KEARSE, Circuit Judge:

This case returns to us in a peculiar posture. Petitioner Marcus Hooper, convicted in 1992 of narcotics and firearm offenses, appeals from the judgment of conviction, entered in the United States District Court for the Western District of New York, Richard J. Arcara, Judge ("1992 Judgment"), and from an April 21, 1996 order ("1996 Order") of that court. The 1996 Order, although purporting to grant a petition pursuant to 28 U.S.C. §(s) 2255, did not address the 1992 Judgment, from which an impermissibly late notice of appeal had previously been filed, see United States v. Hooper, 43 F.3d 26 (2d Cir. 1994) (per curiam); rather, the 1996 Order was fashioned merely to permit an appeal from the 1992 Judgment. On appeal, Hooper challenges the sentence imposed on him in 1992. For the reasons that follow, we dismiss the appeal from the 1992 Judgment for lack of jurisdiction; and, treating the notice of appeal as a motion for a certificate of appealability with respect to so much of the 1996 Order as failed to vacate the 1992 Judgment, we deny the motion.

I. BACKGROUND

In 1992, following his plea of guilty, Hooper was convicted of possession with intent to distribute cocaine, in violation of 21 U.S.C. §(s) 841(a)(1), and possession of a firearm in relation to a drug trafficking offense, in violation of 18 U.S.C. Section(s) 924(c), and was sentenced principally to 94 months' imprisonment, to run consecutively to various New York State sentences imposed on him in 1990 and 1991. His then-attorney filed a notice of appeal after the time to appeal provided by Fed. R. App. P. 4(b) had expired. The district court, finding that the late filing was caused by the attorney's assistant's ignorance as to the deadline imposed by Rule 4(b), an ignorance that could not have resulted from any plausible misconstruction of the law, denied Hooper's motion for an extension of the time to appeal, concluding that the failure did not result from "excusable neglect." This Court eventually affirmed that denial. See United States v. Hooper, 9 F.3d 257 (2d Cir. 1993) ("Hooper I") (remanding for reconsideration of denial of extension of time to appeal in light of Pioneer Investment Services Co. v. Brunswick Associates Ltd., 507 U.S. 380 (1993)); United States v. Hooper, 43 F.3d 26 (2d Cir. 1994) ("Hooper II") (per curiam) (affirming post remand denial of extension of time to appeal).

In 1995, Hooper, proceeding pro se, filed a petition pursuant to 28 U.S.C. §(s) 2255 on the ground that his former attorney's late filing of the notice of appeal constituted ineffective assistance. In the 1996 Order, the district court ruled on the petition as follows:

The petitioner, Marcus Hooper, has filed an application to this Court, pro se for relief pursuant to 28 U.S.C. §(s) 2255 alleging that his conviction in this Court was unlawfully obtained. To that extent, petitioner has sought leave pursuant to 28 U.S.C. §(s) 2255 for leave to appeal the denial of various motions to the Second Circuit Court of Appeals.

The United States Attorney's Office has filed an answering affidavit in opposition to petitioner's application and petitioner has filed the appropriate documentation in this case indicating that he advised his attorney that he wished to appeal various rulings of this Court. After due deliberation and considering all of the documents submitted in support of petitioner's application and this Court having had due deliberation thereon, it is

ORDERED that petitioner's motion for relief pursuant to Title 28 U.S.C. §(s) 2255 is herein GRANTED and Herbert L. Greenman, Esq. is ordered to file within the appropriate statutory period a notice of appeal to the Second Circuit Court of Appeals accordingly.

IT IS FURTHER ORDERED that Herbert L. Greenman, Esq. shall be assigned to perfect petitioner's appeal in all respects.

IT IS SO ORDERED.

Hooper's new attorney duly filed a notice of appeal, stating that the appeal was from the "Judgment of conviction entered in this action on 8/26/92 [and 4/21/96 — 28 U.S.C. § 2255]." (Brackets in original.)

II. DISCUSSION

On appeal, Hooper challenges his sentence, contending that the district court erred (a) in calculating his criminal history category under the federal Sentencing Guidelines ("Guidelines"), (b) in failing to treat him as a minimal participant in the offenses, and (c) in making his federal sentence run consecutively to his state-court sentences. For the reasons that follow, we conclude that the appeal, whether viewed as taken from the 1992 Judgment or from the 1996 Order, is not properly before us, and we therefore dismiss.

