William Lee Shackleford, a California state prisoner, appeals the judgment of the district court denying his petition for a writ of habeas corpus. Shackleford was tried and convicted in state court of first-degree murder.

Three issues have been certified for this appeal: (1) Was Shackleford denied due process because the state trial court gave the jury an erroneous felony-murder instruction? (2) Was Shackleford denied effective assistance of counsel because his trial attorney failed to object to that instruction? (3) Was Shackleford denied effective assistance of counsel because, at a suppression hearing, his trial attorney failed to present evidence of Shackleford’s cocaine use, sleep deprivation, and mental deficiencies when challenging his Miranda waiver and confession? In addition to these issues, Shackleford asks us to consider three additional issues. See 9th Cir. R. 22 — 1(d). We have jurisdiction pursuant to 28 U.S.C. §§ 1291 (1994) and 2253 (Supp. IV 1998). We decline to expand the issues certified for appeal and affirm the district court’s denial of Shackleford’s ha-beas petition.

I. Facts

On June 2, 1988, Shackleford, his friend Sean Harris (“Sean”), Sean’s sister Tracy Harris (“Tracy”), and Tracy’s boyfriend Richard Daniels attended a party hosted by Maria Snider, the victim Shackleford later killed. The group consumed alcohol and smoked crack cocaine brought by Shackleford. Throughout the evening, the other partygoers noticed Snider and Shackleford were acting romantically interested in one another.

Sometime after midnight, the group decided to drive to Tracy and Sean’s mother’s house in Danville, California. Once in the car, however, Tracy and Daniels got into an argument. Tracy struck Daniels across the face. Snider then entered the fray, hitting Daniels on the head. The blow was so severe that it knocked Daniels unconscious and opened a large cut on his head. The group immediately drove Daniels to a hospital, where the wound was stitched and treated. Rather than proceed to Danville, the group returned to Snider’s apartment, where they dropped her off at about 9:00 a.m. Shackleford got out of the car a couple of blocks later. The others assumed he was returning to Snider’s apartment, and left.

At about 11:00 a.m., an upstairs neighbor heard some thumping sounds coming from Snider’s apartment and went down to investigate. The neighbor thought he heard Snider crying inside the apartment and knocked, but when no one answered he went back to his apartment because he assumed it was just an argument. Around noon, Shackleford telephoned Vivian Harris (“Vivian”), Sean and Tracy’s mother, and told her that Snider was dead. Vivian set up a three-way telephone conversation with Tracy, Shackleford, and herself. Shackleford, who was in tears at the time, told Vivian and Tracy that a man wearing a sweat suit and gold chains had visited Snider that morning. According to Shack-leford, Snider asked Shackleford to leave; he did so and when he returned he found Snider dead.

After another telephone conversation, Shackleford, Sean, Sean’s friend, and two of Snider’s coworkers drove to Snider’s apartment. Along the way, Sean contacted a police officer, who followed them. When the group arrived at Snider’s apartment, they found her corpse lying face up on the bedroom floor. Snider was naked except for a towel that covered her face and a piece of cloth that covered her genital area. An electrical cord had been tied and knotted around her neck. When police officers uncovered Snider’s groin, they found a bottle of hair dye inserted in her vagina. There were also cigarette ashes and a burn mark on her stomach.

The police asked Shackleford, Sean, and one of the men who had accompanied them to the apartment to come to the police station to be interviewed. There, Shackle-ford falsely told the detectives his name was William Cooper. He also repeated the story that he left Snider with an unknown man in a sweat suit shortly before her death.

After Shackleford left the police station, Detective Cathy Lee decided to interview him a second time because she found his earlier statement inconsistent. Shackle-ford returned to the police station later that day, between 6:30 and 7:00 p.m. Shackleford repeated his story about the unknown man in the sweat suit but added that after he left Snider’s apartment, he had a telephone conversation with a female friend. The police contacted the friend, who denied speaking with Shackleford. The detectives then advised Shackleford of his Miranda rights, which he waived. The detectives confronted Shackleford with the inconsistencies in his statements and asked him about his parole status. When Shack-leford denied being on parole, the detectives confronted him with the fact that he was scheduled to be on parole for eight more months. Shackleford said his parole would be completed in six months, to which one of the officers responded, “I’m sure we can stretch it out,” adding, “You’re on parole. Don’t be telling me you don’t have to do things.... Because when it comes down to it, I guess I could violate you. Because I had a parolee tell me that one time. I violated his parole just like that.” After a long pause, the agent encouraged Shackleford to take a polygraph test.

