
653 F.3d 1188 (2011)
UNITED STATES of America, Plaintiff-Appellee,
v.
Robert G. WEEKS, Defendant-Appellant.
Nos. 09-4171, 09-4183.
United States Court of Appeals, Tenth Circuit.
August 9, 2011.
*1192 Kent R. Hart, Assistant Federal Defender (Scott Keith Wilson, Assistant Federal Defender and Steven B. Killpack, Federal Defender, with him on the briefs), *1193 Salt Lake City, UT, for Defendant-Appellant.
Diana Hagen, Assistant United States Attorney (Stewart C. Walz, Assistant United States Attorney and Carlie Christensen, Acting United States Attorney, with her on the brief), Salt Lake City, UT, for Plaintiff-Appellee.
Before TYMKOVICH, SEYMOUR, and HOLMES, Circuit Judges.
SEYMOUR, Circuit Judge.
Robert G. Weeks pled guilty to conspiracy to commit securities fraud. He now argues his guilty plea was not knowing and voluntary and was the result of ineffective assistance of counsel. We consolidated his direct appeal with the appeal from the district court's denial of his § 2255 petition. We affirm Mr. Weeks' conviction on his direct appeal, but we reverse the dismissal of his § 2255 petition.

I.
This appeal reaches us in an unusual posture. In 2002, Mr. Weeks pled guilty to conspiracy to commit securities fraud. He agreed to cooperate with the government and to testify against his co-defendants. Four years later, Mr. Weeks was sentenced to a year and a day in prison, and was ordered to pay a fine of $51,643.25.[1] Mr. Weeks did not file a direct appeal.
A year after sentencing, Mr. Weeks filed a timely pro se motion under 28 U.S.C. § 2255 to vacate his conviction, raising a claim of ineffective assistance of counsel on six grounds. The district court denied relief on five of the grounds, but granted an evidentiary hearing on Mr. Weeks' claim that his counsel was ineffective for refusing his request to file a direct appeal from his conviction.
The district court appointed counsel for Mr. Weeks prior to the evidentiary hearing. Counsel filed a motion to expand the issues in Mr. Weeks' 2255 motion and/or to reconsider the court's denial of Mr. Weeks' ineffective assistance claim on the five other grounds. The district court denied the motion. After holding an evidentiary hearing on the one remaining claim, the court found Mr. Weeks' trial counsel ineffective for failing to file a direct appeal. The court entered an amended judgment of conviction to restore Mr. Weeks' right to appeal his conviction.
Mr. Weeks filed a direct appeal. He also appealed the district court's denial of the remainder of his § 2255 ineffective assistance claims without an evidentiary hearing, as well as the denial of his motion to amend the petition. We consolidated the appeals, and we granted a certificate of appealability to Mr. Weeks on the denial of his § 2255 petition. We now consider both of his appeals.

II.
The criminal charges against Mr. Weeks and his co-defendants arose from the unregistered sale of stocks issued by Mr. Weeks' corporation, Pan World Minerals International, Inc., while he was president and CEO. Mr. Weeks pled guilty to violating 18 U.S.C. § 371, by participating in a conspiracy to commit securities fraud.
Because the plea colloquy plays a central role in Mr. Weeks' direct and collateral appeals, we provide relevant parts of the colloquy with minimal editing. The district court first confirmed that Mr. Weeks had read and understood the indictment:

*1194 THE COURT: Mr. Weeks, have you received a copy of the superseding indictment pending against you in this case, that is the written charges in this case?
[MR. WEEKS]: I have.
THE COURT: Have you read the indictment?[[2]]
[MR. WEEKS]: I have.
THE COURT: Have you discussed it with [your attorney] Mr. Barber?
[MR. WEEKS]: Yes.
Rec., vol. IV at 32-33 (emphasis added).
After Mr. Weeks waived his right to have the indictment read aloud, the district court asked the United States to recite the charges against him:
THE COURT: Mr. Walz, will you please set forth the elements of the conspiracy charge, please.
MR. WALZ: Yes, Your Honor. The elements of a conspiracy charge are, one, that there was an agreement by two or more people, two, to violate any criminal statute of the United States. And in this case the criminal statutes alleged were violation of 15 United States Code, Section 78j(b) and the regulation thereunder, Section 10(b)(5), which is securities fraud, and also 15 U.S.C., Section 17b  or, excuse me  it is 17b. And I have forgotten the number.... 77j. And then also 77q(b)  I apologize  which is providing  or it's actually the statute prohibits the receipt of undis[cl]osed compensation when touting the stock.... Also false statements under 18 U.S.C. 1001, and money laundering under various subsections of Section 1956. After the agreement to violate a statute, it has to be done knowingly and intentionally and then there has to be an overt act committed by one or more of the conspirators in furtherance of the illegal agreement.
THE COURT: Mr. Weeks, do you understand the charge against you and what it means?

[MR. WEEKS]: I do, but I need to consult my attorney.

Id. at 33-34 (emphasis added). After Mr. Weeks spoke with his counsel, Mr. James Barber, Mr. Barber explained Mr. Weeks' concern:
MR. BARBER: His question is because of the naming of the statutes that were the object of the conspiracy, Mr. Weeks was concerned that the plea is for some of the substantive counts. That is not correct. It's simply a charge under Section 371, that you conspired to violate the other sections that Stewart just named on the record.... [T]he gist of the offense is that you conspired with other people, more than one, to commit violations of one or more of those various statutes, and that is the charge.

