ORDER
Robert Heiss pleaded guilty pursuant to a written plea agreement to use of inter*600state commerce to effect murder-for-hire, 18 U.S.C. § 1958, and was sentenced to 87 months’ imprisonment and 3 years’ supervised release. Heiss filed a motion to vacate or correct sentence under 28 U.S.C. § 2255, alleging that his trial counsel rendered ineffective assistance by ignoring his request to appeal. The district court denied Heiss’s motion, concluding that the evidence before it conclusively showed that Heiss did not ask his counsel to appeal. But because Heiss alleges facts that, if proven, would entitle him to relief, we vacate and remand for an evidentiary hearing.
In his § 2255 motion Heiss raised a claim that his counsel was per se ineffective for having failed to file a notice of appeal. Heiss alleges in particular: “I asked my attorney ... to appeal my sentence but I have not heard from him since the date of sentencing, 12-16-99.” As relief, Heiss requested the court to restore his appellate rights. The government filed a response, asserting that Heiss had failed to set forth any “basis for a possible claim of ineffective assistance of counsel” because he did not demonstrate that he suffered prejudice as a result of counsel’s failure to file a notice of appeal. Heiss responded, specifying that he asked counsel to file a notice of appeal on the date of his sentencing.
In an order dated May 24, 2000, the district court rejected the government’s argument that Heiss’s ineffective-assistance claim necessarily failed because he did not demonstrate prejudice resulting from counsel’s failure to perfect an appeal. In that same order the district court directed Heiss’s counsel to submit an affidavit specifying whether Heiss had requested him to file a notice of appeal.
Counsel filed an affidavit, in which he noted that as part of the plea agreement Heiss “waived his appellate rights” and the “right to challenge his sentence under 28 U.S.C. § 2255 with the exception of a claim of involuntariness or ineffective assistance of counsel.” Counsel said that prior to sentencing he had discussed with Heiss “his rights to appeal and the time limits for filing a notice of appeal” and explained that “his appellate rights were limited.” Counsel further stated that the first time he heard from Heiss after sentencing was when he received a letter dated February 7, 2000, wherein Heiss “first raised the issue of an appeal.” In that letter, which counsel attached to his affidavit, Heiss made two ambiguous references to an appeal. First, after noting that he would not be sent to a “camp,” Heiss asked, “Do I have any chance to appeal?” Second, after inquiring whether he could be transferred to the MCC, Heiss said, “They tell me I only had ten days to appeal my sentence.” According to counsel, prior to receiving the letter. Heiss never asked him to file a notice of appeal.
Heiss submitted a response to counsel’s affidavit; he styled it “Affidavit of Robert L. Heiss.” Heiss agreed that counsel had spoken to him about his appellate rights and the time limit for filing of a notice of appeal. According to Heiss, however, counsel “glossed through my appelate [sic] rights without emphasizing the significant rights I was waiving.” Heiss further stated that he asked counsel to file a notice of appeal “several times beginning with my sentencing December 16, 1999 but he was totally unresponsive.”
In its supplemental response, the government argued that Heiss’s ineffective-assistance claim failed because he submitted only unsworn statements in support. The government further contended that Heiss’s February 7 letter to counsel did not constitute a request to file a notice of appeal, and that even if it did, such a request was by that point untimely.
*601The district court ultimately denied Heiss’s § 2255 motion. The court credited counsel’s statement in his affidavit that Heiss had not asked him to appeal and concluded that Heiss’s “unsworn assertions to the contrary” did not require it to hold an evidentiary hearing. The district court subsequently granted a certificate of appealability as to the following question: whether Heiss “is entitled to a hearing on the issues of whether (a) he timely requested that his attorney file a notice of appeal and/or (b) if not for deficient performance by his attorney, he would have requested that his attorney file a timely notice of appeal.”
On appeal Heiss argues that the district court erred in denying his § 2255 motion without holding an evidentiary hearing. Heiss’s ineffective-assistance claim is based on this court’s decision in Castellanos v. United States, 26 F.3d 717 (7th Cir.1994), which holds that counsel’s failure to perfect an appeal, despite the defendant’s request, constitutes ineffective assistance without regard to the probability of success on appeal. See Roe v. Flores-Ortega, 528 U.S. 470, 477, 484, 120 S.Ct. 1029, 145 L.Ed.2d 985 (2000). Under 28 U.S.C. § 2255 ¶ 2, a district court has discretion to deny an evidentiary hearing where the “motion and the files and records of the case conclusively show that the prisoner is entitled to no relief.” The salient question here, then, is whether the evidence before the district court conclusively showed that Heiss did not make a timely request to appeal.
We think that the evidence before the district court was largely inconclusive. What we have here is a factual dispute— Heiss said he asked counsel to appeal on the date of his sentencing, and counsel said Heiss did not. Heiss alleges facts that, if proven, would entitle him to relief under Castellanos, and the evidence before the district court did not conclusively defeat Heiss’s claim. Accordingly, Heiss was entitled to an evidentiary hearing. See Daniels v. United States, 54 F.3d 290, 293-94 (7th Cir.1995); Stoia v. United States, 22 F.3d 766, 768 (7th Cir.1994).