A. The Purported Authorization of Appeal from the 1992 Judgment

To the extent that the district court's 1996 Order purported to grant Hooper permission to appeal the 1992 Judgment, that order was beyond the court's authority. Several well-established principles lead to this conclusion.

First, although the district court is empowered to extend the time for appeal from a judgment of conviction, that power is to be exercised only upon a showing of "excusable neglect." Fed. R. App. P. 4(b); see also Fed. R. App. P. 26(b) (court of appeals has no power to extend time for appeal). Second, after a district court judgment has been affirmed on appeal, the law-of-the-case doctrine requires the district court to proceed in accordance with that judgment. See generally United States v. Fernandez, 506 F.2d 1200, 1202 (2d Cir. 1974) ("`Where a case has been decided by an appellate court and remanded, the court to which it is remanded must proceed in accordance with the mandate and such law of the case as was established by the appellate court.'" (quoting 1B Moore's Federal Practice Para(s) 0.404[10], at 571 (2d ed. 1974) (footnotes omitted))); In re Ivan F. Boesky Securities Litigation, 957 F.2d 65, 69 (2d Cir. 1992) ("Under the doctrine of law of the case, a district court generally may not deviate from a mandate issued by an appellate court . . . ."); Carroll v. Blinken, 42 F.3d 122, 126 (2d Cir. 1994) (same). "Indeed, because the district court has no discretion in carrying out the mandate, the appellate court retains the authority to determine whether the terms of the mandate have been scrupulously and fully carried out." In re Ivan F. Boesky Securities Litigation, 957 F.2d at 69 (internal quotation marks omitted); see Carroll v. Blinken, 42 F.3d at 126; Ginett v. Computer Task Group, Inc., 11 F.3d 359, 360 (2d Cir. 1993). Finally, a Section(s) 2255 petition seeking relief from a judgment of conviction may not be used to relitigate questions that were raised and considered on appeal. See generally Giacalone v. United States, 739 F.2d 40, 42 (2d Cir. 1984); Castellana v. United States, 378 F.2d 231, 233 (2d Cir. 1967).

In the present matter, the notice of appeal from the 1992 Judgment was untimely; the district court found that the failure to file a timely notice was inexcusable; and that ruling was affirmed on appeal. Under the above principles, therefore, the district court had no authority either to reopen the issue of excusable neglect or to allow Hooper to appeal from the 1992 Judgment. There being no timely appeal from the 1992 Judgment, this Court has no jurisdiction to entertain this matter as an appeal from that judgment. See, e.g., United States v. Robinson, 361 U.S. 220, 224 (1960) (construing predecessor to Fed. R. App. P. 4(b)); United States v. Koziel, 954 F.2d 831, 833 (2d Cir. 1992).

B. Relief Under 28 U.S.C. §(s) 2255

Although the district court had no authority to revive Hooper's ability to appeal from the 1992 Judgment, it did have the power to entertain his Section(s) 2255 petition for relief on the ground of ineffective assistance of counsel, applying the normal standards for adjudicating such a petition. The district court did not address the merits of Hooper's claim of ineffective assistance. However, the record shows clearly that that claim could not properly have been granted.

In order to establish a constitutional claim of ineffective assistance of counsel, a convicted defendant must show both (1) that counsel's performance fell below an objective standard of reasonableness, and (2) that but for the deficiency, the likely outcome of the proceeding would have been different. See Strickland v. Washington, 466 U.S. 668, 687-96 (1984). There is no question in the present case that the performance prong of the Strickland standard was met, for the district court had held, and this Court had affirmed, that the late filing of the notice of appeal was caused by an ignorance of the Rules that could not have resulted from any plausible misconstruction of the law. The question remains whether the late filing resulted in prejudice. In evaluating the prejudice component of the Strickland test, a court must determine whether, absent counsel's deficient performance, there is a reasonable probability that the outcome of the proceeding would have been different. "A reasonable probability is a probability sufficient to undermine confidence in the outcome." Id. at 694.