Id. 34-35 (emphasis added).
The court confirmed that Mr. Weeks understood the charge and proceeded. As the colloquy continued, Mr. Weeks affirmed that he had read and understood the plea agreement and had discussed it with Mr. Barber. Later, the court asked Mr. Weeks to explain what actions made him guilty of the conspiracy charge:
[MR. WEEKS]: I allowed the stock of a public company to be issued to two individuals who took it offshore and broke the laws of the United States.
THE COURT: You did this knowingly?

[MR. WEEKS]: No, but I was a party to it.

*1195 Id. at 41 (emphasis added). Mr. Barber then volunteered "to direct questions to Mr. Weeks to make it a little bit more clear." Id. at 42. The court replied:
THE COURT: As you can understand, I am concerned when your client says he did not do this knowingly. I think, as Mr. Walz indicated, that part of the conspiracy element  one of the elements is that the activities were done knowingly. So, yes, if you would like to go ahead and try to do that, please do.
MR. BARBER: Mr. Weeks, you knew, did you not, during the period in question that large numbers of Pan World shares were being sold in the marketplace?
[MR. WEEKS]: I knew that, yes.
MR. BARBER: You knew when that was happening, did you not, that those shares were not registered under the Securities Act of 1933?
[MR. WEEKS]: I knew that.
THE COURT: You knew that because your counsel for Pan World had attempted to file a registration statement that would have cured that problem, but the staff of the commission would not permit it to go effective; is that your understanding of it?
[MR. WEEKS]: That is correct.
MR. BARBER: Now these large amounts of shares were therefore sold, were they not, in reliance on purported exemptions from registration?

[MR. WEEKS]: That's correct.

MR. BARBER: One of your co-conspirators was the individual to whom you looked for advice about that issue; was it not?
[MR. WEEKS]: Yes.
MR. BARBER: And you did not specifically speak with counsel and disclose to him all the facts about the sale of those shares before some of those sales were permitted to be effected, did you?
[MR. WEEKS]: That's probably correct, yeah.
MR. BARBER: In fact, you are convinced now that because there was the sale of offshore securities by your confederates in which they received the proceeds but did not acknowledge the fact that the shares were actually being sold for their account and with the proviso that they would receive the use and benefit of those proceeds, that there was a violation of the Securities Act of 1933 because the seller wasn't anybody who was represented to be the seller and, secondly, there may have been antifraud provisions arising from the fact that persons who were in control of Pan World were participating in a huge market for Pan World Shares without disclosing that to the public? That is what happened, isn't it?
[MR. WEEKS]: Yes.

MR. BARBER: I believe that is adequate. You knew those facts were happening?

[MR. WEEKS]: Yes.
MR. BARBER: When they were happening?
[MR. WEEKS]: Yes.
MR. BARBER: You permitted it to happen notwithstanding?
[MR. WEEKS]: That's correct.
THE COURT: Was your decision not to ask more questions a knowing decision, a conscious decision? Was your decision not to ask more questions about what was happening a conscious decision on your part?
[MR. WEEKS]: I don't remember if it were or weren't.

MR. BARBER: You never took the initiative to ascertain by  I mean you didn't know some of the facts; is that correct?

[MR. WEEKS]: That is absolutely correct.


*1196 MR. BARBER: But you also knew that your confederates were receiving substantial sums of money from the sale of Pan World stock?
[MR. WEEKS]: That is true.
MR. BARBER: One of them had the ability to control or to dictate the course of action of Pan World during that period because they were providing all the money that it had available to it; is that correct?
[MR. WEEKS]: That is correct.
MR. BARBER: Notwithstanding that, you did not make any attempt to disclose to the market the fact that the shares of Pan World that were going into the market through a secondary device that was probably illegal as well were being sold on behalf of persons who would be conceived as having been affiliates or controlling persons of the issuer?
[MR. WEEKS]: That's correct.
Id. at 42-45 (emphasis added).
At the court's request, the government then summarized the evidence that would have been used against Mr. Weeks if there had been a trial.[3] The government claimed to have evidence that Mr. Weeks "was aware" that brokers were paid for selling Pan World stock, but that these brokers were not disclosed to customers. It also asserted Mr. Weeks "knew or had to know" that proceeds from the sale of Pan World shares under an S-8 exemption, which prohibits using the stock for money raising, were being sent back to Pan World. Mr. Weeks agreed the government's description of his conduct was "reasonably fair." Id. at 48. The government did not state it had evidence Mr. Weeks knew, at the time, that these activities were illegal.
The court asked both the prosecutor and defense counsel whether they believed that an adequate basis for the plea had been established. Both attorneys agreed that it had. After the court advised Mr. Weeks of his rights, Mr. Weeks pled guilty and agreed that he was pleading guilty "voluntarily and of [his] own free will." Id. at 51. Four years later, Mr. Weeks was sentenced to a year and a day in prison, and ordered to pay a fine of $51,643.25.
Mr. Weeks now asserts that his guilty plea was not knowing and voluntary. In his pro se § 2255 motion, he articulated an ineffective assistance of counsel claim based generally on six grounds for relief: (1) failure to meet and confer with the defendant in a meaningful manner; (2) failure to conduct meaningful due diligence and discovery; (3) failure to inform the petitioner regarding the superseding indictment; (4) failure to file a motion to dismiss; (5) fraud on the court; and (6) failure to file an appeal. As supporting facts, Mr. Weeks asserted that Mr. Barber had never met with him to review, discuss, or analyze the 160,000 pages of documents involved in the case. Mr. Barber did not review or even organize the vast quantity of documents underlying the claims against Mr. Weeks. Mr. Barber failed to prepare for pre-trial hearings and never conferred with, counseled, or prepared Mr. Weeks for these pre-trial hearings. Mr. Barber never deposed or conducted interviews with possible witnesses. Mr. Barber did not advise Mr. Weeks of the second superseding indictment before his arraignment or explain the importance and effect of that indictment's addition of a conspiracy charge. Mr. Weeks then asserted:
As the trial date approached, the petitioner realized more and more that he *1197 was faced with a Faustian choice  go to trial unprepared or plead guilty. Nevertheless, the petitioner wanted to go to trial. The petitioner believed in the system, however flawed the apparent circumstances. Counsel, knowing full well he was wholly unprepared for a complex, international securities fraud and conspiracy trial, demanded that the petitioner plead guilty, and unbeknownst to the petitioner and without his authority, negotiated his guilty plea with the Government, and from a position of weakness. Upon learning this, the petitioner refused to participate in what he believed was a fraud on the Court and unethical conduct by his counsel. Yet as a man of principal [sic] and conscience, the petitioner remained steadfast in his refusal to plead guilty. Then, counsel, using egregious and unconscionable tactics against his client, stated that the petitioner would lose the trial and receive a sentence of seven years imprisonment. Further, counsel was desperate not to go to trial, and leaned heavily on [] his client to plead guilty as a cover for his lack of thorough pre-trial consultation, investigation and preparation of the petitioner's case. Finally, the petitioner's constitution and resolve collapsed in the face of the Government's relentless eight-year prosecution, combined with his counsel's ultimate refusal to take his case to trial.
Supp. Rec., vol. II at 32-33.
Mr. Weeks said he "struggled mightily at his plea and sentencing hearings in his colloquy and allocution before the Court," id. at 33, and that he "never admitted to `willfully and knowingly' committing the crime of conspiracy," id. He further asserted that shortly after sentencing, he demanded that Mr. Barber "retract his guilty plea or appeal his conviction." Id. at 35. Mr. Barber refused, and represented to Mr. Weeks that he could not retract his guilty plea. He also incorrectly told Mr. Weeks that he had waived his right to appeal his conviction.

