ORDER DENYING CERTIFICATE OF APPEALABILITY
TIMOTHY M. TYMKOVICH, Circuit Judge.
A Kansas jury found Kyle Cavaness guilty of premeditated first-degree murder, conspiracy to commit premeditated first-degree murder, and aggravated kid-naping. Now a state prisoner, Cavaness seeks a certificate of appealability (COA) to enable him to appeal the district court’s dismissal of his petition for a writ of habe-as corpus under 28 U.S.C. § 2254.
Exercising jurisdiction under 28 U.S.C. §§ 1291 and 2258(a), we DENY the application for a COA and DISMISS the appeal.
I. Background
The Kansas Supreme Court set forth the following account of Cavaness’s role in the gruesome murder of Deangelo Wheeler:
Kyle Cavaness’ sister, Alisha, testified that in October 2002, she was living with the defendant and Ryan [her boyfriend] at a home in Wyandotte County. The victim, Deangelo Wheeler, had also been staying at the home for a few days before the murder.
Alisha testified that on the night of October 9, 2002, Alisha, Cavaness, and Wheeler left the house to purchase crack cocaine while Robbie [a friend] and Ryan remained at the house. When they returned to the house, Alisha, Ca-vaness, and Ryan smoked the crack while Robbie and Wheeler smoked marijuana. Around 5 a.m., Ryan and Wheeler left to buy more crack, leaving Alisha, Cavaness, and Robbie at the house.
When Ryan and Wheeler returned, Wheeler realized his marijuana joint was missing and accused Alisha, Cavaness, and Robbie of stealing it while he was gone. Robbie and Wheeler got into a heated verbal argument which eventually involved everyone. Wheeler was told to leave, but he refused. After about an hour, Alisha, believing that the men were about to fight, went into her bedroom. The men went outside. Cavaness had a baseball bat, Ryan had bolt cutters, and Robbie had a wooden pole. Wheeler had no weapon. Alisha heard someone other than Wheeler yell, “Hit him.” She then heard someone say, “Get him back in the house.” When the men carried Wheeler back into the house, Alisha observed that there was a big, bleeding gash on his forehead and that he appeared to be unconscious. Alisha returned to her bedroom. When she heard a few more blows, she called Cavaness into her bedroom and asked him whether Wheeler was alive. Cavaness replied, “Yes.” Alisha stated that, from the time the men came back inside the house, Cavaness spent “[ajlmost the entire time” in Alisha’s bedroom but did come and go from her room, as did Ryan and Robbie. Alisha heard one of the men say that they could not let Wheeler go in that condition, and no one disagreed.
Cavaness called the next-door neighbor, Michael, asking him for something with which to tie up Wheeler. When Michael brought telephone wire over to the house to bind Wheeler, he saw Wheeler lying on the floor with his feet moving. Michael left and returned later at which time he observed that Wheeler’s feet were bound. He heard Wheeler moaning or calling out.
Alisha testified that about a half hour after the men brought Wheeler into the house, Robbie came into the bedroom and said that he had broken Wheeler’s neck and that he was dead. Robbie and Ryan then wrapped the body in a tarp and put it on the deck.
Ashley testified that she was close friends with Robbie. On October 10, 2002, Robbie called Ashley and asked her to come over to his apartment because he needed to talk to her. When she arrived, Robbie told Ashley that he had killed someone the night before. Later the same day, Robbie and Ashley drove to Cavaness’ house. Alisha, Ryan, and Cavaness were at the home. Ashley noticed blood on a recliner in the living room, as well as blood on the walls and ceiling. Robbie, Ryan, and Cavaness began describing how they had beaten and eventually killed the victim the night before. Ashley described Cavaness as smiling and laughing during the conversation. At one point Cavaness lifted a dustpan to show Ashley a puddle of blood hidden underneath. Robbie pointed out to Ashley where the victim’s body was outside. Ashley heard the men discuss disposing of the body by burning it or throwing it in the river and disposing of their bloody clothes by burning them. That evening, the three men dumped Wheeler’s body into the river. Alisha later helped Cavaness and Ryan try to clean up the living room by scrubbing blood off the walls. The next day, Ashley went to the police.
