ORDER DENYING CERTIFICATE OF APPEALABILITY*
Eric William Bly, a federal prisoner proceeding pro se, seeks a certificate of ap-pealability (COA) to appeal the district court’s dismissal of his “Review for Lack *748of Subject Matter Jurisdiction,” which the district court construed as a motion under 28 U.S.C. § 2255. We deny a COA, but we vacate the district court’s judgment and remand with instructions to dismiss for lack of jurisdiction.
Mr. Bly’s filing cited new legal authority to reassert an argument he raised during his first § 2255 proceeding — that the district court lacked jurisdiction to consider a certain motion for reconsideration and to order that his nine twenty-year sentences would run consecutively rather than concurrently. See United States v. Bly, 328 F.3d 1262, 1264 (10th Cir.2003). The district court concluded that the filing was a § 2255 motion and dismissed it as barred by the limitations period in § 2255(f).
To appeal the decision, Mr. Bly must secure a COA. To do so, he must show “that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right and that jurists of reason would find it debatable whether the district court was correct in its procedural ruling.” Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000).
Reasonable jurists could debate whether the district court was correct in its procedural ruling. Because the filing attacked the validity of Mr. Bly’s sentence and reargued claims made previously under § 2255, the district court was correct in construing it as a § 2255 motion. See Gonzalez v. Crosby, 545 U.S. 524, 531-32, 125 S.Ct. 2641, 162 L.Ed.2d 480 (2005); United States v. Nelson, 465 F.3d 1145, 1148-49 (10th Cir.2006). But because Mr. Bly already has pursued relief under § 2255, the filing was a second or successive § 2255 motion. And Mr. Bly had not obtained this court’s authorization to file it, as required by 28 U.S.C. § 2255(h). Accordingly, the district court did not have jurisdiction to decide any issues in the case; its alternatives were to dismiss the filing for lack of jurisdiction or to transfer it to this court for authorization. See In re Cline, 531 F.3d 1249, 1251-52 (10th Cir.2008); Nelson, 465 F.3d at 1148.
Reasonable jurists could not debate, however, whether Mr. Bly’s filing states a valid claim of the denial of a constitutional right. Mr. Bly claims that the district court lacked jurisdiction to consider the government’s motion to reconsider and then order his sentences to run consecutively. As discussed, he is subject to the restrictions of § 2255(h), which affords relief only in limited circumstances, and his filing does not identify a new Supreme Court decision or new evidence that would allow his claim to proceed under § 2255(h). Further, this court already has explained why the district court had jurisdiction to consider the government’s motion to reconsider. See Bly, 328 F.3d at 1264-65. Finally, and perhaps most importantly, the sentence that Mr. Bly is serving did not arise from the government’s motion to reconsider. Although the district court granted the motion to reconsider and revised Mr. Bly’s sentence, see id. at 1264, on appeal we remanded the case to the district court to vacate that sentence and to conduct further proceedings because the revised sentence had been imposed in Mr. Bly’s absence, see id. at 1267. On remand, the district court resentenced Mr. Bly. See United States v. Bly, 142 Fed.Appx. 339, 342 (10th Cir.2005). Mr. Bly is in custody on that later sentence, not on the earlier sentence that arose from the government’s motion to remand.
Mr. Bly argues that a motion asserting a lack of subject-matter jurisdiction cannot be restricted or procedurally defaulted. However, “[t]he subject-matter jurisdiction of lower federal courts is within the plenary control of Congress,” Alva *749v. Teen Help, 469 F.3d 946, 950 (10th Cir.2006), and it is Congress who has required federal prisoners to obtain authorization for second or successive § 2255 motions before pursuing them in district court, see 28 U.S.C. § 2255(h). If Congress had wished to exclude from § 2255(h) challenges to the district court’s jurisdiction, it could have done so. See also Cline, 531 F.3d at 1253 (considering jurisdictional claims as successive claims).
Mr. Bly also argues that the district court failed to comply with Castro v. United States, 540 U.S. 375, 383, 124 S.Ct. 786, 157 L.Ed.2d 778 (2003), which requires the court to notify a prisoner before recharacterizing a filing as a § 2255 motion. That restriction applies only to filings that would become a prisoner’s first § 2255 motion, however; the court is not required to give notice where a filing is a second or successive § 2255 motion. See Nelson, 465 F.3d at 1149 (“If the prisoner has filed once, any future motion will be subject to the same constraints whether it is a second § 2255 motion or a third.”).
Mr. Bfys motion for leave to proceed without prepayment of fees and costs is granted. Because Mr. Bly cannot satisfy both parts of the Slack test, the application for COA is denied. But “[w]hen the lower federal court lacks jurisdiction, we have jurisdiction on appeal, not of the merits but merely for the purpose of correcting the error of the lower court in entertaining the suit.” Bender v. Williamsport Area Sch. Dist., 475 U.S. 534, 541, 106 S.Ct. 1326, 89 L.Ed.2d 501 (1986) (brackets omitted) (internal quotation marks omitted). Accordingly, the district court’s judgment is vacated and the case is remanded to the district court with instructions to dismiss for lack of jurisdiction.