George Terrell, Jr. appeals the district court’s denial of his motion to reopen and reduce sentence. For the reasons which follow, we affirm the denial of relief as modified.
Facts and Procedural History
In November of 1998, Mr. Terrell pled guilty to bank robbery. Under the Sentencing Guidelines, Mr. Terrell had a criminal history category of VI (based on his prior convictions) and an offense level of 22, which led to a sentencing range of 84— 105 months in prison. The district court sentenced him to 84 months in prison.
Mr. Terrell did not file a direct appeal. Instead, in March of 2000, he filed a timely motion to vacate under 28 U.S.C. § 2255, alleging ineffective assistance of counsel. In his motion, Mr. Terrell did not challenge or otherwise attack the prior convictions that were used in computing his criminal history category.
In March of 2001, while the motion to vacate was pending before the district court, Mr. Terrell filed a state habeas corpus petition attacking his prior convictions.
In an order dated April 24, 2002, the district court denied the motion to vacate. Mr. Terrell filed a timely notice of appeal on May 8, 2002. We refer to this appeal as the “ § 2255 appeal.”
On May 9, 2002, the state court issued an order setting aside eight of Mr. Terrell’s prior convictions. Had these eight convictions not been used to compute the criminal history category, Mr. Terrell’s sentencing range under the Sentencing Guidelines would have been 46-57 months (based on a criminal history category of II and an offense level of 22).
On June 4, 2002, while the § 2255 appeal was pending in this Court, Mr. Terrell filed a motion to reopen and to reduce sentence in the district court. This motion was based on the state court’s order, and Mr. Terrell asked the district court to resentence him based upon his new criminal history category. See generally United States v. Walker, 198 F.3d 811, 813 (11th Cir.1999) (under § 2255, a district court may “reopen and reduce a federal sentence, once a defendant has, in state court, successfully attacked a prior state conviction previously used in enhancing the federal sentence”). The district court *851concluded that Mr. Terrell’s motion to reopen and reduce sentence was a second or successive motion to vacate under § 2255, and denied it on August 14, 2002. Mr. Terrell filed a timely notice of appeal.
On November 21, 2002, this Court dismissed Mr. Terrell’s § 2255 appeal for failure to timely file the initial brief.
In this appeal, a panel of this Court issued a certificate of appealability on October 22, 2003. The certificate was limited to two issues: (1) whether the district court correctly construed Mr. Terrell’s motion to reopen and reduce sentence as a motion to vacate under § 2255; and (2) whether the district court erred in dismissing Mr. Terrell’s motion as second or successive.
Discussion
Our review on appeal is limited to the two issues in the certificate of appealability. See Murray v. United States, 145 F.3d 1249, 1251 (11th Cir.1998) (“we hold that in an appeal brought by an unsuccessful habeas petitioner, appellate review is limited to the issues specified in the COA”). As to those issues, we hold that Mr. Terrell’s motion to reopen and reduce sentence was a motion to vacate under § 2255, and that the district court correctly treated it as a second or successive motion to vacate.
A
In Gonzalez v. Crosby, — U.S. -, 125 S.Ct. 2641, 2648-49, — L.Ed.2d - (2005), the Supreme Court held that a Rule 60(b) motion for relief from judgment in a habeas corpus case brought under 28 U.S.C. § 2254 is properly characterized as a second or successive petition pursuant to 28 U.S.C. § 2244(b) if, among other things, it “seeks to add a new ground for relief.” Although Gonzalez addressed a Rule 60(b) motion and decided the issue only under § 2254, see id. at 2646 n. 3, we believe that its holding and rationale apply equally to § 2255, and that it controls the disposition of this appeal.
In his motion to reopen and reduce sentence, Mr. Terrell sought to set aside his 84-month sentence and obtain a lower sentence based upon the vacatur of some of his prior state court convictions. Regardless of how Mr. Terrell characterized his motion, see Melton v. United States, 359 F.3d 855, 857 (7th Cir.2004), the claim he asserted was a brand new substantive claim for relief on the merits, and one that had not been presented in his initial § 2255 motion. The district court correctly treated the motion to reopen and reduce sentence as a § 2255 motion to vacate, see Walker, 198 F.3d at 813, and, under Gonzalez, correctly ruled that it was a second or successive motion to vacate.
Mr. Terrell, relying on the Second Circuit’s decision in Ching v. United States, 298 F.3d 174, 175-77 (2d Cir.2002), argues that his motion to reopen and reduce sentence should not have been characterized as a second or successive motion to vacate because his appeal from the initial denial of § 2255 relief was still pending at the time he filed the motion. According to Mr. Terrrell, his initial § 2255 motion had not been conclusively denied by this Court, so his motion should have been construed as a motion to amend the initial § 2255 motion.
Upon review, we believe Ching is distinguishable. In Ching the district court, after remand, had before it both the initial § 2255 motion and a subsequent motion. Under these circumstances, the Second Circuit held that “in general, when a § 2255 motion is filed before adjudication of an initial § 2255 motion is complete, the district court should construe the second § 2255 motion as a motion to amend the pending § 2255 motion.” 298 F.3d at 177. *852The circumstances here are different. When Mr. Terrell filed his motion to reopen and reduce sentence, the district court had already denied the initial § 2255 motion. In other words, there was no pending § 2255 motion in the district court when Mr. Terrell filed his motion and, hence, there was nothing to amend. At this time, moreover, the initial § 2255 motion is no longer pending anywhere, and it would make no sense to remand and direct the district court to treat the motion to reopen and reduce sentence as a motion to amend an initial § 2255 motion that no longer exists. This reading of Ching, we believe, is consistent with subsequent Second Circuit precedent. See Whab v. United States, 408 F.3d 116, 119 (2d Cir.2005) (where subsequent § 2255 motion will not be before the district court together with initial § 2255 motion, because in the meantime a COA has been denied on the initial § 2255 motion, there is “no reason ... to instruct the district court to treat the new petition as a motion to amend the initial petition”).
B
There is one more matter to address. When a person files a second or successive motion to vacate without having obtained the appropriate authorization from the court of appeals, the proper remedy is to dismiss the claims raised in the motion. See 28 U.S.C. § 2244(b)(2)-(3). The district court properly concluded, consistent with the text of § 2244(b)(2)-(3), that it could not hear Mr. Terrell’s motion to reopen and reduce sentence, but it denied the motion instead of dismissing it. So that there is no confusion should there be any later proceedings regarding Mr. Terrell, the district court shall, on remand, modify its order to reflect that the motion is dismissed.
Conclusion
The district court’s decision is affirmed as modified.
AFFIRMED AS MODIFIED.
ANDERSON, Circuit Judge, concurs in the judgment.