After Cavaness’ arrest, [two detectives] interviewed him. Cavaness waived his Miranda rights and made a videotaped statement which was played for the jury but is not included in the record on appeal. According to the detectives’ testimony about the statement, Cavaness admitted to participating in the beating of Wheeler, although he also stated Robbie was leading the attack. Cavaness said that after Wheeler was brought
back into the house, he struck Wheeler between one to three more times with the bat. Cavaness also admitted to having a discussion about whether the men could allow Wheeler to leave the house alive. He stated that the decision to kill Wheeler was a group decision. The entire ordeal lasted 2 hours. After the interview, Cavaness showed the detectives where the men had thrown Wheeler’s body into the river and where they had burned the clothes they had been wearing.
An underwater search and rescue team located Wheeler’s body a few days after the murder. The body was wrapped in a blue tarp with two bricks attached. The head was covered by a white plastic bag; the legs were bound and the hands tied behind the back.
State v. Cavaness,
278 Kan. 469, 101 P.3d 717, 719-20 (2004) (individuals’ surnames substituted without brackets).
After he was found guilty and sentenced, Cavaness sought post-conviction relief under Kan. Stat. Ann. 60-1507 (2003), alleging that his trial counsel provided ineffective assistance and that his incriminating statement, which was videotaped, should have been suppressed. The hearing was assigned to the judge who presided over Cavaness’s trial. After appointing counsel and conducting an evidentiary hearing in which both Cavaness and his trial counsel testified, the judge denied relief. The Kansas Court of Appeals (KCA) affirmed that decision.
Cavaness v. State,
176 P.3d 250 (Kan.App.2008) (unpublished decision),
rev. denied
(July 3, 2008).
Cavaness then turned to the federal courts, filing a § 2254 habeas petition with the district court that raised similar claims. After concluding Cavaness failed to show he was entitled to habeas corpus relief on any claim, the district court denied his petition. This appeal and COA request followed.
II. Discussion
The Antiterrorism and Effective Death Penalty Act (AEDPA) conditions a petitioner’s right to appeal a denial of habeas relief under § 2254 upon receiving a COA. We may issue a COA only if the applicant demonstrates a “substantial showing of the denial of a constitutional right,” § 2253(c)(2), such that “reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.”
Miller-El v. Cockrell,
537 U.S. 322, 338, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).
When a petitioner’s claims were adjudicated on the merits in state court proceedings, we may grant habeas 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” or was “based on an unreasonable determination of the facts in light of the evidence presented in the State court proceedings.” § 2254(d). AEDPA’s deferential treatment of state court decisions is incorporated into our consideration of a COA request.
Dockins v. Hines,
374 F.3d 935, 938 (10th Cir.2004).
Cavaness raised three issues in his ha-beas petition. First, he contended trial counsel was ineffective for not moving to suppress the incriminating statement Ca-vaness made to police officers after his arrest. Second, he claimed trial counsel was deficient for admitting during closing arguments that his client intentionally killed the victim. Third, he contended the trial court denied him the right to a fair trial by refusing to instruct the jury on the lesser-included offense of unintentional second-degree murder. Now that the district court dismissed his habeas petition,
Cavaness asserts the court erred in not granting him a COA. We address each argument in turn.
A. Failure to Move to Suppress Ca-vaness’s Incriminating Statement
Cavaness’s first claim is that his trial counsel provided ineffective assistance by not moving to suppress the incriminating statement Cavaness made to the police. He contends he was provided deficient counsel because no reasonably competent attorney would have wanted the statement admitted at trial. He also claims the statement should have been suppressed because the detectives interviewing him denied him the right to counsel.
To prevail on a claim of ineffective assistance, Cavaness must show his counsel’s performance “fell below an objective standard of reasonableness” and “the deficient performance prejudiced the defense.”
Strickland v. Washington,
466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Our review of counsel’s performance under
Strickland
is highly deferential: “counsel is strongly presumed to have rendered adequate assistance and made all significant decisions in the exercise of reasonable professional judgment.”
Id.
at 690, 104 S.Ct. 2052. “To be deficient, the performance must be outside the wide range of professionally competent assistance. In other words, it must have been completely unreasonable, not merely wrong.”
Hooks v. Workman,
606 F.3d 715, 723 (10th Cir.2010) (quotation marks omitted).
The challenge is even greater for a petitioner under § 2254, as our review in such circumstances is “doubly deferential.”
Knowles v. Mirzayance,
556 U.S. 111, 129 S.Ct. 1411, 1420, 173 L.Ed.2d 251 (2009). When assessing a state prisoner’s ineffective-assistance-of-counsel claim on habeas review, we “defer to the state court’s determination that counsel’s performance was not deficient and, further, defer to the attorney’s decision in how best to represent a client.”