III.

A. Direct Appeal
We first address Mr. Weeks' direct appeal.[4] Mr. Weeks contends the district court erred in accepting his guilty plea to the crime of conspiracy. He pled guilty under 18 U.S.C. § 371, which requires "(1) an agreement with another person to violate the law, (2) knowledge of the essential objectives of the conspiracy, (3) knowing and voluntary involvement, and (4) interdependence among the alleged conspirators." United States v. Wardell, 591 F.3d 1279, 1287 (10th Cir.2009) (internal quotation marks omitted). Additionally, "[d]uring the conspiracy, at least one of the coconspirators must commit an overt act in furtherance of the conspiracy." Id. Mr. Weeks maintains he did not understand that conspiracy requires an agreement to violate the law and knowledge of the illegality of the agreement. He also asserts that during the plea colloquy he *1198 "never admitted that he agreed to break the law." Aplt. Br. at 24.
The government responds that the district court was "diligent in ensuring that Weeks fully understood the elements of the offense to which he was pleading guilty," and that Mr. Weeks admitted the essential elements of the offense. Aple. Br. at 20. The government also argues that even if Mr. Weeks did not admit to committing the crime, his plea was nonetheless valid as an Alford plea. See North Carolina v. Alford, 400 U.S. 25, 37, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970) (holding that a guilty plea accompanied by protestations of innocence is valid when the "defendant intelligently concludes that his interests require entry of a guilty plea and the record before the judge contains strong evidence of actual guilt").
Mr. Weeks did not move to withdraw his guilty plea before he was sentenced, and he never objected on the basis that his plea was not knowing and voluntary. In fact, he told the district court the contrary during his plea colloquy by stating that he understood the charge and was voluntarily entering his guilty plea. "Whether a guilty plea was entered knowingly and intelligently is generally a question of law subject to de novo review." United States v. Vidal, 561 F.3d 1113, 1118 (10th Cir.2009). But where, as here, the defendant did not raise the objection below, we review for plain error. Id.; see also United States v. Vonn, 535 U.S. 55, 59, 122 S.Ct. 1043, 152 L.Ed.2d 90 (2002). "Plain error occurs when there is (1) error, (2) that is plain, which (3) affects the defendant's substantial rights, and which (4) seriously affects the fairness, integrity, or public reputation of judicial proceedings." United States v. Landeros-Lopez, 615 F.3d 1260, 1263 (10th Cir.2010) (internal quotation marks omitted). An error is "plain" if it is clear or obvious under current, well-settled law. United States v. Olano, 507 U.S. 725, 734, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993); United States v. Edgar, 348 F.3d 867, 871 (10th Cir.2003). We "apply the plain error rule less rigidly when reviewing a potential constitutional error, such as accepting a plea that is not knowing and intelligent." Vidal, 561 F.3d at 1119 (citation and internal quotation marks omitted).
"[B]ecause a guilty plea is an admission of all the elements of a formal criminal charge, it cannot be truly voluntary unless the defendant possesses an understanding of the law in relation to the facts." United States v. Gigot, 147 F.3d 1193, 1198 (10th Cir.1998) (quoting McCarthy v. United States, 394 U.S. 459, 466, 89 S.Ct. 1166, 22 L.Ed.2d 418 (1969)) (internal quotation marks omitted). If the defendant does not have any real understanding of the nature of the crime charged, then the plea cannot be a "`deliberate' choice between `available alternatives.'" Id. at 1199; see also Hicks v. Franklin, 546 F.3d 1279, 1284 (10th Cir.2008) ("The defendant receives `real notice' of the charge when he has been informed of both the nature of the charge to which he is pleading guilty and its elements.").