During the interrogation, Shackleford stated several times that he was tired and asked if he could lie down for forty-five minutes. One of the detectives told him that it would be better to take the polygraph test first; Shackleford agreed and took the test. The test began at 11:20 p.m. Although not under arrest, Shackle-ford was once again advised of his Miranda rights, which he waived. He initially repeated his story about the man in the sweat suit, but shortly before midnight, he changed his story and said that a man named JoJo Muldroe killed Snider. Shackleford said he found Muldroe leaning over Snider’s body and chased him from Snider’s apartment.

The police then brought Muldroe to the station. During the taped confrontation that followed, Muldroe denied killing Snider. The detectives observed that Mul-droe did not have any marks on his face, although Shackleford claimed to have hit him while chasing him from Snider’s apartment. Shackleford was arrested and thereafter confessed to killing Snider. He told Detective Lee that Snider agreed to have sex with him in exchange for drugs. After having sex, the two sat in Snider’s kitchen and smoked some crack cocaine Shackleford had brought. When Shackle- ford tried to leave, Snider became angry because she wanted to smoke more of his cocaine. According to Shackleford, she became so agitated that she began to hit him and threatened him with a small knife.

Shackleford explained to the detectives that he fought back, telling them: “I ain’t gonna let nobody just put their hands on me.... ” Shackleford told the detectives that after pushing Snider into the bedroom, he put her in a headlock and choked her until she fell to the ground. Although she got up to resume the fight, Shackle-ford subdued her and tied her up with an electrical cord. He said he then removed Snider’s clothing and, after smoking a cigarette, burned Snider’s stomach with it because “she was trying to make [him] feel pain.” Later, while Snider was on the floor, still breathing, he said, he cinched the electrical cord around her neck to choke her. Shackleford told the detectives that even with the electrical cord around her neck, Snider cried and continued to make breathing sounds for ten minutes. At some point, he put a bottle of hair dye in her vagina. Shackleford said he became scared, and when Snider stopped breathing, he returned to the kitchen, smoked the rest of his cocaine, and left the apartment. He maintained he did not intend to kill Snider and that her death was an accident.

At trial, Shackleford testified. He dismissed his confession as a lie and repeated his story about the man in the sweat suit. He said he had lied to the police when he told them his name was “Cooper” because he was on parole and feared that he was violating the conditions of his parole by coming in contact with the police. He said he told the detectives Muldroe killed Snider because he thought they did not believe his story about the man in the sweat suit. He said he confessed because he thought it was the only way he could get the detectives to stop interrogating him so that he could go home and rest.

A jury convicted Shackleford of first-degree murder and he was sentenced to thirty years to life. The California Court of Appeal affirmed his conviction and the California Supreme Court denied his petition for review and his petition for a writ of habeas corpus, both without comment.

Shackleford then filed a petition for a writ of habeas corpus in federal district court. In that petition, as amended, he alleged that (1) his conviction and sentence were unconstitutional because he was mentally incompetent throughout the legal proceedings; (2) he was denied due process when his confession was introduced at trial; (3) he was denied due process because the trial court gave the jury an erroneous felony-murder instruction; and (4) he was denied effective assistance of counsel.

Shackleford’s ineffective assistance of counsel claim incorporated several sub-claims. He asserted he was denied effective assistance because his trial attorney failed to object to the erroneous felony-murder instruction, to investigate and present evidence of Shackleford’s drug use in challenging his confession, to present an intoxication defense, to effectively argue to the jury that his confession was unreliable, and to request an involuntary manslaughter instruction.

The district court denied Shackleford’s habeas petition, but granted a certificate of appealability on two issues: (1) Did the trial court’s erroneous felony-murder instruction deprive him of due process? (2) Did Shackleford’s trial attorney’s failure to object to that instruction deprive him of his right to counsel? A motions panel of this court expanded the certificate to include the issue of whether Shackleford’s trial counsel was ineffective because, at the suppression hearing, he failed to present evidence of Shackleford’s cocaine use, fatigue, and mental deficiencies when challenging his Miranda waiver and confession. The motions panel denied Shackle-ford’s request to expand the certificate to add additional issues.

