E. GRADY JOLLY, Circuit Judge:

Anthony Charles Williams was convicted in a Texas court of capital murder. In the separate punishment phase of the trial, the court sentenced Williams to death based on the jury's responses to the two special issue questions. Williams sought federal habeas relief based on claims of improper juror selection, ineffective assistance of counsel, and violations of his fifth and sixth amendment rights resulting from the state's use of psychiatric evidence in rebutal at the trial's punishment phase. The district court dismissed his application but granted a certificate of probable cause. We affirm the judgment denying him relief.

I

On the evening of June 12, 1978, at approximately 8:45 p.m., thirteen-year-old Vicky Lynn Wright went with her sister to the Big Texas Bowling Alley in Houston, Texas. Shortly after their arrival, Vicky went outside to get some change left in a friend's car, a 1977 El Camino. When she did not return, her sister and friends went to the parking lot to look for her. They discovered that the El Camino was gone. They called Vicky's parents and the police. The police arrived at approximately 11:00 p.m.

Between 9 and 10 p.m. that evening, a few of Williams' friends saw him driving an El Camino recklessly. He stopped the car to talk to them, and told them the car belonged to his girl friend. Williams had blood on his shirt that he claimed to have received in a fight.

At 1 a.m. on June 13, 1978, A.L. Anderson noticed the El Camino, with its flashers on, in front of her house. She awoke at 4 a.m. and noticed that the car was still there. She reported it to the police. After day break, Anderson went outside and saw blood stains inside the El Camino. She called the police a second time, and they arrived at approximately 7:30 a.m. A tire, hub cap and part of the jack were missing from the vehicle. The spare tire had been put on the car.

Vicky's body was discovered in a wooded area near Williams' neighborhood at approximately 4:40 p.m. on June 13, 1978. The police discovered skid marks, a package of Kool cigarettes, matches and a blood-stained board near her body. An autopsy showed that Vicky died from a skull fracture and intercranial hemorrhage from a blunt trauma to the head. The evidence showed that the skull fracture could have been caused by the board found at the scene of the homicide. Bloody material was found in her vagina; seminal fluid was found in her mouth and rectum.

Detective Zeringue arrived at the scene of the homicide about 6:30 p.m. He showed people gathering at the site a picture of the El Camino. Two of Williams' friends recognized the vehicle and told the detective that they had seen Williams driving it the night before. The police went to Williams' home. Williams ran out the back gate to a nearby abandoned house. The police found him hiding in the attic. Williams was arrested at 7:55 p.m. The police read Williams his Miranda warnings and took him to the police station.

At the station, Williams gave a written confession, admitting that he accosted Vicky at the bowling alley, took her to a dark place by the bayou, and hit her in the face with his fist and with a board. He denied having sex with her.

Williams' palm prints and a finger print were found on the El Camino. Type O blood, which was Vicky's blood type, was found on the board, on Williams' clothes and inside the El Camino.

Williams was indicted for the capital murder of Vicky Lynn Wright while in the course of committing kidnapping, robbery and aggravated rape. He pled not guilty. At the conclusion of the guilt phase of the trial, the jury found Williams guilty of capital murder.

During the punishment phase, the state presented evidence of four extraneous and unadjudicated offenses that Williams allegedly committed: (1) the rape of a sixteen-year-old acquaintance in April 1978; (2) the abduction and sodomy-rape of a woman on April 5, 1978; (3) the abduction of a woman from a post office, her rape and nonfatal shooting on June 1, 1978; and (4) the abduction and sodomy-rape of a woman on June 10, 1978. Each of these victims testified and three identified Williams as their assailant. In the fourth crime, Williams was identified by a witness who interrupted the crime.

The state also presented a witness who testified that Williams suspiciously approached her in her apartment complex parking lot after midnight on April 5, 1978. According to her testimony, Williams requested help with jumping his car battery, but walked off when she told him that her boy friend, who was upstairs, would help.

As evidence in mitigation of punishment, the defense offered the testimony of Williams' family and friends who promised that they would help to rehabilitate him if he were given a life sentence. These witnesses testified that Williams had been hit by an automobile at the age of six. Since the accident, he had been a slow learner and had complained of headaches.

The defense also introduced psychiatric testimony indicating that Williams was borderline mentally retarded. The state rebutted with its own psychiatric testimony.

On September 25, 1978, the jury answered "yes" to both special issue questions, and the court assessed punishment at death. Williams appealed to the Texas Court of Criminal Appeals, which affirmed on October 14, 1981. Williams v. State, 622 S.W.2d 116 (Tex.Crim.App. 1981) (en banc). The United States Supreme Court denied certiorari on March 8, 1982. Williams v. Texas, 455 U.S. 1008, 102 S.Ct. 1646, 71 L.Ed.2d 876 (1982).