"Rule 11 of the Federal Rules of Criminal Procedure `is designed to assist the district judge in making the constitutionally required determination that a defendant's guilty plea is truly voluntary.'" Gigot, 147 F.3d at 1197 (quoting McCarthy, 394 U.S. at 465, 89 S.Ct. 1166). Before a district court may accept a guilty plea, it must "determine that the defendant understands ... the nature of each charge to which the defendant is pleading." Fed.R.Crim.P. 11(b)(1). Rule 11 also requires a district court to "determine that there is a factual basis for the plea" before it enters judgment on a guilty plea. Fed.R.Crim.P. 11(b)(3). "This rule is intended `to ensure the accuracy of the plea *1199 through some evidence that a defendant actually committed the offense.'" Landeros-Lopez, 615 F.3d at 1263 (quoting United States v. Keiswetter, 860 F.2d 992, 995 (10th Cir.1988)). It therefore "protect[s] a defendant who is in the position of pleading voluntarily ... but without realizing that his conduct does not actually fall within the charge." McCarthy, 394 U.S. at 467, 89 S.Ct. 1166 (quoting Fed.R.Crim.P. 11, Notes of Advisory Committee on Criminal Rules (1966)) (internal quotation marks omitted).
The transcript of the plea colloquy reflects that the district court carefully followed the Rule 11 procedures. Nevertheless, Mr. Weeks contends he pled guilty without actually understanding the true nature of the crime of conspiracy. He asserts that he never actually admitted to agreeing with his alleged coconspirators to violate securities laws, as opposed to finding out the illegality of the activities after the fact.
As we have noted above, a guilty plea cannot "be voluntary in the sense that it constituted an intelligent admission that he committed the offense unless the defendant received real notice of the true nature of the charge against him...." Henderson v. Morgan, 426 U.S. 637, 645, 96 S.Ct. 2253, 49 L.Ed.2d 108 (1976) (internal quotation marks omitted). In order to establish an involuntary plea under Henderson, Mr. Weeks must: "(1) show that the [intent] element was a critical element of [the charge]; (2) overcome the presumption that his attorney explained this element to him at some other time prior to his guilty plea; and (3) demonstrate that, prior to his guilty plea, he did not receive notice of this element from any other source." Allen v. Mullin, 368 F.3d 1220, 1241 (10th Cir. 2004) (alteration in original) (internal quotation marks omitted).
The problem for Mr. Weeks is the high hurdle of the plain error test. From a review of the plea colloquy, it is not "obvious," as required by the plain error test, that Mr. Weeks misunderstood, and thereby failed to admit to, the charges against him; the court, his counsel, and the prosecutor all provided further explanations of the charge in response to his assertion in the plea colloquy that he did not "knowingly" allow the stock of his company to be sold offshore in violation of the law. See Rec., vol. IV at 42-48. The plea colloquy is sufficiently confusing that, even after multiple readings, it is difficult to determine whether Mr. Weeks understood and admitted to all of the essential elements of conspiracy.
Several facts in particular convince us that any error is not plain. After the government stated the elements of the conspiracy, Mr. Weeks informed the court that he had read and understood both the indictment and the plea agreement.[5] Generally, when a defendant is provided with a copy of his indictment "[s]uch circumstances, standing alone, give rise to a presumption that the defendant was informed of the nature of the charge against him." Bousley v. United States, 523 U.S. 614, 618, 118 S.Ct. 1604, 140 L.Ed.2d 828 (1998) (citing Henderson, 426 U.S. at 647, 96 S.Ct. 2253). In addition, the district court emphasized that one of the elements of conspiracy is that "the activities were done knowingly." Rec., vol. IV at 42. Mr. Weeks admitted he knew that unregistered Pan World shares were being sold *1200 by his confederates in the marketplace. He also agreed that he is "convinced now... that there was a violation of the Securities Act of 1933," and that he "knew those facts were happening ... [w]hen they were happening." Id. at 43-44. Both prosecution and defense counsel informed the court that they believed an "adequate basis for the plea [had] been established" during the plea colloquy. Id. at 49.
At the end of the colloquy, Mr. Weeks pled guilty to the conspiracy charge without any further claim that he did not knowingly violate the law. Furthermore, four years passed between Mr. Weeks' guilty plea and sentencing, during which time Mr. Weeks raised no concerns about the validity of his guilty plea. Under these circumstances, it is neither obvious nor plain that Mr. Weeks' plea was involuntary. Accordingly, we affirm Mr. Weeks' conviction.[6]