We find no merit to the government’s assertion that an evidentiary hearing was not required because Heiss presented only unsworn statements in support of his claim. The government overlooks the fact that by signing his § 2255 motion Heiss swore to the truth of his allegations. Heiss alleges in his motion that he asked counsel to file a notice of appeal but had not heard from counsel since the date of sentencing. Heiss is proceeding pro se, and a liberal reading of Heiss’s allegations supports an inference that he timely requested counsel to appeal. See McNeil v. United States, 508 U.S. 106, 113, 113 S.Ct. 1980, 124 L.Ed.2d 21 (1993) (filings of pro se prisoner must be liberally construed); Winsett v. Washington, 130 F.3d 269, 280 (7th Cir.1997). Moreover, we do not think that the district court properly credited counsel’s version over Heiss’s where it never told Heiss that he needed to submit a response to counsel’s affidavit or that he was required to reduce the allegations of his § 2255 motion to affidavit form. Heiss did file what he styled “Affidavit of Robert L. Heiss,” and if the district thought this “affidavit” was insufficient, it should have given Heiss the opportunity to correct the deficiency. Cf. Lewis v. Faulkner, 689 F.2d 100 (7th Cir.1982).
We also reject the government’s assertion that other evidence before the district court further contradicted Heiss’s allegation that he asked counsel to appeal. The government first points to the appeal waiver in the plea agreement. But we do not understand how the presence of an appeal waiver defeats Heiss’s allegation that he asked counsel to appeal. Second, the gov*602ernment points to Heiss’s letter of February 7. The government basically reads into this letter an implicit concession by Heiss that he did not ask counsel to appeal because he did not mention that request in the letter. But Heiss’s letter is ambiguous at best and in our view does not conclusively defeat his assertion that he asked counsel to appeal.
The government alternatively argues for the first time on appeal that counsel cannot be deemed ineffective for failing to file a notice of appeal because Heiss waived his right to appeal in the plea agreement. But because the government did not raise this argument in the district court, it is waived on appeal. See Cossel v. Miller, 229 F.3d 649, 653 (7th Cir.2000). In any event, the government’s argument is without merit.
Our starting point is the plea agreement, in particular the waiver, which reads in relevant part:
The defendant is also aware that Title 18, United States Code, Section 3742 affords a defendant the right to appeal the sentence imposed. Acknowledging this, the defendant knowingly waives the right to appeal any sentence within the maximum provided in the statute of conviction (or the manner in which that sentence was determined), in exchange for the concessions made by the United States in this Plea Agreement .... The waiver in this paragraph does not apply to a claim of involuntariness, or ineffective assistance of counsel, which relates directly to this waiver or its negotiation.
Heiss’s appellate rights may have been limited by the waiver but the waiver does not foreclose all appellate review. For instance, although Heiss waived the right to appeal his sentence, he did not waive the right to attack the circumstances underlying his guilty plea. See Bridgeman v. United States, 225 F.3d 589, 591-92 (7th Cir.2000); Jones v. United States, 167 F.3d 1142, 1144-45 (7th Cir.1999). The plea agreement itself makes this clear: exempted from the waiver are claims of involuntariness and ineffective assistance of counsel. As we noted in United States v. Behrman, 235 F.3d 1049, 1052 (7th Cir. 2000), “just as we are willing to enforce waivers of appeal, we enforce them only to the extent of the agreement.” Moreover, the waiver does not completely foreclose review of Heiss’s sentence. We considered an almost identical waiver in Behrman, and held the defendant there had surrendered only the right to appeal a sentence within the maximum provided in the statute of conviction. See id. As in Behrman, the statute of conviction here provides for imprisonment and a fine, but it makes no mention of other aspects of Heiss’s sentence, such as supervised release. Based on the plain language of the waiver, Heiss still has the right to appeal, although that right is limited. Deprivation of that right, no matter how limited, is all that Heiss needs to show for the presumption of prejudice to attach. See Roe, 528 U.S. at 483, 120 S.Ct. 1029; Castellanos, 26 F.3d at 719.
One final matter. While his § 2255 motion was pending, Heiss submitted an “Addendum,” in which he raised a number of claims beyond the ineffective-assistance claim alleged in his original § 2255 motion. The district court construed that filing as a request to amend the § 2255 motion and denied it. The court reasoned: “If Heiss desires to raise other issues in a § 2255 motion, he should file a separate motion and clearly state all claims that he desires to raise. The present § 2255 motion, limited to the right to appeal, will not bar a subsequent § 2255 motion as a successive motion.” But Heiss is entitled to only one round of collateral review, Talbott v. Indiana, 226 F.3d 866, 869 (7th Cir.2000), *603and would be barred from filing a second collateral attack absent this court’s permission. See 28 U.S.C. § 2255 18. The district court’s conclusion that Heiss could file another § 2255 motion would have been correct only had it granted relief on his Castellanos claim. See Shepeck v. United States, 150 F.3d 800, 801 (7th Cir.1998). But that was not the case here. Therefore, on remand, if Heiss moves to amend his motion, the district court should determine whether leave should be granted. See Johnson v. United States, 196 F.3d 802, 805-06 (7th Cir.1999).
The judgment of the district court is VACATED, and this case is REMANDED for proceedings consistent with this order.