Crawley v. Dinwiddle,
584 F.3d 916, 922 (10th Cir.2009). We also recognize that, “because the
Strickland
standard is a general standard, a state court has ... more latitude to reasonably determine that a defendant has not satisfied that standard.”
Knowles,
129 S.Ct. at 1420 (citation omitted).
The circumstances around Cavaness’s statement were explored during the state court evidentiary hearing on his ineffective-assistance-of-counsel claims. During this hearing, Cavaness testified that, after his arrest but before his statement was videotaped, he asked one of the detectives questioning him whether he should have an attorney. According to Cavaness, the detective responded by telling him “it was my decision, but his recommendation was that I do not get a lawyer this time and to help them. It would look better in front of a jury or whatever I face.” R., Vol II, Doc. 8 at 70. The detective did not ask Cavaness whether he was asking for an attorney.
Id.
at 71.
In addition, Cavaness’s trial counsel testified his handwritten notes recorded that “Defendant was told it would look better for him if he didn’t have a lawyer and cooperated with the police.”
Id.
at 73. Trial counsel also testified his client had sent him a letter stating, “I realize I shouldn’t have told the cops everything, but I was raised to be honest and it didn’t seem to me that I would be charged for that night what I didn’t do.”
Id.
at 77.
After reviewing the record, the state court found no deficient performance under the first
Strickland
prong because (1) it was unlikely that a motion to suppress would have been granted, and (2) the decision to forego a motion to suppress was a reasonable, strategic decision to use the
statement to bolster the defense theory that the crime was not premeditated. The court also found no prejudice under the second
Strickland
prong, particularly in light of the “very credible evidence of the defendant’s guilt in this case separate and apart” from Cavaness’s statement and trial testimony, including the testimony of three eyewitnesses. The KCA affirmed the state court’s application of
Strickland
after concluding its factual findings were supported by substantial evidence and its legal conclusions were legally sound.
We may grant a COA only if Cavaness demonstrates either (1) the KCA unreasonably applied
Strickland
to the facts of his ease, or (2) the KCA’s findings were based on an unreasonable determination of the facts in light of the evidence. Particularly in light of the “doubly deferential” review we give to state court determinations of ineffective-assistanee-of-counsel claims, Cavaness fails to satisfy either burden. After reviewing the record, we must defer to the KCA’s finding that trial counsel provided sufficient performance in presenting a defense strategy of persuading the jury and the court his client was less culpable than the others in causing Wheeler’s death.
Likewise, we must give credence to the KCA’s finding that the decision not to seek the statement’s suppression did not affect the trial’s outcome — particularly since that finding was based on the conclusion of the judge who presided at both Cavaness’s evidentiary hearing and his trial.
As part of his attempt to show deficient performance under the first
Strickland
prong, Cavaness contends that, if trial counsel had properly investigated the circumstances surrounding the videotaped statement, he would have discovered the detectives unconstitutionally denied his client the right to counsel. The KCA disagreed with this argument, holding the detectives had no obligation to cease questioning in the absence of an unequivocal request by Cavaness for counsel or to stop the interrogation.
Cavaness v. State,
176 P.3d 250 (2008) (citing
Davis v. United States,
512 U.S. 452, 114 S.Ct. 2350, 129 L.Ed.2d 362 (1994)). Cavaness contends this holding is contrary to clearly established law because “the police cannot actively dissuade the accused from exercising that right.” Aplt. Br. at 15.
This misrepresents the evidence in the record. Cavaness never testified at his evidentiary hearing that the detectives told him “if he exercised his right to counsel, the jury would use it against him,” as he now claims in his COA request.
See id.
at 16. Rather, Cavaness testified they said “it would look better in front of a jury if he answered the detectives questions.” R., Vol II, Doc. 8 at 70. While the Constitution prevents a jury from drawing a
negative
inference from a defendant’s exercise of his Fifth Amendment right to remain silent, it does not bar a jury from drawing a
positive
inference from the decision to waive that right.
Nor does
Davis
prohibit the detectives’ alleged response. In
Davis,
the Supreme Court clarified that questioning may continue “if a suspect makes a reference to an attorney that is ambiguous or equivocal in that a reasonable officer in light of the circumstances would have understood only that the suspect
might
be invoking the right to counsel.” 512 U.S. at 459, 114 S.Ct. 2350 (emphasis in original). As the district court noted, Cavaness’s question as
to whether he should have an attorney was similar to the defendant’s statement in
Davis
— “Maybe I should talk to a lawyer,”
see id.
at 455, 114 S.Ct. 2350 — which the Supreme Court held was not a clear invocation of the right to counsel. And since neither
Davis
nor any other Supreme Court decision specifies a limitation on how police should respond to an ambiguous reference to an attorney, the KCA’s holding is not contrary to “clearly established Federal law, as determined by the Supreme Court.”