B. Collateral attack.
In Mr. Weeks' collateral attack, he contends the district court erred in denying his § 2255 petition without holding an evidentiary hearing because his pro se petition raised issues regarding the ineffective assistance of his trial counsel which, if true, would entitle him to relief.[7] He claims his counsel's ineffectiveness caused his guilty plea to be involuntary because it directly resulted in his pleading guilty to conspiracy without understanding the nature of the conspiracy charge in the second superseding indictment and consequently without admitting to all the elements of the conspiracy.[8]
"Unless the motion and the files and records of the case conclusively show that the prisoner is entitled to no relief, the court shall ... grant a prompt hearing thereon, determine the issues and make findings of fact and conclusions of law with respect thereto...." 28 U.S.C. § 2255(b). Accordingly, "[r]eview in a section 2255 habeas action entails a two-step inquiry: (1) whether the defendant is entitled to relief if his allegations are proved; and (2) whether the district court abused its discretion by refusing to grant an evidentiary hearing." United States v. Whalen, 976 F.2d 1346, 1348 (10th Cir.1992).
We first consider whether Mr. Weeks has articulated facts which, if proven, would entitle him to relief. When a habeas petitioner challenges his guilty plea on the ground that he was denied his Sixth Amendment right to effective assistance of counsel, he must satisfy two criteria to show entitlement to relief. First, he must show that his counsel's representation "fell below an objective standard of reasonableness." Strickland v. Washington, 466 U.S. 668, 688, 104 S.Ct. 2052, 80 L.Ed.2d 674 *1201 (1984). Second, he "must show that the deficient performance prejudiced the defense." Id. at 687, 104 S.Ct. 2052; see also Hill v. Lockhart, 474 U.S. 52, 56-58, 106 S.Ct. 366, 88 L.Ed.2d 203 (1985); United States v. Harms, 371 F.3d 1208, 1211 (10th Cir.2004). To demonstrate prejudice, the petitioner "must show that there is a reasonable probability that, but for the counsel's errors, he would not have pleaded guilty and would have insisted on going to trial." Hill, 474 U.S. at 59, 106 S.Ct. 366.
"Where, as here, the defendant is represented by counsel during the plea process and enters his plea upon the advice of counsel, the voluntariness of the plea depends on whether counsel's advice was within the range of competence demanded of attorneys in criminal cases." Id. at 56, 106 S.Ct. 366 (internal quotation marks omitted). In Henderson v. Morgan, 426 U.S. 637, 96 S.Ct. 2253, 49 L.Ed.2d 108 (1976), the Supreme Court "clearly established the rule that a defendant must receive notice of all critical elements of the charge to which he pleads guilty." Hicks v. Franklin, 546 F.3d 1279, 1284 (10th Cir.2008) (discussing Henderson). Thus, an individual may bring an ineffective assistance of counsel claim based on the argument that he lacked notice of the elements of the crime:
[I]f the defendant's attorney does not supply his client with notice of the critical elements of the crime to which he is pleading guilty, and the defendant does not learn this information from another source, the attorney has deprived the defendant of his right to make a fully informed and voluntary decision regarding the prosecution's plea offer.... [T]he Sixth Amendment requires that the defendant's attorney supply his client with the requisite notice in order to ensure that the ensuing plea is knowing and voluntary.
Miller v. Champion, 161 F.3d 1249, 1255 (10th Cir.1998).[9]
To establish that his plea was involuntary under Henderson and that his counsel's advice was outside the range of competence demanded of attorneys in criminal cases, Mr. Weeks must "(1) show that the [intent] element was a critical element of [the charge]; (2) overcome the presumption that his attorney explained this element to him at some other time prior to his guilty plea; and (3) demonstrate that, prior to his guilty plea, he did not receive notice of this element from any other source." Id.; see also Henderson, 426 U.S. at 646-47, 96 S.Ct. 2253. "As to the second requirement, we will not indulge the presumption unless there is factual basis in the record to support it." Allen, 368 F.3d at 1241 (citing Miller, 161 F.3d at 1255).
If the facts Mr. Weeks alleged in his petition are true, then he has made a credible claim that his plea was involuntary because of his attorney's ineffectiveness. First, Mr. Weeks alleges he did not understand the elements of conspiracy. According to the petition, Mr. Weeks' counsel failed to properly advise Mr. Weeks of the charges in the second superseding indictment. As a result, he did not understand that his lack of intent to commit a crime, i.e., his lack of knowledge of the illegality of the activities to which he had agreed, provided a valid defense to the conspiracy charge. Supp. Rec., vol. II at 28-29.
*1202 Knowledge of an agreement to violate the law is a critical element of the offense to which Mr. Weeks pled guilty. See Allen, 368 F.3d at 1242 ("[W]e do not gainsay that the intent element of a criminal offense is a critical element of the charge."). As we have recognized above, an individual cannot knowingly and voluntarily plead guilty to conspiracy without understanding that the crime of conspiracy requires a knowing agreement to violate the law. "Moreover, a conspiracy conviction requires at least the degree of criminal intent necessary for the substantive offense itself. Thus, mere knowledge or acquiescence in the purposes of the conspiracy is not sufficient to establish the defendant's willful entry into the conspiracy." United States v. Weidner, 437 F.3d 1023, 1033 (10th Cir.2006) (citations and internal quotation marks omitted). An agreement with others that certain activities be done, without knowing at the time of the agreement that the activities violate the law, is therefore insufficient to establish conspiracy. Mr. Weeks' petition alleges facts which, if true, satisfy this first requirement.
