincing evidence that any promise was made to Malone in exchange for his testimony, we do not grant habeas relief on this claim.
D
Finally, Amunga argues that he was deprived of his constitutional right to effective assistance of counsel when defense counsel “failfed] to present testimony by an expert witness to explain to the trial court and to the jury the psychological effect of Sgt. Palmatier’s extensive interrogation on the voluntariness, reliability and credibility of Amunga’s subsequent statement to police.” Appellant’s Br. at 39-40. To prove that counsel afforded unconstitutionally ineffective assistance, Amunga must establish that his attorney’s performance was deficient and that such deficiency prejudiced his defense. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2dd 674 (1984). To establish ineffectiveness, a “defendant must show that counsel’s representation fell below an objective standard of reasonableness.” Id. at 688. The objective standard of reasonableness is a “highly deferential” one and includes “a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance.” Id. at 689.
On October 3, 1990, defense counsel filed a motion to suppress Amunga’s statements to the police, expecting the trial court to grant the motion because “the proofs were so overwhelming that the confession was under duress.” J.A. at 1270 (Bennett Test.). At the suppression hearing, defense counsel offered the transcript of Dr. Abramsky’s testimony in People v. DeLi-sle, 183 Mich.App. 713, 455 N.W.2d 401 (Mich.Ct.App.1990) (per curiam), where the Michigan Court of Appeals affirmed the trial court’s decision to suppress as involuntary a statement made after Palmatier interrogated the defendant in that case. See id. at 403-05. The trial court granted the prosecutor’s motion to strike the transcript, concluding that “Doctor Abramsky’s examination of Mr. De[L]isle ... has no connection with this case.” J.A. at 552. The trial court then suggested that defense counsel contact Dr. Abramsky “and get your own examination.” J.A. at 552. On Friday, October 19, 1990, after hearing from several (but no expert) witnesses, the trial court found that Amunga’s statements were voluntary and denied the motion to suppress.
On Monday, October 22, 1990, the day before the trial began, defense counsel asked the trial court to appoint a psychologist or psychiatrist to review Amunga’s videotaped statements. The trial court asked why defense counsel had waited until then to make this motion: “This tape has been around since, what, February? Isn’t it a bit late now to examine the tapes here on the eve of trial?” J.A. at 736. The prosecutor observed that defense counsel’s request seemed to be an attempt to “present testimony to the jury that it should have presented during the motion to suppress.” J.A. at 741. After asking defense counsel for legal precedent, the trial court denied the motion. Tr. I at 17. Although the jury never heard from a psychologist, defense counsel did question Amunga and the police at trial about Amunga’s sobriety and his physical and mental condition at the time he was interrogated.
*543In Michigan, the trial court decides whether a statement was made voluntarily; the jury’s determination is “limited to truthfulness, i.e., weight and credibility.” Walker, 132 N.W.2d at 91; see also People v. Cipriano, 431 Mich. 315, 429 N.W.2d 781, 790 (Mich.1988). Amunga maintains that defense counsel was constitutionally deficient in failing to present expert testimony about his psychological state after Palmatier’s interrogation to the trial court, which could have found his statements to be involuntary and suppressed them, or to the jury, which could have found the voluntary statements to be untruthful. We have previously indicated that the failure of defense counsel to engage a competent psychiatrist would be relevant in determining whether a defendant received ineffective assistance of counsel. Skaggs v. Parker, 235 F.3d 261, 267 n. 2 (6th Cir.2000), cert, denied, — U.S.-, 122 S.Ct. 322, 151 L.Ed.2d 241 (2001). Skaggs, however, involved an indigent criminal defendant’s constitutional right to have access to psychiatric assistance under Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985). This case does not involve such a right. Instead, Amunga believes that he received ineffective assistance because the expert testimony that defense counsel failed to present would have aided the trial court and the jury in evaluating the volun-tariness and truthfulness of Amunga’s statements to the police. Cf. People v. Hamilton, 163 Mich.App. 661, 415 N.W.2d 653, 655-56 (Mich.Ct.App.1987) (holding that expert testimony on the defendant’s psychological makeup was admissible to help the jury assess the reliability and credibility of his statements to the police).
We note the trial court’s finding that “defense counsel erred in not having backup psychological expert testimony in case the Court denied Defendant’s motion to suppress.” J.A. at 168. Defense counsel did not obtain an expert witness for the suppression hearing or the trial However, as discussed above, he did refer to the psychological effects of Palmatier’s interrogation while questioning witnesses, as well as during opening and closing arguments. We believe that Amunga cannot show prejudice. Although expert testimony by a psychologist could have helped Amunga, any error by defense counsel in failing to present such testimony would not have affected the judgment. See Strickland, 466 U.S. at 694 (requiring defendants to “show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different,” with a reasonable probability being one “sufficient to undermine confidence in the outcome”).