See
§ 2254(d).
In summary, Cavaness has not met his burden of establishing he is entitled to habeas relief under § 2254(d) on the ground of trial counsel’s failure to move to suppress his incriminating statement to the police.
B. Trial Counsel’s Statements During Closing Argument
Next, Cavaness contends trial counsel was ineffective for not consulting with his client before informing the jury, during closing argument, that his client intentionally killed the victim. The district court found Cavaness defaulted this claim by failing to raise it before the state court, and we agree.
“Under the doctrine of exhaustion, a state prisoner must generally exhaust available state court remedies before filing a habeas corpus action in federal court.”
Demarest v. Price,
180 F.3d 922, 932 (10th Cir.1997) (citing
Picard v. Connor,
404 U.S. 270, 275, 92 S.Ct. 509, 30 L.Ed.2d 438 (1971)).
The exhaustion doctrine requires a state prisoner to fairly present his or her claims to the state courts before a federal court will examine them. ‘Fair presentation’ of a prisoner’s claim to the state courts means that the substance of the claim must be raised there. The prisoner’s allegations and supporting evidence must offer the state courts a fair opportunity to apply controlling legal principles to the facts bearing upon his constitutional claim. Therefore, although a habeas petitioner will be allowed to present ‘bits of evidence’ to a federal court that were not presented to the state court that first considered his claim, evidence that places the claims in a significantly different legal posture must first be presented to the state courts.
Id.
(citations and quotation marks omitted).
Cavaness acknowledges he did not raise this issue in his state post-conviction proceeding or appeal. Aplt. Br. at 22. And he does not dispute the district court’s finding that he can no longer receive state-court review of this claim because Kansas law prohibits a second or successive motion for collateral review. However, Cavaness contends “state court remedies were essentially exhausted because the substance of this claim rests on evidence presented in the post-conviction proceeding about [trial counselj’s general failure to adequately communicate with his client.”
Id.
We disagree. Cavaness’s general allegations that trial counsel inadequately consulted with him before and during trial were insufficient to fairly present to the state court the issue of trial counsel’s unilateral decision to make a particular admission during closing argument. The focus of the state court’s evidentiary hearing was on (1) the decision not to move to suppress Cavaness’s statement to the police, and (2) the amount of preparation Cavaness received before he testified at trial. Trial counsel’s closing argument was never mentioned. Under these circumstances, the state court did not receive a fair opportunity to consider this claim.
Without state-court exhaustion, a COA may be granted only if “there is an absence of available State corrective process” or if “circumstances exist that render such process ineffective to protect the rights of the applicant.” § 2254(b)(1). Because Ca-vaness can identify no such interference with State process, he has no excuse for failing to exhaust available state remedies.
Consequently, Cavaness’s claim related to trial counsel’s closing argument is defaulted and cannot serve as the basis for habeas relief.
C. Refusal of a Jury Instruction on a Lesser-included Offense
Cavaness’s third claim is that the trial court unconstitutionally refused to instruct the jury on a lesser-included offense. He argues Kansas law required an instruction on the crime of unintentional second-degree murder because the evidence indicates he did not intend to kill Wheeler.
As the district court correctly noted, we previously have held that the failure to instruct the jury on a lesser-included offense in a non-capital case is not a ground for granting federal habeas corpus relief.
See Dockins,
374 F.3d at 938;
Chavez v. Kerby,
848 F.2d 1101, 1103 (10th Cir.1988). No subsequent Supreme Court decision has set forth clearly established Federal law inconsistent with these precedents. Consequently, we find Cavaness cannot raise a debatable claim that he is entitled to habeas relief due to the absence of this jury instruction.
D. The District Court’s Denial of a COA
Finally, Cavaness contends the district court erred in denying him a COA because he has made a “substantial showing of the denial of a constitutional right,” § 2253(c)(2), such that “reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.”
Miller-El,
537 U.S. at 338, 123 S.Ct. 1029. As we have already demonstrated, we disagree.
III. Conclusion
For the foregoing reasons, we DENY Cavaness’s request for a COA and DISMISS his appeal. We also DENY Cavaness’s motion to proceed in forma pauper-is.