
508 F.3d 563 (2007)
John DOE, Petitioner-Appellant,
v.
Jeanne S. WOODFORD, in her capacity as Director of the California Department of Corrections; Joseph L. McGrath, Warden, in his capacity as Warden, Pelican Bay State Prison, Respondents-Appellees.
No. 06-16154.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted February 15, 2007.
Filed November 27, 2007.
*564 *565 Donald L. Lipmanson, Ukiah, CA, for the petitioner-appellant.
Dorian Jung, Office of the Attorney General, State of California, San Francisco, CA, for the respondents-appellees.
Before: J. CLIFFORD WALLACE, RICHARD D. CUDAHY,[*] and M. MARGARET McKEOWN, Circuit Judges.
CUDAHY, Circuit Judge:
In 1998, the petitioner, John Doe, pleaded guilty to first degree murder. Doe filed a petition for writ of habeas corpus in the California state trial court alleging ineffective assistance of counsel and that his plea was not voluntary and intelligent. After holding a three-day evidentiary hearing, the state court denied the petition without opinion. The California Court of Appeal and the California Supreme Court also summarily denied the petition. Doe then filed the present petition in the Northern District of California. The district court denied the petition but issued a certificate of appealability as to the voluntariness of the plea given the length of time the petitioner had to consider the proposed plea agreement. The petitioner appeals the denial of the petition and raises uncertified issues concerning ineffective assistance of counsel as well. We decline to expand the certificate of appealability and affirm the denial of the petition as to the certified issue.

FACTUAL AND PROCEDURAL BACKGROUND
On the morning of February 2, 1997, Petitioner John Doe was allegedly angry *566 with George Steven Wilson because Wilson had moved out of the petitioner's family ranch.[1] Doe told a number of people that he had decided to kill Wilson. Wilson was last seen alive that evening with Doe and Doe's companions, Donovan Williams and Dillon Bacon. When Doe, Williams and Bacon were seen later that evening without Wilson, they reported that his truck had become stuck in the mud and that Wilson had stayed behind with it.
Wilson was later found dead near his truck with three bullet wounds in his head. Doe had previously identified the place where Wilson's body was found as a good place to carry out a murder. Doe was subsequently taken into custody. While incarcerated, a jailhouse informant reported that Doe had told him where Doe had hidden the murder weapon. A gun was subsequently recovered at that location, and ballistics tests confirmed that it had been used in the killing.
On May 12, 1997, the Lake County District Attorney filed an information charging Doe with first degree murder pursuant to California Penal Code § 187(a). The information also included enhancements for: personal use of a firearm in the commission of the first degree murder charge pursuant to California Penal Code § 1203.06(a)(1)(A); being armed in the commission of the charged felony pursuant to California Penal Code § 12022.5(a); and personal infliction of great bodily injury pursuant to California Penal Code § 1203.075(a)(1).
Doe's trial began with jury selection on March 17, 1998. On that same day, Doe gave a statement to police detectives from the Lake County Sheriff's Office. In the statement, Doe reported that he witnessed Donovan Williams, one of the other individuals with Wilson the night of his murder, shoot Wilson in the head three times. He further reported that Williams had given him the murder weapon to dispose of.
On March 19, 1998, after the jury had been empaneled, Doe's trial counsel and the prosecutor asked the court to delay opening arguments to allow them time to discuss a plea arrangement. (See Petitioner's ER at 63-64.) The court agreed and allowed a two-hour recess until 4:30 that afternoon. Shortly before 5:00 p.m., Doe's trial counsel informed the court that they had reached a resolution. Doe then entered a negotiated plea of guilty to a charge of first degree murder pursuant to People v. West.[2] Pursuant to the plea agreement, the enhancements were dismissed, a case against Doe concerning an unrelated drug charge was also dismissed and the prosecution agreed to not pursue a possible burglary charge involving the suspected murder weapon or any perjury charges against Doe's girlfriend. On April 13, 1998, Doe was sentenced to prison for an indeterminate term of 25 years to life.