As to the second requirement of Miller, there is a factual basis in the record to support a presumption that Mr. Barber properly explained the elements of conspiracy to Mr. Weeks. During the plea colloquy, Mr. Weeks confirmed he had fully discussed the charge against him with Mr. Barber and was fully satisfied with Mr. Barber's counsel, advice, and representation. But Mr. Weeks' petition alleges adequate facts which, if proved, would overcome this presumption. Mr. Weeks' petition asserts that his attorney inadequately counseled and advised him on the second superseding indictment (which added the conspiracy count), and that as a result he did not "understand the relative meaning and import of a superseding indictment and its securities fraud and conspiracy charges" until during his imprisonment. Supp. Rec., vol. II at 28.
Mr. Weeks' statements during the plea colloquy appear to lend some support to his claim that Mr. Barber failed to properly explain to him the meaning of the elements of conspiracy. After the charges against Mr. Weeks were read aloud, he asked to consult with his lawyer, suggesting he had questions about the charge. Moreover, Mr. Weeks' description of his own conduct suggests he may have misunderstood the elements of conspiracy. When the court asked him to describe "what you did that you believe makes you guilty of the conspiracy charge," he replied, "I allowed the stock of a public company to be issued to two individuals who took it offshore and broke the laws of the United States." Rec., vol. IV at 41. But Mr. Weeks immediately denied having done this "knowingly," and explained instead that he "was a party to it." Id. "[W]here a defendant affirmatively indicates to the court that he does not understand a critical element of the charge against him, the presumption that a defendant has been sufficiently notified by defense counsel of what he is being asked to admit will typically be unwarranted." Hicks, 546 F.3d at 1285.
Third, although Mr. Weeks was informed generally of the elements of conspiracy during the plea colloquy, the facts he alleges, if proved, could show he did not receive true notice of the nature of the crime from a source other than his attorney. "In the ordinary case, a correct statement of the law from the trial judge will assuage any doubts that a defendant has not received notice of the nature of the charges against him." Id. For a defendant to have true notice of the elements of a crime, however, he or she must not only hear a recitation of the elements, but must also understand their meaning. See, e.g., Gigot, 147 F.3d at 1198 ("[B]ecause a *1203 guilty plea is an admission of all the elements of a formal criminal charge, it cannot be truly voluntary unless the defendant possesses an understanding of the law in relation to the facts." (internal quotation marks omitted)). If Mr. Weeks was operating under an incorrect understanding of the elements of conspiracy to violate securities laws, as he alleges in his petition, nothing said during the plea colloquy would necessarily have corrected his misunderstanding.
After Mr. Weeks denied acting "knowingly," the district court expressed concern about Mr. Weeks' statement. It then said, "I think, as Mr. Walz [the prosecutor] indicated, that part of the conspiracy element  one of the elements is that the activities were done knowingly." Rec., vol. IV at 42 (emphasis added). That statement did not expressly inform Mr. Weeks he had to know the activities violated the securities law when he agreed to them  only that he had to knowingly agree to the activities. The court asked Mr. Barber to try to clear matters up. Clarity was not necessarily the result of Mr. Barber's questioning. He asked Mr. Weeks about his knowledge of the "activities," that is, his conduct and that of the other defendants. Mr. Weeks admitted he knew that large numbers of Pan World shares were being sold in the market place and that they were not registered. But Mr. Barber then said, "Now these large amounts of shares were therefore sold, were they not, in reliance on purported exemptions from registration?" Id. at 43. To which Mr. Weeks responded, "That's correct." Id. Mr. Barber followed up by getting Mr. Weeks to agree that, "In fact, you are convinced now that ... there was a violation of the Securities Act of 1933." Id. (emphasis added). Mr. Barber then declared, "I believe that is adequate." Id. However, an admission by Mr. Weeks that he knew about the "activities" of his co-conspirators when they were occurring, and that he now knows those activities violated the law, is not definitively an admission he knew at the time he agreed to the activities that they were illegal. And according to Mr. Weeks' petition, he never admitted to "knowingly" violating the law.
At the plea hearing, the prosecutor described in great detail the activities of Mr. Weeks' co-conspirators in marketing shares of Pan World in return for "undisclosed compensation," that Mr. Weeks' wife received a payment of $3,000 from a company owned by one of the co-conspirators, that a man in California was paid to recommend that people buy the stock, that Mr. Weeks appeared in television infomercials with the man, and that a company in the West Indies controlled by Mr. Weeks' co-conspirators received 106 million shares of company stock, and that profits from these stock sales were funneled back into the company. Id. at 45-47. The prosecutor then concluded by stating:
Accordingly, as president, and given all the facts and the fact that one of his co-conspirators was his brother, and the fact that he received some of the monies, although certainly much less than the other co-conspirators, circumstantially we believe that we could prove Mr. Weeks knew these facts sufficient to convict him of the conspiracy count.
Id. at 47-48. Thereafter, the following occurred:
THE COURT: Mr. Weeks, do you dispute anything that Mr. Walz just stated?
MR. BARBER: Is what he said, in essence, the truth? That doesn't necessarily mean you can conclude that all the details 
THE COURT: Not all the details. I don't expect you to know all the stock amounts.
MR. BARBER: As a general description of your conduct, is that reasonably fair?

