OPINION

MERRITT, Circuit Judge.

Todd Dunham is serving a 299-month prison sentence for conspiracy to distribute marijuana, cocaine and heroin in violation of 21 U.S.C. §§ 841(a)(1) and 846 and being a felon in possession of a firearm in violation of 18 U.S.C. § 922(g)(1). In this appeal, he challenges the District Court's denial of his motion under 28 U.S.C. § 2255 for ineffective assistance of counsel and its subsequent refusal to rule on the merits of his Rule 60(b) motion to vacate the earlier § 2255 denial. For the reasons discussed below, we affirm the decisions of the District Court.

I.

While in prison for a 1994 conviction for conspiracy to possess and distribute marijuana, Todd Dunham managed a drug trafficking ring that brought marijuana, cocaine and heroin from Mexico to dealers in Lansing, Michigan. With the aid of his girlfriend, Dunham also smuggled drugs into federal prison and distributed them to other inmates. After he was released from prison, federal agents searched the home of Dunham's girlfriend in Lansing and collected evidence that indicated Dunham was smuggling drugs and had become affiliated with Mexican prison gangs. In May 1999, Dunham was arrested and charged with seven narcotics and firearms violations.

On June 14, 2000, Dunham pled guilty to one count of conspiracy to distribute marijuana, cocaine and heroin in violation of 21 U.S.C. §§ 841(a)(1) and 846 and one count of being a felon in possession of a firearm in violation of 18 U.S.C. § 922(g)(1). In August 2000, Dunham moved to withdraw, claiming his guilty plea had been coerced through prosecutorial misconduct and his own counsel's lack of preparation. The District Court denied the motion and sentenced Dunham to 299 months' imprisonment on the conspiracy charge and 120 months' imprisonment on the firearms charge to run concurrently. Dunham appealed his sentence through new counsel, specifically objecting to a two-point increase for obstruction of justice. The Sixth Circuit affirmed the sentence. United States v. Dunham, 295 F.3d 605 (6th Cir.2002).

In June 2003, Dunham filed a § 2255 motion to vacate his conviction and sentence on the grounds of: (1) violation of double jeopardy; (2) ineffective assistance of trial counsel for failing to raise the double jeopardy issue; (3) ineffective assistance of appellate counsel for failing to raise the double jeopardy issue; and (4) violation of his due process rights stemming from the denial of his motion to remove his trial counsel after he pled guilty. On April 5, 2004, the District Court denied the motion in a 13-page opinion.

On April 23, 2004, Dunham moved for reconsideration of his § 2255 motion. The District Court denied the motion to reconsider on May 17, 2004. In July 2004, Dunham moved to amend his motion to reconsider. In November 2004, the District Court denied the motion to amend because it had already denied the motion to reconsider.

Dunham appealed all three rulings, claiming that he never received the District Court's May 17, 2004, ruling denying his motion to reconsider. In an order dated February 9, 2005, a three judge panel of the Sixth Circuit found that it did not have jurisdiction over Dunham's appeal of the April 5, 2004, and May 17, 2004, decisions by the District Court because Dunham failed to comply with the timeliness provision of Federal Rule of Appellate Procedure 4(a). Then, in May 2005, the Sixth Circuit granted Dunham a certificate of appealability on the issue of ineffective assistance of counsel "particularly as it relates to sentencing pursuant to United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005)."

Meanwhile, Dunham revisited the District Court on May 9, 2005, to file a motion under Federal Rule of Civil Procedure 60(b), requesting that the court vacate its April 5, 2004, and May 17, 2004, rulings, once again claiming that he did not receive the May 17, 2004, denial of his motion to reconsider. Ten days later, the District Court dismissed the motion as moot, since the Sixth Circuit had accepted Dunham's § 2255 appeal, docketed as case number 04-2567. Dunham timely appealed the Rule 60(b) denial.

In this appeal, Dunham raises two issues: (1) ineffective assistance of counsel "as it relates to Booker;" and (2) the District Court's mootness decision on his Rule 60(b) motion. In his brief, Dunham expands his ineffective assistance of counsel argument to include his trial counsel's failures to raise a double jeopardy objection and to adequately discuss the consequences of a guilty plea.

II.