II. Standard of Review

We review de novo the denial of a petition for a writ of habeas corpus. See Bean v. Calderon, 163 F.3d 1073, 1077 (9th Cir.1998), cert. denied, 528 U.S. 922 , 120 S.Ct. 285 , 145 L.Ed.2d 239 (1999); Allen v. Crabtree, 153 F.3d 1030, 1032 (9th Cir.1998), cer t. denied, 525 U.S. 1091 , 119 S.Ct. 846 , 142 L.Ed.2d 700 (1999). Shackle-ford’s federal habeas petition, which he filed on September 13, 1996, is governed by the Antiterrorism and Effective Death Penalty Act (“AEDPA”). Under the relevant provision of the AEDPA, a federal court may grant relief only if 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) (Supp. IV 1998).

In Williams v. Taylor, 529 U.S. 362 , 120 S.Ct. 1495 , 146 L.Ed.2d 389 (2000), the Supreme Court resolved much of the debate concerning how to interpret 28 U.S.C. § 2254 (d)(1). See Van Tran v. Lindsey, 212 F.3d 1143, 1149 (9th Cir.2000), cert. denied, — U.S. -, 121 S.Ct. 340 , 148 L.Ed.2d 274 (2000). It clarified that the “contrary to” and “unreasonable application” clauses have distinct meanings. See Williams, 120 S.Ct. at 1519-22 ; Van Tran, 212 F.3d at 1150 .

Under the “contrary to” clause, a federal court should grant the writ (1) when the state court has failed to apply the correct controlling authority from the Supreme Court or (2) when the state court has applied the correct controlling authority from the Supreme Court to a case involving facts “materially indistinguishable” from those in a controlling case, but has nonetheless reached a different result. See Van Tran, 212 F.3d at 1150 (citing Williams, 120 S.Ct. at 1519-20 ); see also LaJoie v. Thompson, 217 F.3d 663, 667-68 (9th Cir.2000) (quoting Van Tran, 212 F.3d at 1149-50 ).

Under the “unreasonable application” clause, a federal court should grant the writ when the state court’s application of clearly established federal law is “objectively unreasonable.” See Williams, 120 S.Ct. at 1521 . Athough in Williams the Court declined to define “unreasonable,” we have held that a judgment is “objectively unreasonable” when it is clearly erroneous. See Van Tran, 212 F.3d at 1152-54 . It is not enough that a petitioner convinces the court that he has the better of two reasonable legal arguments. The court must be left “with a ‘firm conviction’ that one answer, the one rejected by the [state] court, was correct and the other, the application of the federal law that the [state] court adopted, was erroneous.... ” Id. at 1153-54 .

III. The Felony-Murder Instruction

We first consider Shackleford’s contention that he was denied due process by the trial court’s felony-murder instruction. We conclude that, although the trial court erred in giving the felony-murder instruction, that error was harmless under Brecht v. Abrahamson, 507 U.S. 619, 637 , 113 S.Ct. 1710 , 123 L.Ed.2d 353 (1993).

The trial court, after explaining that a willful and deliberate killing is first-degree murder, told the jury,

There is no question that this instruction was erroneous. Indeed, the State concedes as much. The instruction told the jury that Shackleford could be found guilty of first-degree murder provided he “committed the crime of torture.” But torture was not one of the five felonies enumerated in the 1988 version of California Penal Code section 189 that would have triggered the felony-murder rule. See Cal. Pen.Code § 189 (West 1988).- As a result, a killing that occurred during the infliction of torture was not first-degree murder without a finding of malice. See People v. Dillon, 34 Cal.3d 441 , 194 Cal.Rptr. 390 , 668 P.2d 697, 710 (1983); People v. Mattison, 4 Cal.3d 177 , 93 Cal.Rptr. 185 , 481 P.2d 193, 196 (1970). As the California Supreme Court explained in Mattison ,