*1204 [MR. WEEKS]: Yes.
Id. at 48. But Mr. Weeks was not specifically asked if he knew at the times these activities were occurring they violated the securities laws. And although Mr. Weeks' statements indicate he was part of an agreement to sell the unregistered shares overseas, arguably none of his statements indicate he knew this activity was illegal. In fact, Mr. Weeks also said that the shares of stock were sold "in reliance on purported exemptions from registration." Id. at 43. Thus, the record does not expressly contradict Mr. Weeks' allegation in his petition that he "never admitted to `willfully and knowingly' committing the crime of conspiracy." Supp. Rec., vol. II at 33.
Mr. Weeks has also alleged facts that would rebut the presumption that he was informed of the nature of the charge against him when he was provided a copy of the indictment. See Bousley, 523 U.S. at 618, 118 S.Ct. 1604. Although the second superseding indictment included the elements of conspiracy, nothing in the charge itself necessarily contradicts Mr. Weeks' alleged misunderstanding of the law.[10] Especially when the charges are as complex as those involved in this conspiracy to commit securities fraud, it is particularly important to explain the nature of the elements to the defendant. Cf. Hicks, 546 F.3d at 1285 ("[I]t is particularly necessary to explain the depraved mind element to a defendant because it is a complex concept."); Gigot, 147 F.3d at 1198-99 (finding that an explanation of the elements of the crime was constitutionally required where the charges were "far from simple or straightforward"); accord United States v. Lalonde, 509 F.3d 750 (6th Cir.2007) ("[T]he amount of discussion required to properly inform the defendant of the charges against him varies based upon the complexity of the charges."). Mr. Weeks' allegations, if proved, would establish his plea was involuntary under Henderson as a result of his counsel's ineffectiveness. See Allen, 368 F.3d at 1241. This satisfies the first prong of an ineffective assistance of counsel claim. See id.
To satisfy the second prong, Mr. Weeks "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, 474 U.S. at 59, 106 S.Ct. 366.[11]*1205 Again, Mr. Weeks' habeas petition provides sufficient support for this prong, if proved. He alleges he firmly believed he was innocent, and on many occasions he "professed his innocence and lack of intent to commit a crime to [his] counsel." Supp. Rec., vol. II at 32. He alleges he did not understand his lack of intent to commit a crime provided a defense to the charges against him. Id. at 29. He also alleges that his counsel's lack of preparation for the pending trial and counsel's refusal to try the case nevertheless pushed him into entering a guilty plea because he felt he had no realistic choice. Id. at 32. Finally, none of the evidence described by the government at the plea colloquy necessarily proves that Mr. Weeks understood Pan World's unregistered sale of stock was illegal. Under the facts alleged in the habeas petition, if Mr. Weeks had understood the government was required to prove he knew his co-conspirators were violating the law, there is a reasonable probability he would not have pled guilty. Accordingly, Mr. Weeks has articulated sufficient facts, if proven, to show he had ineffective assistance of counsel before and during the plea proceedings, which resulted in an unknowing guilty plea.
The government correctly points out that a district court is not required to conduct an evidentiary hearing when a petitioner's allegations merely contradict his earlier sworn statements. Hedman v. United States, 527 F.2d 20, 21 (10th Cir.1975) (per curiam). "Solemn declarations in open court carry a strong presumption of verity. The subsequent presentation of conclusory allegations unsupported by specifics is subject to summary dismissal, as are contentions that in the face of the record are wholly incredible." Blackledge v. Allison, 431 U.S. 63, 74, 97 S.Ct. 1621, 52 L.Ed.2d 136 (1977). Accordingly, the "truth and accuracy" of a defendant's statements during the Rule 11 proceeding "should be regarded as conclusive in the absence of a believable, valid reason justifying a departure from the apparent truth of his Rule 11 statements." Hedman, 527 F.2d at 22.
The government relies on Hedman to contend that Mr. Weeks' ineffective assistance claims are undermined by his own sworn statements during the plea colloquy and in his written statement in advance of plea. Mr. Weeks stated under oath during the plea colloquy that he had fully discussed the charge against him with Mr. Barber and was fully satisfied with Mr. Barber's counsel, advice, and representation. He also swore in his written statement that he was satisfied with his lawyer and had discussed the case as much as he wished to. According to the government, these statements are conclusive and refute any argument that Mr. Barber's representation was inadequate.
These facts are not dispositive, however, because Mr. Weeks' habeas petition is not based on mere conclusory assertions that contradict earlier statements made under oath. Mr. Weeks provides a valid reason, if believed, for now claiming his representation was inadequate, and his claim is not contradicted by evidence in the record. As discussed above, Mr. Weeks' apparent confusion during the plea colloquy arguably gives some support to his claim that counsel was inadequate in preparing for trial and in preparing Mr. Weeks for the plea hearing. According to Mr. Weeks, he believed at the time that Mr. Barber's representation was adequate because he was unaware he had been misinformed of the elements of conspiracy to commit securities fraud. But now that he understands the true nature of the crime, he alleges, he realizes his counsel misinformed him. Mr. *1206 Weeks' allegations, taken as true, would entitle him to relief.
Reviewing Mr. Weeks' pro se petition liberally, as we must, we conclude the district court abused its discretion when it denied Mr. Weeks' claim that Mr. Barber had provided ineffective assistance of counsel in relation to the plea agreement without permitting further development of the record. It bears emphasis, of course, that we are not deciding the merits of Mr. Weeks' petition. We recite the plea colloquy and Mr. Weeks' allegations in detail only to underscore that Mr. Weeks has made a claim which, if believed, would entitle him to habeas relief. Accordingly, an evidentiary hearing is necessary to determine if Mr. Weeks' allegations are, in fact, true. We therefore vacate the district court's order denying in part Mr. Weeks' § 2255 motion. The matter is remanded for an evidentiary hearing and a new determination based thereon.[12]