The Texas Court of Criminal Appeals stayed Williams' execution pending his application for state habeas relief. After exhausting his state appeals, Williams filed for federal habeas relief in the United States District Court for the Southern District of Texas on October 4, 1985. A stay was granted on October 7, 1985. Judge Bue dismissed his application, Williams v. McCotter, Civ. No. H-85-5650 (S.D.Tex. March 17, 1986), and issued a certificate of probable cause to appeal to this court on May 29, 1986. Williams' stay of execution remains in effect pending the outcome of this appeal.

II A.

Williams first contends that the trial court failed to correctly apply the Witherspoon standard in excluding prospective juror Mary Oligney for cause, based on her views against the death penalty. Witherspoon v. Illinois, 391 U.S. 510, 88 S.Ct. 1770, 20 L.Ed.2d 776 (1968). At voir dire, Oligney equivocated in her answers to questions regarding her ability as a juror to follow Texas law, even if it meant that the defendant would receive the death penalty. Williams claims that Oligney was not excludable under Witherspoon because her voir dire responses, although conflicting, did not indicate that Oligney's views against the death penalty would prevent or substantially impair her performance as a juror. Williams further argues that because his trial took place before the Supreme Court decided Adams v. Texas, 448 U.S. 38, 100 S.Ct. 2521, 65 L.Ed.2d 581 (1980), the trial judge excluded Oligney solely on the basis of Article 12.31(b) of the Texas Penal Code and disregarded the Witherspoon standard. It therefore follows, he argues, that the trial court's exclusion of Oligney cannot be given the presumption of correctness mandated by 28 U.S.C. § 2254(d), as explained in Wainwright v. Witt, 469 U.S. 412, 105 S.Ct. 844, 83 L.Ed.2d 841 (1985).

We disagree. While Oligney initially equivocated in her answers at voir dire, she subsequently concluded that regardless of the circumstances she "would say `no' with the death." IV Trial Transcript at 1292. Oligney's ultimate statement of irrevocable opposition to the death penalty justified her exclusion under Witherspoon. Willie v. Maggio, 737 F.2d 1372 (5th Cir.), cert. denied, 469 U.S. 1002, 105 S.Ct. 415, 83 L.Ed.2d 342 (1984); Williams v. Maggio, 679 F.2d 381, 385-89 (5th Cir. 1982) (en banc), cert. denied, 463 U.S. 1214, 103 S.Ct. 3553, 77 L.Ed.2d 1399 (1983).

Moreover, the Texas Court of Criminal Appeals reviewed this case after Adams was decided and held that Oligney's views would have prevented or substantially impaired her performance as a juror. Williams, 622 S.W.2d at 118. It is clear that the Texas appellate court applied the proper Witherspoon standard, and we must accord its determination a presumption of correctness under section 2254(d). Summer v. Mata, 449 U.S. 539, 546, 101 S.Ct. 764, 768, 66 L.Ed.2d 722 (1981).

B.

Williams also challenges the trial court's refusal to exclude for cause Alva Jean Wagner, the twelfth juror selected. Williams argues that during the voir dire examination, Wagner exhibited an overall prejudice and strong bias in favor of the death penalty and also revealed her inability to consider life imprisonment as punishment for a capital murder conviction. Comparing the trial court's exclusion of Oligney for cause at the state's request with the court's refusal to grant the defense's challenge for cause against Wagner, Williams complains that the trial court favored the state and did not apply the Witherspoon standard evenly.

Again, the Texas Court of Criminal Appeals considered this argument and we see no basis to question its conclusion. That court found that Wagner was not unwilling to follow the law in determining whether the accused was guilty of capital murder; nor was she incapable of considering life imprisonment as an appropriate punishment. Under Witherspoon, Wagner was a qualified juror because she was capable of voting for life imprisonment. Oligney, however, was excludable because she was incapable of voting for the death penalty in a capital murder case. Williams, 622 S.W.2d at 119. We conclude therefore that the Texas courts correctly and consistently applied the Witherspoon standard to the challenges for cause made by the prosecution and the defense.

III

Williams urges that his counsel failed to provide him with effective assistance, particularly at the punishment phase of the trial. Although Williams claims that several aspects of his counsel's performance were deficient, he chiefly objects to his counsel's failure to investigate the extraneous, unadjudicated offenses presented by the state as proof of Williams' future dangerousness and his counsel's failure to engage in discovery of some sort with respect to these offenses. Williams alleges in his brief that he "specifically informed counsel that he did not commit [the extraneous offenses] and was unaware of such charges until they were introduced by the state." However, his counsel submitted an affidavit in the state court proceedings, which is in the record before us, that specifically denies that Williams ever made this statement to him. The state trial court made a finding of fact in the habeas proceedings that the facts asserted by the defense counsel in his affidavit were true. In accord with Sumner v. Mata, 449 U.S. 539, 101 S.Ct. 764, we apply "the presumption of correctness," which is mandated by 28 U.S.C. § 2254 for factual determinations made by state courts, and therefore accept the state trial court's finding of fact. The application of Sumner is particularly appropriate in this case because Williams' allegation is contained only in statements in his brief and is unsupported by any record evidence. Moreover, that Williams was unlikely to have made such a statement is substantiated by Williams' failure, even now, to offer any suggestion of evidence to support his innocence except his simple denial of the charges to counsel. Accepting, therefore, the state court's finding that Williams did not make the alleged statement to his counsel, we need consider no further this allegation as a basis for a claim of ineffectiveness.