On March 30, 2000, Doe filed a petition for habeas corpus in the Superior Court of Lake County. In May of 2001, the court held a three-day evidentiary hearing on the habeas petition. On June 6, 2001, the court denied the petition without opinion. The petition was also summarily denied by the California Court of Appeal, First Appellate District Division and by the California Supreme Court. On September 30, 2004, Doe filed the present federal petition *567 for writ of habeas corpus. The district court denied the petition but granted a certificate of appealability as to one issue: whether the petitioner's plea agreement was involuntary in light of the fact he was allowed only two hours to accept or reject it.

STANDARD OF REVIEW
The Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA") governs our review of Doe's petition for writ of habeas corpus. Relevant for this review, a federal court can grant a state prisoner's petition for a writ of habeas corpus if the state court's decision: 1.) was "contrary to . . . clearly established Federal law, as determined by the Supreme Court of the United States"; or 2.) "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).
A state court's decision is "contrary to" clearly established federal law "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 decides a case differently than [the Supreme Court] has on a set of materially indistinguishable facts." Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). As for "unreasonable application," a federal court may grant relief "if the state court identifies the correct governing legal principle from [the Supreme Court's] decisions but unreasonably applies that principle to the facts of the prisoner's case." Id. at 413, 120 S.Ct. 1495. When a claim falls under the "unreasonable application" clause, the state court's application of the Supreme Court precedent must be "objectively unreasonable," not just incorrect. Wiggins v. Smith, 539 U.S. 510, 520-21, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003).
Lacking a reasoned opinion from the state court, we review the record independently to determine whether the state court decision was objectively unreasonable. Reynoso v. Giurbino, 462 F.3d 1099, 1109 (9th Cir.2006) (citing Pham v. Terhune, 400 F.3d 740 (9th Cir.2005) (per curiam)).

DISCUSSION
I. Scope of Certificate of Appealability
The district court certified only the issue whether Doe's plea was involuntary in light of the fact he was allowed only two hours to accept or reject it. In his opening brief, the petitioner also raised the other issue in his habeas petition under the heading of "Uncertified Issue." We construe this inclusion and designation as a motion to expand the Certificate of Appealability ("COA"). 9th Cir. R. 22-1(e).
"The required showing for originally obtaining a COA on a claim remains the standard by which this court reviews the broadening of a COA. A habeas petitioner's assertion of a claim must make a `substantial showing of the denial of a constitutional right.'" Hiivala v. Wood, 195 F.3d 1098, 1104 (9th Cir.1999) (quoting 28 U.S.C. § 2253(c)(2)). In order to make this showing, a petitioner "must demonstrate that the issues are debatable among jurists of reason; that a court could resolve the issues [in a different manner]; or that the questions are adequate to deserve encouragement to proceed further." Barefoot v. Estelle, 463 U.S. 880, 893 n. 4, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983) (alteration in original, internal quotation marks omitted); accord Slack v. McDaniel, 529 U.S. 473, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000).
The uncertified issue here involves ineffective assistance of counsel. Doe posits *568 two grounds for the appeal of this issue. First, Doe argues that his attorneys were deficient in failing to investigate potential mental defenses. Second, Doe contends that his attorneys' decision to allow him to be interviewed by the Lake County Sheriff's Office constitutes ineffective assistance of counsel. He further argues that he was prejudiced by the ineffectiveness of counsel since he would have gone to trial rather than plead guilty. The district court denied relief as to the petitioner's ineffective assistance of counsel argument and also declined to certify this issue. We agree with the district court that the petitioner has failed to "make a substantial showing of the denial of a constitutional right" (see 28 U.S.C. § 2253(c)(2)) and therefore decline to expand the COA to consider the merits of this issue.