IV.
In sum, we AFFIRM Mr. Weeks' conviction. However, we VACATE the dismissal of Mr. Weeks' § 2255 petition without an evidentiary hearing, and we REMAND to the district court for further proceedings in light of this opinion.
NOTES
[1]  The delay in Mr. Weeks' sentencing was part of the plea agreement. The United States agreed to Mr. Weeks' request that he be sentenced at the time of or after the sentencing of his co-defendants, who were going to trial.
[2]  Neither the original indictment nor the first superseding indictment included a conspiracy charge. It was added in the second superseding indictment.
[3]  The plea agreement did not contain a statement of facts or a description of the conspiracy charge.
[4]  In the plea agreement, Mr. Weeks waived his right "to appeal any sentence imposed upon [him], and the manner in which the sentence is determined...." Rec., vol. II at 442. When reviewing an appeal brought by a defendant who entered into an appeal waiver, we must determine "(1) whether the disputed appeal falls within the scope of the waiver of appellate rights; (2) whether the defendant knowingly and voluntarily waived his appellate rights; and (3) whether enforcing the waiver would result in a miscarriage of justice as we define herein." United States v. Hahn, 359 F.3d 1315, 1325 (10th Cir.2004) (en banc). We agree with both parties that Mr. Weeks' appeal does not fall within the scope of the waiver, because he is contesting the voluntariness of his plea, not raising sentencing issues.
[5]  As discussed further below, Mr. Weeks asserts in his § 2255 petition that he actually did not receive the second superseding indictment, which added the conspiracy charge. However, based upon this record, we cannot reach such a conclusion, particularly in view of Mr. Weeks' representations to the district court at the plea proceeding that related to the conspiracy charge.
[6]  Because we conclude the district court did not plainly err when it determined Mr. Weeks had admitted all the elements of the offense, we need not decide whether Mr. Weeks' plea could be characterized as an Alford plea.
[7]  We review Mr. Weeks' pro se § 2255 petition liberally. See United States v. Pinson, 584 F.3d 972, 975 (10th Cir.2009). "If a district court can `reasonably read the pleadings to state a valid claim on which the petitioner could prevail, it should do so.'" United States v. Guerrero, 488 F.3d 1313, 1316 (10th Cir.2007) (quoting Barnett v. Hargett, 174 F.3d 1128, 1133 (10th Cir.1999)).
[8]  In his plea agreement, Mr. Weeks waived his right to collaterally challenge his "sentence... and the manner in which the sentence is determined." Rec., vol. II at 442. However, "a plea agreement waiver of postconviction rights does not waive the right to bring a § 2255 petition based on ineffective assistance of counsel claims challenging the validity of the plea or the waiver." United States v. Cockerham, 237 F.3d 1179, 1187 (10th Cir.2001). Because Mr. Weeks' § 2255 petition alleges that ineffective assistance of counsel rendered his guilty plea invalid, Mr. Weeks did not waive the right to bring his claim.
[9]  Miller, Hicks, Hill, and Henderson all involved petitions for habeas relief brought by state prisoners pursuant to § 2254. "Section 2255 is the statutory equivalent of § 2254 for federal prisoners." Yellowbear v. Wyo. Att'y Gen., 525 F.3d 921, 924 n. 2 (10th Cir.2008) (citing Davis v. United States, 417 U.S. 333, 344, 94 S.Ct. 2298, 41 L.Ed.2d 109 (1974) ("§ 2255 was intended to mirror ... § 2254 in operative effect.")).
[10]  Mr. Weeks' petition also alleges he did not receive a copy of the second superseding indictment. During the plea colloquy, Mr. Weeks stated he had received a copy of the superseding indictment. An evidentiary hearing will clarify whether he received and reviewed the second superseding indictment, which added the conspiracy charge.
[11]  In a small number of our prior cases we have required the defendant to show a reasonable probability both that he would have proceeded to trial and that the jury would have acquitted him. See Miller v. Champion (Miller I), 161 F.3d 1249, 1257 (10th Cir. 1998) ("However, under Hill v. Lockhart, whether a defendant could have been convicted of the crime to which he pleaded guilty is not the test. Rather, we must determine whether it is likely that a jury would have acquitted him of that crime."); Braun v. Ward, 190 F.3d 1181, 1188-89 (10th Cir.1999) ("In this case, [demonstrating prejudice] requires [the defendant] to establish a reasonable probability that he would have pled not guilty and that a jury either would not have convicted him of first degree murder or would not have imposed the death penalty."). However, in Miller v. Champion (Miller II), 262 F.3d 1066 (10th Cir.2001), we explicitly rejected the requirement that a defendant must show a reasonable probability he would have prevailed had he gone to trial. See id. at 1072-74. We concluded such a requirement "does not reflect the law as established by the Supreme Court or as applied in the Tenth Circuit," id. at 1073, pointing out that our cases had never "required a showing of probable success at trial in order to establish prejudice." Id. at 1074. We raise this point again here to reaffirm the holding in Miller II.
[12]  Contrary to the district court's conclusion, we have determined that, when read liberally, Mr. Weeks' pro se § 2255 petition asserted a claim that his counsel's ineffectiveness caused him to plead guilty involuntarily because he did not understand, and therefore could not admit to, an essential element of the crime. Consequently, on remand the district court should reconsider the motion by Mr. Weeks' appointed counsel to amend the petition. "Pursuant to Rule 15(c) of the Federal Rules of Civil Procedure, an untimely amendment to a timely § 2255 motion which, by way of additional facts, clarifies or amplifies a claim or theory in the original motion may, in the District Court's discretion, relate back to the date of the original motion...." United States v. Espinoza-Saenz, 235 F.3d 501, 505 (10th Cir.2000); see also Mayle v. Felix, 545 U.S. 644, 655, 125 S.Ct. 2562, 162 L.Ed.2d 582 (2005) ("Amendments made after the statute of limitations has run relate back to the date of the original pleading if the original and amended pleadings arise out of the same conduct, transaction, or occurrence." (quoting Fed.R.Civ.P. 15(c)) (alteration and internal quotation marks omitted)).