CONCLUSION
For the foregoing reasons, we AFFIRM the judgment of the district court.
. The doctor who treated Amunga later opined that Amunga’s wound was "consistent with a glancing blow to the edge of a table,” as Amunga had related, and "was not caused by a knife.” Joint Appendix (“J.A.”) at 1070.
. Malone testified at trial that he accompanied Amunga to the Amungas' apartment in the early hours of January 23, 1990. When they saw another man leaving the apartment, Amunga became enraged. Amunga then argued with Wanda about the man and asked for some money. Wanda ultimately gave Amunga fifty dollars, which he then gave to Malone with instructions to go to the store *535and buy cigarettes. When Malone returned after five or seven minutes, Amunga ordered him at gunpoint to throw away a bloody knife wrapped in a towel. Amunga then drove away. At this point, Malone looked in the kitchen window and saw Wanda’s body on the floor. Malone went back to the store and called for a taxicab; after waiting for fifteen minutes, he accepted a stranger's offer of a ride. Malone did not go back to the Amun-gas’ apartment: "I felt that [Amunga] had done some damage to Wanda. And I didn’t want to get involved in it. I was scared." J.A. at 762. When Malone saw Amunga later that night, Amunga stated that he would give Malone one thousand dollars if Malone kept silent and kill him if he did not. Amunga then gave Malone one hundred dollars.
. Because Amunga does not appear to contest the validity of his repeated waivers of his Miranda rights, this claim arises under the Due Process Clause rather than the Self-Incrimination Clause. See Oregon v. Elstad, 470 U.S. 298, 304, 105 S.Ct. 1285, 84 L.Ed.2d 222 (1985) ("The Court in Miranda required suppression of many statements that would have been admissible under traditional due process analysis by presuming that statements made while in custody and without adequate warnings were protected by the Fifth Amendment.").
. We note that the trial court prefaced its finding of voluntariness by stating that "it’s always difficult to be totally objective as a fact finder when one has been given the opportunity to review evidence and become convinced that the person actually is involved in the crime which has been charged.” J.A. at 717.
. At the suppression hearing, Amunga testified that in the wake of his wife’s murder he had been "emotionally drained” and upset by media coverage that portrayed him as a suspect, to the point where he contemplated committing suicide. J.A. at 581. On January 30, 1990, Amunga began to move out of his home and to drink heavily. On January 31, Amunga went to sleep between 4:00 and 5:00 a.m. and woke up about four hours later, when he continued to pack and to drink. An *538acquaintance confirmed that Amunga drank alcohol on January 31 from 10:30 a.m. until 11 p.m., when the police picked Amunga up for questioning.
. We note that the trial court accepted defense counsel's characterization of Palmatier's interrogation as "10 percent dealing with polygraph and 90 percent dealing with psychological brainwash.” J.A. at 902. If so, then it is arguable that whatever portion of the videotaped interrogation that did not deal with the polygraph might have been admissible. Defense counsel did not make such a motion, however.
. However, a defendant's statements made before, during, or after a polygraph test are not necessarily inadmissible. Ray, 430 N.W.2d at 628-29. Ray is not applicable because Palmatier’s questions rather than Amunga’s answers are at issue in this case.
. Defense counsel did argue at trial that cautionary instructions would cure any prejudice that might result from the admission of the polygraph evidence, which prejudice Amunga should be able to waive in any event. Cf. United States v. Shafer, 987 F.2d 1054, 1057-58 (4th Cir.1993) (suggesting, in a case where the district court ordered a mistrial "solely because of the prosecution's gross negligence” in disclosing documents, that “the court could have inquired into [the defendant’s willingness to waive the prejudice he may have suffered from these late disclosures and continue the trial”). The prejudice in this case, however, would have arguably implicated the jury’s "core function of making credibility determinations in criminal trials.” Scheffer, 523 U.S. at 312-13.
. As the trial court observed, Malone could have been charged as an accessory. Amunga essentially equates the prosecutor's failure to bring any charges against Malone with a promise of leniency in exchange for his testimony. However, the Supreme Court has reversed convictions only where the prosecution promised immunity or consideration for cooperation. See Giglio v. United States, 405 U.S. 150, 153, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972); Napue v. Illinois, 360 U.S. 264, 265, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959).
The record in this case does not suggest that Malone had a particular deal when he testified at Amunga’s trial. However, although some officers denied making any promises to Malone about dismissing charges, others testified that Malone was told he would not be charged if he had not been involved in Wanda’s murder:
I think promises was a poor choice of words. Earlier in the day, when Detective Dral and myself had talked with Mr. Ma*542lone, at his residence, he made mention of the fact that if I know something, what will happen to me. And I told him that, if he was not involved in the planning of the murder, or the actual murder itself, that he would not be charged with anything.
J.A. at 1252 (Heikela Test.).