93 Cal.Rptr. 185 , 481 P.2d at 196 .

Because the trial court’s felony-murder instruction permitted the jury to convict Shackleford of first-degree murder by reference to a predicate felony that did not exist, the error was contrary to clearly established federal law. See Suniga v. Bunnell, 998 F.2d 664, 669-70 (9th Cir.1993). Relying on Suniga , Shackleford argues that the instructional error infected the entire trial, and therefore we should not apply a harmless error analysis. See id. at 670 . We disagree. In Suniga , the jury could have convicted the defendant of second-degree murder, without ever considering malice, simply by using, improperly, assault with a deadly weapon as the predicate felony. Here, the jury could not have convicted Shackleford of first-degree murder by torture without finding malice. Suniga is inapplicable. See Ficklin v. Hatcher, 177 F.3d 1147, 1151 (9th Cir.1999), ce rt. denied, 528 U.S. 941 , 120 S.Ct. 352 , 145 L.Ed.2d 275 (1999) (explaining that Suniga is “inapplicable” when a reviewing court “can tell with certainty from the jury instructions that the jury rested its verdict on a ground that did not implicate petitioner’s constitutional rightfs]”).

Shackleford was found guilty of first-degree murder by torture. See Cal. Pen. Code § 189 . In California, at the time of Shackleford’s conviction, to find a defendant guilty of first-degree murder by torture, a jury had to find, just as Shackleford’s jury was instructed, that the defendant killed the victim with malice aforethought and that the killing was committed with the intent to cause cruel pain and suffering for the purpose of revenge, extortion, persuasion, or for any other sadistic purpose. See People v. Davenport, 41 Cal.3d 247, 221 . Cal.Rptr. 794, 710 P.2d 861, 872 (1985); People v. Wiley, 18 Cal.3d 162 , 133 Cal.Rptr. 135 , 554 P.2d 881, 883-84 (1976). “The defendant need not have an intent to kill the victim — the malice element of murder may be supplied by an intentional act involving a high degree of probability of death which is committed with conscious disregard for human life.” Davenport, 221 Cal.Rptr. 794 , 710 P.2d at 872-73 (citations omitted); see also Wiley, 133 Cal.Rptr. 135 , 554 P.2d at 884 .

Shackleford argues the jury could not have found that he acted with malice. He emphasizes that even during his confession, he told the detectives he did not want to kill Snider and that her death was “an accident.” He adds that after Snider’s death, he was remorseful. But as the state court pointed out, it was irrelevant whether Shackleford intended to kill Snider because it is sufficient that he acted with a conscious disregard for life, knowing that his actions would have a high probability of causing death. See Davenport, 221 Cal.Rptr. 794 , 710 P.2d at 872-73 ; see also Wiley, 133 Cal.Rptr. 135 , 554 P.2d at 884 .

Not only could the jury have found malice, the jury had to have found malice. Snider died by strangulation. By finding that Shackleford killed her, the jury necessarily found that Shackleford strangled her to death. A pathologist testified at trial that given the garrote used, it took at least ten minutes for Snider to die. Moreover, the evidence showed that Snider sobbed as she slowly strangled to death, and that during this time Shackleford listened to her sobs while he held the electric cord cinched fast around her neck until she died.

“[Hjomicide by strangulation indicates malice.” People v. La Vergne, 64 Cal.2d 265 , 49 Cal.Rptr. 557 , 411 P.2d 309, 313 (1966); see also People v. Caldwell, 43 Cal.2d 864 , 279 P.2d 539, 542 (1955). The jury had to have found that Shackleford knew there was a great risk that Snider would die from the strangling. As the state court grimly noted: “One ordinarily cannot strangle and garrote someone and listen to their labored breathing for ten minutes as they expire without appreciating that the conduct is life threatening.” People v. Shackleford, No. A046989 (Ca.Ct. App. filed July 18, 1991), at 11. The result is that the jury had to have found that Shackleford killed Snider with malice while he tortured her. And that was the verdict: guilty of first-degree murder by torture.

We conclude that, although the trial court’s felony-murder instruction was contrary to clearly established federal law, it did not have a “substantial and injurious effect or influence in determining the jury’s verdict.” Brecht, 507 U.S. at 623 , 113 S.Ct. 1710 . Accordingly, the error was harmless.