In the present case, the court could not find the requisite prejudice. Hooper had pleaded guilty and hence had waived any challenges except those that could properly be termed jurisdictional, see, e.g., Hayle v. United States, 815 F.2d 879, 881 (2d Cir. 1987); LaMagna v. United States, 646 F.2d 775, 778 (2d Cir.), cert. denied, 454 U.S. 898 (1981), and those arising from sentencing, see generally United States v. Madkour, 930 F.2d 234, 236 (2d Cir.), cert. denied, 502 U.S. 911 (1991). On this appeal, his only challenges are to sentencing, and their lack of substance negates any possibility that a timely direct appeal would have led to any change in Hooper's sentence.

One challenge is to the court's calculation of Hooper's criminal history category, a calculation that even Hooper characterizes as having been in accordance with "the strict terms of" the applicable Guideline. (Hooper brief on appeal at 7.) Another challenge is to the court's refusal to deem Hooper a minimal participant in the offenses underlying his conviction. His brief makes no showing, however, that he carried his burden, see, e.g., United States v. Garcia, 920 F.2d 153, 156 (2d Cir. 1990) (per curiam), of establishing that he was entitled to that treatment.

Hooper's principal argument is that in sentencing him for the Section(s) 924(c)(1) firearm offense, the district court erroneously believed that it did not have the power to make that sentence run concurrently with his state-court sentences. This contention is meritless because the plain language of the statute deprived the district court of that power:

Notwithstanding any other provision of law, the court shall not place on probation or suspend the sentence of any person convicted of a violation of this subsection, nor shall the term of imprisonment imposed under this subsection run concurrently with any other term of imprisonment . . . .

18 U.S.C. §(s) 924(c)(1) (emphasis added). With respect to whether the phrase "any other term of imprisonment" includes a term of imprisonment imposed by a state court, every Circuit considering that question, save one, answered it in the affirmative. See, e.g., United States v. Thomas, 77 F.3d 989, 990-91 (7th Cir. 1996) (per curiam); United States v. McLymont, 45 F.3d 400, 401-02 (11th Cir.) (per curiam), cert. denied, 115 S.Ct. 1723 (1995); United States v. Ospina, 18 F.3d 1332, 1335-36 (6th Cir.), cert. denied, 512 U.S. 1226 (1994). But see United States v. Gonzales, 65 F.3d 814, 819 (10th Cir. 1995), vacated and remanded, 117 S.Ct. 1032 (1997). Although a timely appeal from the 1992 Judgment would have predated these cases, they nonetheless would properly have been considered by the district court in ruling on the merits of Hooper's present Section(s) 2255 petition, for the determination as to whether there was prejudice within the meaning of Strickland, unlike the assessment as to the reasonableness of counsel's performance, may be made with the benefit of hindsight, see, e.g., Lockhart v. Fretwell, 506 U.S. 364, 372 (1993). Indeed, we now note that in United States v. Gonzales, 117 S.Ct. 1032 (1997), decided just weeks before the oral argument of this appeal, the Supreme Court has ruled that the "the plain language of . . . Section(s) 924(c) forbids a federal district court to direct that a term of imprisonment under that statute run concurrently with any other term of imprisonment, whether state or federal." 117 S.Ct. at 1038. Clearly Hooper's challenge to the district court's imposition of consecutive sentences cannot be sustained.

Finally, we note that since the judgment of conviction was not vacated, and since the district court could not validly grant permission for Hooper to appeal that judgment, the 1996 Order may be viewed as a denial of Hooper's Section(s) 2255 petition. As such a denial, the 1996 Order would not be appealable unless Hooper obtained a certificate of appealability determining that he has made a "substantial showing of the denial of a constitutional right," 28 U.S.C. §(s) 2253. See, e.g., Lozada v. United States, No. 96-2887, 1997 WL 99719, at *6 (2d Cir. Mar. 7, 1997); Thye v. United States, 96 F.3d 635, 636 (2d Cir. 1996) (per curiam). Treating Hooper's notice of appeal as a request for such a certificate, and having the benefit of the briefs submitted thereafter, see Lozada v. United States, 1997 WL 99719, at *7; Fed. R. App. P. 22(b), we deny a certificate of appealability because there is no substantial showing of the denial of a constitutional right.

CONCLUSION

We have considered all of Hooper's arguments on this appeal to the extent that they are properly before us, and we have found in them no jurisdictional basis for appeal and no substantive basis for a certificate of appealability. The appeal is dismissed for lack of jurisdiction.