With respect to Williams' other allegations of ineffectiveness, see supra note 3, he has shown no prejudice. Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).

IV

The final claim raised by Williams is that his fifth and sixth amendment rights were violated when the state's psychologist testified during the penalty stage of the trial. He claims that the basis of the testimony was a pretrial psychiatric examination, conducted without advising Williams of his right to remain silent and his right to consult with counsel. Because the state's psychiatric evidence was based on an unwarned examination, he argues that the Supreme Court's holding in Estelle v. Smith, 451 U.S. 454, 101 S.Ct. 1866, 68 L.Ed.2d 359 (1981), supports the conclusion that his rights were violated.

First, we hold that Estelle v. Smith does not control this case. In Smith, a capital murder defendant, who was examined pretrial by a state psychiatrist, was given no Miranda warnings prior to the examination, and his counsel was not notified in advance that the examination would encompass the issue of the defendant's future dangerousness. At trial, the state introduced psychiatric evidence that was obtained from this examination and used the evidence to prove the defendant's future dangerousness. The defendant offered no psychiatric evidence at trial and had never indicated that he would rely on a psychiatric defense. The Supreme Court held that where the defendant neither initiated a psychiatric defense nor introduced any psychiatric evidence at trial, the state's introduction of evidence obtained from the unwarned psychiatric examination violated the defendant's fifth and sixth amendment rights. Smith, 451 U.S. at 468-71, 101 S.Ct. at 1875-77. The Court noted, however, that "a different situation arises where a defendant intends to introduce psychiatric evidence at the penalty phase." Id. at 472, 101 S.Ct. at 1878.

Williams' case is easily distinguished from Smith because Williams' counsel was given advance written notice that the scope of the state's psychiatric examination would include a determination of Williams' future dangerousness. I Trial Transcript at 13-15. Furthermore, Williams' case presents the "different situation" to which the Court referred in Smith. At trial, it was Williams who first introduced psychiatric evidence on the issue of future dangerousness. On these facts alone, it is obvious that Williams' Smith claim is baseless.

Second, the factual basis of Williams' argument is further flawed because the record clearly reveals that the evidence complained of is not subject to exclusion on fifth and sixth amendment grounds. The record shows that the defense made no objection whatsoever, before trial or at trial, to the state's psychiatric evidence. Indeed, the only objection Williams now raises, or has ever raised, relates solely to the state's psychiatric testimony regarding future dangerousness. However, none of the testimony on future dangerousness given by the state's psychologist, Dr. Jerome Brown, was obtained from or based upon his interview with Williams. Instead, Dr. Brown's scant testimony regarding future dangerousness reflected only his personal opinion based on his years of professional experience. Thus, because no statement made to Dr. Brown by Williams was the subject, directly or indirectly, of his testimony, we hold that there is no factual basis on which to predicate a fifth or sixth amendment objection.

Finally, we note that even if we were to assume that a factual predicate exists in the record upon which Williams could base a fifth or sixth amendment claim, Vardas v. Estelle, 715 F.2d 206 (5th Cir. 1983), makes it clear that Williams waived his right to object to the state's use of psychiatric evidence on the issue of future dangerousness. Vardas stands for the proposition that when a defendant introduces psychiatric evidence on a critical issue, he waives his fifth and sixth amendment objections to the state's psychiatric testimony, provided that the state's evidence is used solely in rebuttal and properly limited to the issue raised by the defense. Id. at 209-10. Here, Williams not only put into issue the question of future dangerousness through the testimony of his psychiatrist, but he also initiated questioning on his own future dangerousness in the cross-examination of the state's psychologist. Having first been raised by the defense, it was perfectly proper for the state to explore this issue on the redirect examination of its psychologist.

V

In conclusion, we hold that the jury was properly selected in accord with the Witherspoon standard, that Williams has failed to allege a sufficient claim of ineffective assistance of counsel, and that Williams' fifth and sixth amendment rights were not violated by the state's use of psychiatric evidence during the trial's punishment phase. The district court's denial of Williams' petition for writ of habeas corpus is therefore.

AFFIRMED.