The state appellate court also found that the erroneous felony-murder instruction was harmless. Because we conclude the error was harmless under Brecht , and since the state appellate court’s decision came to the same conclusion, that decision was not contrary to, or an unreasonable application of, clearly established federal law. See Van Tran, 212 F.3d at 1155, 1159 (denying writ because state court decision was not “contrary to” or “unreasonable application” of federal law); Delgado v. Lewis, 223 F.3d 976, 981-82 (9th Cir.2000) (granting writ because state court decision was both “contrary to” and “unreasonable. application” of federal law). But cf. LaJoie, 217 F.3d at 673 n. 13 (granting writ because state court decision was “unreasonable application” of federal law); Williams, 120 S.Ct. at 1516 (reversing denial of writ because state court decision “was contrary to, or involved an unreasonable application of, clearly established Federal law”).

IY. Counsel’s Failure to Object to the Felony-Murder Instruction

We reject Shackleford’s argument that his trial counsel rendered ineffective assistance by failing to object to the felony-murder instruction. The applicable law that guides our analysis is supplied by Strickland v. Washington, 466 U.S. 668 , 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984), which is “clearly established Federal law” under the AEDPA. See Van Tran, 212 F.3d at 1156; Delgado, 223 F.3d at 980 . To show that an attorney’s representation of a client was ineffective under Strickland , the petitioner must establish that (1) the attorney’s representation fell below an objective standard of reasonableness; and (2) the deficient representation prejudiced the defense. 466 U.S. at 687 , 104 S.Ct. 2052 ; Schell v. Witek, 218 F.3d 1017, 1028 (9th Cir.2000).

We need not consider whether Shackle-ford’s counsel’s representation fell below an objective standard of reasonableness because, in light of our foregoing analysis, Shackleford cannot show prejudice; he cannot show that had his trial counsel objected, and had the erroneous instruction not been given, there was a reasonable probability that the result of the proceedings would have been different. See Strickland, 466 U.S. at 691 , 104 S.Ct. 2052 ; Williams v. Calderon, 52 F.3d 1465, 1470 (9th Cir.1995).

Y. Counsel’s Failure to Present Evidence at the Suppression Hearing

Shackleford next contends he was denied effective assistance of counsel because his trial counsel did not present evidence at the suppression hearing concerning his cocaine use, fatigue, and mental deficiencies. Such evidence, he argues, would have shown that he was not competent to waive his Miranda rights and that his confession was the product of coercion.

A defendant’s waiver of his Miranda rights is valid if it is voluntary, knowing, and intelligent. Miranda v. Arizona, 384 U.S. 436, 444, 475 , 86 S.Ct. 1602 , 16 L.Ed.2d 694 (1966); Moran v. Burbine, 475 U.S. 412, 421 , 106 S.Ct. 1135 , 89 L.Ed.2d 410 (1986) (quoting Miranda, 384 U.S. at 444, 475 , 86 S.Ct. 1602 ). The fact that a suspect is under the influence of drugs or medication is irrelevant if the suspect’s statement was “the product of a rational intellect and a free will.” Mincey v. Arizona, 437 U.S. 385, 398 , 98 S.Ct. 2408 , 57 L.Ed.2d 290 (1978) (quoting Townsend v. Sain, 372 U.S. 293, 307 , 83 S.Ct. 745 , 9 L.Ed.2d 770 (1963)); see also United States v. George, 987 F.2d 1428, 1430-31 (9th Cir.1993); United States v. Lewis, 833 F.2d 1380, 1884-85 (9th Cir.1987); United States v. Martin, 781 F.2d 671, 673-74 (9th Cir.1985); cf. Mincey, 437 U.S. at 396-402 , 98 S.Ct. 2408 (holding that an interrogation was not voluntary where the defendant was in the intensive care unit of a hospital, was unable to speak and had to communicate through writing, repeatedly asked for the interview to cease, gave some incoherent answers, and lost consciousness several times during the interrogation).

Shackleford has not shown a reasonable probability that had his counsel submitted evidence of his drug use, fatigue, and mental deficiencies, his waiver of his Miranda rights would have been found to be not voluntary, knowing, and intelligent. The trial court noted that, during the interrogation, Shackleford was capable of asking lucid questions. Although Shackleford may have had some level of mental disability, he was coherent and articulate throughout the interrogation. He demonstrated a full awareness of the nature of the right being abandoned and the consequences of his decision to abandon it. See Moran, 475 U.S. at 421 , 106 S.Ct. 1135 .