A. Ineffective assistance of counsel claim

Pursuant to his certificate of appealability, Dunham argues that his trial counsel was ineffective for failing to raise what is now commonly known as a Booker argument. Specifically, Dunham contends that a reasonably effective counsel would have objected to his sentence because the District Court considered evidence that was not admitted to by Dunham or found by a jury. To show a Sixth Amendment violation for ineffective assistance of counsel, Dunham must show (1) that his lawyer's performance was deficient as compared to an objective standard of reasonable performance, and (2) that there is a reasonable probability that the lawyer's errors prejudiced the outcome of the proceedings. Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).

We note at the outset that Dunham pled guilty and was sentenced in 2000 and his direct appeal concluded in 2002, three years before the Supreme Court decided United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). Dunham argues that Booker should be applied to him retroactively, because his sentence was handed down after Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). This fact is important, according to Dunham, because Apprendi's holding that the enhancement of a sentence under New Jersey's sentencing guidelines violated the Sixth Amendment should have put his counsel on notice to argue that his sentence was similarly unconstitutional because it was based on facts not admitted by Dunham or found by a jury. Dunham's argument is unavailing because this court specifically rejected this type of Apprendi-based argument in the period before Booker was decided. United States v. Koch, 383 F.3d 436 (6th Cir.2004) (en banc). In Koch, this court held that neither Apprendi, nor Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004), required that the Federal Sentencing Guidelines be overturned. Assuming that Dunham's counsel was ineffective for failing to make an Apprendi argument, Koch forecloses the possibility that the argument would have led to a different result in his case.

The only other way Dunham could have been eligible for relief under Booker was to have a direct appeal pending when the case was decided in 2005. Because Dunham was sentenced in 2000 and his direct appeal was decided in 2002, there is no chance that his appeal could have remained pending more than two years later. In short, there is no way Dunham could have obtained Booker relief on direct appeal, even if his attorney had raised the issue. Since Dunham cannot satisfy the second prong of Strickland, we affirm the District Court's decision to deny his § 2255 motion for ineffective assistance of counsel.

Appellate review of a petitioner's § 2255 motion is limited to those issues specified in the certificate of appealability. Pruitt v. United States, 233 F.3d 570, 572-73 (8th Cir.2000); McNeely v. Blanas, 336 F.3d 822, 832 n. 10 (9th Cir.2003). Dunham's certificate of appealability authorizes him to pursue an appeal for ineffective assistance of counsel "particularly as it relates to sentencing pursuant to" Booker, Despite this apparent limitation, Dunham expands upon his ineffective assistance of counsel argument to include claims that his counsel was ineffective for failing to adequately discuss the consequences of his guilty plea and for failing to raise a double jeopardy objection. For us to consider these claims would not only go beyond the scope of the certificate of appealability, it would contravene this court's February 2005 order that Dunham failed to timely appeal the District Court's denial of his § 2255 motion. Because Dunham did not receive a certificate of appealability for these ineffective assistance claims, we do not reach their merits.

B. Rule 60(b) motion

Dunham next appeals the District Court's denial of his Rule 60(b) motion to vacate its decision regarding his § 2255 motion and subsequent motion to reconsider. The District Court did not reach the merits of this motion, instead finding that the issue was moot since the Court of Appeals had already accepted jurisdiction over Dunham's appeal.

The traditional rule is that "a timely appeal divests the district court of jurisdiction to reconsider its judgment until the case is remanded by the Court of Appeals." Pittock v. Otis Elevator Co., 8 F.3d 325, 327 (6th Cir.1993). This court has carved out an exception to this rule that allows a District Court to entertain a motion for relief from judgment after an appeal has been filed if it so chooses. First National Bank of Salem, Ohio v. Hirsch, 535 F.2d 343, 346 (6th Cir.1976). The decision of whether to hear this type of post-judgment motion while an appeal is pending is within the District Court's discretion, and there is no error where the District Court decides to let the appeal run its course. LSJ Investment Co. v. O.L.D., Inc., 167 F.3d 320, 324 (6th Cir.1999).

In this case, Dunham filed a notice of appeal challenging all of the District Court's rulings on his § 2255 motion on December 6, 2004. Several of the issues raised in his appeal were denied as untimely in an order dated February 9, 2005; the remainder of Dunham's claims are adjudicated in this appeal. Since Dunham sought relief from the denial of his § 2255 motion in the Court of Appeals before filing his Rule 60(b) motion on May 9, 2005, the District Court could have, but was not obligated to address the merits of his motion. Seeing no error in the District Court's dismissal of Dunham's Rule 60(b) motion, we affirm its decision.

For the foregoing reasons, the decisions of the District Court are affirmed.