To show ineffective assistance of counsel, Doe must demonstrate (1) that the defense attorney's representation "fell below an objective standard of reasonableness" and (2) that the attorney's deficient performance prejudiced the defendant such that "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland v. Washington, 466 U.S. 668, 668, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). In a guilty-plea case, like the present case, "in order to satisfy the `prejudice' requirement, the defendant must show that there is a reasonable probability that, but for counsel's errors, he would not have pleaded guilty and would have insisted on going to trial." Hill v. Lockhart, 474 U.S. 52, 59, 106 S.Ct. 366, 88 L.Ed.2d 203 (1985).[3]
Petitioner's argument that his trial counsel was deficient for failing to investigate mental state defenses is a far fetch. "Trial counsel has a duty to investigate a defendant's mental state if there is evidence to suggest that the defendant is impaired." Douglas v. Woodford, 316 F.3d 1079, 1085 (9th Cir.2003). In the present case, there was no evidence to suggest that the petitioner was impaired. The two pre-trial psychiatric evaluations of Doe by Drs. Drury and Rossoff not only determined that he was competent to stand trial, but also concluded that the petitioner did not suffer from mental disorders. Doe points to the psychiatric evaluation of Dr. Drury, who examined Doe prior to trial. (Petitioner's ER at 1-6.) That evaluation describes Doe's prior medical history, including his suicidal thoughts as a young teenager, his abuse of methamphetamines and prescription drugs for several years before the crime and head injuries Doe suffered in an auto accident in early 1996 and a motorcycle accident in December 1996. (Id. at 4.) After considering this and the other information contained in his evaluation, Dr. Drury concluded that "[b]ased upon personal information, it is my opinion that he is essentially free of major signs of mental disorder, mental diseases or psychiatric disease." (Id. at 6.) In addition, Dr. Thomson  the expert psychiatrist who testified at the evidentiary hearing on Doe's state court habeas petition  agreed that he had no doubt that Doe was competent to stand trial. (Respondent's ER at 141.) Although Dr. Thomson testified that Doe experienced some symptoms of "classical drug induced paranoia" as a result of his prior substance abuse (id. at 73) and that he thought Doe *569 may have suffered from some form of organic brain injury due to his prior head injuries (id. at 135-38, 144-45), he testified that Doe did not possess any "major" or "full blown" mental illness or mental disorder (id. at 74-75, 89).
The petitioner draws a distinction between competency evaluations and investigating mental defenses, arguing that a psychiatric evaluation that concludes that an individual is competent to stand trial is not the same as investigating mental defenses. Although this might be true, the duty to investigate mental defenses is only triggered "if there is evidence to suggest the defendant is impaired." Douglas, 316 F.3d at 1085. The defendant fails to point to any credible evidence of mental incapacity which would have triggered a duty on the part of his counsel to investigate for possible defenses. Moreover, petitioner's trial counsel made a reasonable strategic choice to rely on petitioner's claims of innocence and decided not to pursue further investigations into petitioner's mental state since he testified that a mental state defense "would have been inconsistent" with the theory of the case. (Petitioner's ER at 167.) See Siripongs v. Calderon, 133 F.3d 732, 734 (9th Cir.1998) (holding that "[w]here the attorney has consciously decided not to conduct further investigation because of reasonable tactical evaluations, the attorney's performance is not constitutionally deficient"). Therefore, Doe has failed to make a substantial showing of the denial of a constitutional right based on his trial counsel's performance.
Doe also fails to show that his trial counsel's decision to allow him to make a statement to police detectives on March 17 fell below an objective standard of reasonableness. The record supports a finding that the decision was strategic. As his counsel explained at the evidentiary hearing, without the statement, there would have been no reason for the prosecutor to participate in further plea bargain negotiations. (See Respondent's ER at 324.) Moreover, the present case is distinguishable from Harris ex rel. Ramseyer v. Wood, 64 F.3d 1432, 1436 (9th Cir.1995), a case relied on by the petitioner, in which we found the trial counsel's performance to be deficient in allowing the defendant to give a statement to police. Importantly, unlike the statement in Harris ex rel. Ramseyer, here, there were certain restrictions placed on the use of Doe's statement. Namely, it could not be used in the prosecutor's case-in-chief. (See Petitioner's ER at 9.) And, perhaps even more importantly, Doe's statement was also not directly incriminating since he did not confess to murdering the victim; rather, he explained that Donovan Williams killed the victim.
Because the ineffective assistance of counsel claims raised by the petitioner are not "debatable among jurists of reason," we decline to expand the COA and, therefore, dismiss the petitioner's uncertified issue for lack of jurisdiction.
II. Voluntariness of plea
We now turn to the certified issue. The petitioner argues that the voluntariness of his plea was undermined by the short period of time  two hours  that he had to consider the plea agreement.[4] Doe *570 further argues that the limited length of time, in combination with his mental defects, rendered his plea involuntary.