Nor has Shackleford shown a reasonable probability that his confession would have been suppressed if his counsel had presented the evidence on which Shackleford now relies. The state trial court, over a period of two days, listened to a tape recording of the confession, took testimony from Detective Lee, who was cross-examined by Shackleford’s counsel, and heard extensive argument from counsel for both sides. After all of this, the court found that Shackleford was “articulate and responsive to questions” and his confession was voluntary and intelligent. The failure to introduce evidence of his drug use, fatigue, and mental deficiencies did not prejudice him. His claim of ineffective assistance of counsel fails. See Strickland, 466 U.S. at 687 , 104 S.Ct. 2052 .

VI. Request for Expanded Certificate of Appealability

Finally, we turn to Shackleford’s request for an expanded certificate of appealability (COA). Shackleford seeks certification of three additional issues: (1) whether he was denied due process by the admission of his confession; (2) whether he was denied effective assistance of counsel because his trial counsel failed to pursue an intoxication defense; and (3) whether he was denied effective assistance of counsel because his trial counsel failed to call into question the reliability of his confession.

The right to appeal is governed by the COA requirements found at 28 U.S.C. § 2253 (c) (Supp. IV 1998). See Slack v. McDaniel, 529 U.S. 473 , 120 S.Ct. 1595, 1600 , 146 L.Ed.2d 542 (2000). To obtain a COA, a prisoner must make “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253 (c)(2) (Supp. IV 1998). In order to make such a showing a prisoner must demonstrate “that reasonable jurists could debate whether (or, for that matter, agree that) the petition should have been resolved in a different manner or that the issues presented were ‘adequate to deserve encouragement to proceed further.’ ” Slack, 120 S.Ct. at 1603-04 (internal quotation marks omitted) (quoting Barefoot v. Estelle, 463 U.S. 880 , 893 n. 4, 103 S.Ct. 3383 , 77 L.Ed.2d 1090 (1983)); see also Lambright v. Stewart, 220 F.3d 1022, 1025 (9th Cir.2000) (quoting Barefoot, 463 U.S. at 893 n. 4, 103 S.Ct. 3383 ).

We deny Shackleford’s motion to expand the COA because reasonable jurists could not debate the district court’s rulings on the additional issues he wishes to pursue. The threatened revocation of his parole if he did not take a polygraph test and his fatigue do not, within the context of the rest of the evidence in the case, create a substantial showing that his confession was involuntary; relying on an intoxication defense would have weakened his defense; and his counsel’s failure to produce evidence of his mental deficiencies and history does not raise a substantial issue of a constitutional violation because, during closing argument, his counsel effectively brought Shackleford’s confusion to the jury’s attention by drawing upon evidence from the trial.

CONCLUSION

We DENY Shackleford’s motion to expand the COA, and we AFFIRM the district court’s judgment denying his habeas petition.

AFFIRMED.

. As the California Court of Appeal pointed out, the jurors could not have relied only on the cigarette burns or bottle insertion to find torture. There was only one perpetrator. If the jurors found that Shackleford used the cigarette and/or bottle with torturous intent, they would have found that he strangled the victim, and there was no reason to suppose his intent changed as he turned from one torment to another. Shackleford’s own statements indicate that he tied the cord around Snider’s neck between burning her and inserting the bottle. People v. Shackleford, No. A046989 (Ca.Cl.App. filed July 18, 1991), at 10 n. 2. . The California Supreme Court denied review of Shackleford’s direct appeal and habe-as petition without comment. In this circumstance, we "look through” the unexplained California Supreme Court decisions to the last reasoned decision, the state appellate court's decision, as the basis for the state court’s judgment. See Ylst v. Nunnemaker, 501 U.S. 797, 803-04 , 111 S.Ct. 2590 , 115 L.Ed.2d 706 (1991). . The State contends that we should not reach the merits of this claim because Shack-leford never exhausted this claim in state court. See 28 U.S.C. § 2254 (b)(1)(A) (Supp. IV 1998). The State's argument is incorrect: Shackleford raised this claim in his 1999 state habeas petition filed with the California Supreme Court.