The test for determining whether a plea is valid is "whether the plea represents a voluntary and intelligent choice among the alternative courses of action open to the defendant." Hill, 474 U.S. at 56, 106 S.Ct. 366 (quoting Alford, 400 U.S. at 31, 91 S.Ct. 160) (quotation marks omitted); Boykin v. Alabama, 395 U.S. 238, 242-43, 89 S.Ct. 1709, 23 L.Ed.2d 274 (1969). "[T]he record must affirmatively disclose that a defendant who pleaded guilty entered his plea understandingly and voluntarily." Brady v. United States, 397 U.S. 742, 747 n. 4, 90 S.Ct. 1463, 25 L.Ed.2d 747 (1970). A guilty plea is coerced where a defendant is "induced by promises or threats which deprive[the plea] of the nature of a voluntary act." Iaea v. Sunn, 800 F.2d 861, 866 (9th Cir. 1986) (quotation marks and citation omitted). To determine the voluntariness of the plea, we look to the totality of the circumstances, examining both the defendant's "subjective state of mind" and the "constitutional acceptability of the external forces inducing the guilty plea." Id.
The case law on this issue is quite limited.[5] However, the amount of time Doe had to consider the plea is only relevant if it somehow rendered his plea coerced, and therefore involuntary. Recall that the jury had already been empaneled and that the court had delayed opening arguments until the following morning in order to provide Doe's counsel and the prosecution an opportunity to reconsider a plea bargain. Therefore, there was a plausible reason for the arguably short two hours Doe had to consider the proposed plea agreement. With this in mind, the proper question for review is whether the state court decision was contrary to, or involved an unreasonable application of, clearly established federal law, as determined by the Supreme Court. We conclude that it was not.
In accepting Doe's plea, the state trial court conducted a thorough plea colloquy. As the district court noted, the transcript of the plea colloquy covers sixteen pages. As is evidenced from the following exchange, the state trial court specifically addressed the adequacy of the length of time the defendant had to discuss the plea agreement with his counsel.
The Court: Now, have you talked about this case with your lawyers?
[Petitioner]: Yes.
The Court: And you believe you've had enough time to talk with them about your case?
[Petitioner]: I guess.
The Court: Well, is that a yes or a no?
[Counsel]: Maybe you could ask the next question first and maybe then he'll be able to answer this question.
The Court: Have you told your attorneys all the facts and circumstances that are known to you about your case?
[Petitioner]: Yes.
The Court: You've had enough time to talk with them about your case?
[Petitioner]:Yeah.
The Court: Is that a yes? I just need to be sure.
[Petitioner]:Yes.

*571 The Court: Okay. Are you pleading guilty freely and voluntarily?
[Petitioner]: Yes.
(Respondent's ER at 30.) Based in part on this exchange, the trial court found that the petitioner "understands the consequences to him of his plea of guilty. His plea of guilty is freely and voluntarily given, and there's a factual basis for his plea of guilty." (Id. at 36.)
In Blackledge v. Allison, 431 U.S. 63, 97 S.Ct. 1621, 52 L.Ed.2d 136 (1977), the Supreme Court held that findings made by the judge accepting the plea "constitute a formidable barrier in any subsequent collateral proceedings. Solemn declarations in open court carry a strong presumption of verity." Id. at 74, 97 S.Ct. 1621; cf. Chizen v. Hunter, 809 F.2d 560, 562 (9th Cir.1986) (holding that the defendant overcame statements made at his plea colloquy and showed his plea was involuntary where the plea was induced by misrepresentations by the defendant's counsel as to what the defendant's sentence would in fact be under the plea agreement). In a case where the defendant decided to plead guilty after trial had begun, the Tenth Circuit rejected the defendant's claim that the limitations on time for him to consider a plea bargain rendered it involuntary, relying in part on the defendant's "participat[ion] in a [plea] colloquy that leaves little doubt that his plea was knowing and voluntary." United States v. Graham, 466 F.3d 1234, 1239 (10th Cir.2006).[6]
The petitioner contends that the court should have questioned the voluntariness of his plea in light of Doe's "I guess" response, instead of "shoehorn[ing]" Doe's answer in a way that masked his grave doubts about whether to plead." (Petitioner's Opening Br. at 13.) The trial court, however, did respond to Doe's "I guess" answer. The court again asked if he had enough time to talk to his attorneys about the plea. (Respondent's ER at 30.) When Doe responded "Yeah," the court asked Doe to clarify, "Is that a yes?" Id. Moreover, earlier in the exchange when Doe did not understand a question, he had clearly answered "No." (See id. at 27.)
Doe argues that the limited time he had to consider the plea agreement must be considered in light of his "mental state." The petitioner relies on the testimony of Dr. Thomson offered at the evidentiary hearing. Dr. Thomson testified to certain "factors," namely immaturity, history of brain head-injury accidents, history of methamphetamine use and limited education, which impacted the defendant's mental state at the time he considered the plea agreement. (Petitioner's ER at 75.) When pressed, however, Dr. Thomson admitted that there was no evidence to support a "major mental illness diagnosis." (Id. at 80-81.) Moreover, Dr. Drury, who provided a competency evaluation prior to trial, found Doe to be "essentially free of major signs of mental disorder, mental disease or psychiatric disease" and concluded that he was competent to stand trial. (Id. at 6.) The competency standard to plead guilty is the same as that to stand trial. Miles v. Stainer, 108 F.3d 1109, 1112 (9th Cir.1997) (citing Godinez v. Moran, 509 U.S. 389, 402, 113 S.Ct. 2680, 125 L.Ed.2d 321 (1993)). Any evidence of mental deficiencies did not undermine the voluntariness of Doe's plea even in light of the alleged limitation to two hours he claims he had to consider the proposed plea agreement.
*572 Doe's testimony at the evidentiary hearing describes the difficulty he had in making the decision to plead guilty. (Respondent's ER at 136-41.) Recall, however, that Doe was offered identical terms shortly after he was arrested, more than a year before he pleaded guilty. We have no doubt that the decision to plead guilty is a difficult one for many defendants, but the fact that one struggles with the decision, and might later even come to regret it, does not render it coerced. See Johnson v. United States, 539 F.2d 1241, 1243 (9th Cir.1976). Here, Doe participated in a thorough plea colloquy, in which he answered in the affirmative that his plea was voluntary under the circumstances and, specifically answered in the affirmative when asked if he had had enough time to discuss the plea with his attorneys. We conclude that the California Supreme Court was not objectively unreasonable in its application of controlling federal law by determining that Doe's plea was voluntary. See Lockyer v. Andrade, 538 U.S. 63, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003).
AFFIRMED.
NOTES
[*]  The Honorable Richard D. Cudahy, Senior United States Circuit Judge for the Seventh Circuit, sitting by designation.
[1]  The facts are derived from the decision of the California Court of Appeal, First Appellate Division, denying Doe's direct appeal. Case No. A083099 (filed Oct. 12, 1999). These facts are not disputed.
[2]  People v. West, 3 Cal.3d 595, 91 Cal.Rptr. 385, 477 P.2d 409 (1970) does not require an admission of guilt and is the California equivalent of an Alford plea. See North Carolina v. Alford, 400 U.S. 25, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970).
[3]  The district court, at times in its opinion, does not rely on the correct standard for demonstrating prejudice in a plea bargain case. However, the district court found, and we agree, that Doe has failed to demonstrate that his trial counsel's performance "fell below an objective standard of reasonableness"  the first prong of the Strickland test  and therefore, this apparent error is harmless.
[4]  The total amount of time the petitioner had to consider the plea is in dispute. The transcript reflects that the trial proceedings were suspended for a little more than two hours before Doe informed the trial court that he had accepted a plea agreement. However, the respondent argues that the petitioner had more time than those two hours to consider the plea. His trial counsel testified that the plea negotiations happened over a couple of days. Even the petitioner acknowledges that the "proposed disposition was identical to an offer that Doe had rejected shortly after arraignment following his arrest." (Petitioner's Opening Br. at 12.)
[5]  This court has held that nine days to consider a plea bargain was not inadequate. United States v. Estrada-Plata, 57 F.3d 757, 760-61 (9th Cir.1995).
[6]  Although Graham involved a direct appeal from a plea to a federal offense and the plea was taken pursuant to Federal Rule of Criminal Procedure 11, the plea colloquy demonstrated voluntariness under the same constitutional standard applicable in this case. See Alford, 400 U.S. at 31, 91 S.Ct. 160; Brady, 397 U.S. at 748, 90 S.Ct. 1463.
