*58 SUMMARY ORDER
UPON DUE CONSIDERATION of this appeal from a judgment of the United States District Court for Connecticut (Dominic J. Squatrito, Judge), it is hereby
ORDERED, ADJUDGED AND DECREED that the judgment of the district court is AFFIRMED.
Petitioner-appellant Dennis Sanders (“Sanders”) appeals from an order of the United States District Court for Connecticut (Dominic J. Squatrito, Judge) denying his motion to vacate his sentence pursuant to 28 U.S.C. § 2255. On November 12, 1996, Sanders pled guilty pursuant to a plea agreement to one count of carrying a firearm in relation to a narcotics trafficking offense in violation of 18 U.S.C. § 924(c)(1) (“firearm count”) and one count of possession of cocaine base with intent to distribute in violation of 21 U.S.C. § 841(a)(1) (“narcotics count”). On February 6, 1997, the district court sentenced Sanders to a term of imprisonment of 123 months, consisting of sixty months on the firearm count to run consecutively with 63 months on the narcotics count. Sanders did not directly appeal his sentence. Instead, in a motion dated December 1,1997, Sanders moved pro se to vacate his sentence pursuant to 28 U.S.C. § 2255. The district court denied his motion in an order entered on June 1, 1999, and Sanders appeals from this denial.1
We review a district court’s denial of a § 2255 motion de novo. See Cuoco v. United States, 208 F.3d 27, 30 (2d Cir. 2000). “[A] collateral attack on a final judgment in a federal criminal case is generally available under § 2255 only for a constitutional error, a lack of jurisdiction in the sentencing court, or an error of law or fact that constitutes ‘a fundamental defect which inherently results in a complete miscarriage of justice.’ ” United States v. Bokun, 73 F.3d 8,12 (2d Cir.1995) (quoting Hill v. United States, 368 U.S. 424, 428, 82 S.Ct. 468, 7 L.Ed.2d 417 (1962)). A petitioner cannot assert claims he faded to raise at trial, sentencing, or on direct appeal “unless [he] can show cause for the default and prejudice resulting from it.” Ciak v. United States, 59 F.3d 296, 302 (2d Cir.1995) (internal quotation marks omitted). A petitioner cannot avoid this rule of procedural default merely by asserting that his counsel made a significant error by failing to raise the claim; rather, petitioner must show that counsel’s performance was constitutionally ineffective. See Murray v. Carrier, 477 U.S. 478, 487-88, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986).
Sanders contends that the district court erred by sentencing him under the penalty provision for crack cocaine contained in Section 2D1.1 of the United States Sentencing Guidelines (“U.S.S.G.” or the “Guidelines”) because the Government did not meet its burden at sentencing to demonstrate that the substance he possessed was crack cocaine rather than some other form of cocaine base. “Insofar as claims regarding a sentencing court’s error in failing to properly apply the Sentencing Guidelines are neither constitutional nor jurisdictional, ... absent a complete miscarriage of justice, such claims will not be considered on a § 2255 motion where the *59defendant failed to raise them on direct appeal.” Graziano v. United States, 83 F.3d 587, 590 (2d Cir.1996).
Sanders is unable to show such a complete miscarriage of justice in his case. The Government presented evidence that the cocaine base Sanders possessed was crack cocaine. Sanders admitted in his plea allocution and at sentencing that he possessed “cocaine base” and that the cocaine base was “rock-like” and packaged in “Ziplock baggies” in the manner in which crack cocaine is packaged for street level sale. See United States v. Canales, 91 F.3d 363, 368 (2d Cir.1996) (observing that crack is the most common form of cocaine base); U.S.S.G. § 2Dl.l(c), note (D) (describing crack cocaine as “appearing in a lumpy, rocklike form”). Sanders did not object to the presentence report’s calculation of his offense level using crack cocaine as the substance he possessed. In essence, Sanders’ argument is that the Government failed to prove that he possessed crack cocaine because it did not present evidence that the cocaine base contained sodium bicarbonate. However, we have held that proof of presence of sodium bicarbonate is not necessary to show that a substance is crack cocaine for sentencing purposes. See United States v. Diaz, 176 F.3d 52, 119 (2d Cir.1999); Canales, 91 F.3d at 368. Finally, even assuming ar-guendo that the district court erroneously sentenced Sanders for possession of crack cocaine rather than some other form of cocaine base, Sanders’ sentence could be reduced, at the most, by three months because he is subject to a five year statutory minimum term of imprisonment for possession of more than five grams of any type of cocaine base. 18 U.S.C. § 841(b)(1)(b); see United States v. Jackson, 59 F.3d 1421, 1424 (2d Cir.1995) (per curiam) (interpreted the statutory meaning of cocaine base to include all forms of cocaine base, not just crack cocaine); United States v. Palacio, 4 F.3d 150, 154-55 (2d Cir.1993) (same). Therefore, under these circumstances, we do not find a complete miscarriage of justice.2
Sanders further argues that the district court erred by failing to grant him a hearing on his § 2255 motion and by permitting the Government to submit a laboratory report that had not been part of the record at the plea allocution and sentencing. A judge has discretion in determining whether to hold an evidentiary hearing in association with a petitioner’s § 2255 motion. See Rule 8(a), Rules Governing Section 2255 Proceedings for the United States District Court. Given the evidence that the Government had already presented evidence at the plea allocution and sentencing that the substance Sanders possessed was crack cocaine, the district court’s decision that a hearing was not necessary was not an abuse of its discretion. See United States v. Stantini, 85 F.3d 9, 17 (2d Cir.1996). We also find that *60any error made by the district court in allowing the Government to submit the report was harmless because the report contained substantially the same evidence as the New Haven Police Department incident report, which was in evidence at the plea allocution and sentencing.
Sanders also contends that his counsel was ineffective because the attorney “failed to conduct an investigation of the laboratory analysis of the seized substance and merely accepted the government’s contention that the substance was crack cocaine.” The district court denied this ground for § 2255 relief, finding that Sanders was unable to show either that his counsel’s representation was unreasonable under prevailing professional norms or that, but for the deficiency, there is a reasonable probability that the result of the proceeding would have been different. See Strickland v. Washington, 466 U.S. 668, 688-94,104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Although the district court denied Sanders’ motion for a certificate of appeal-ability on this issue, Sanders raises this argument on appeal.
Because the district court did not grant a certificate of appealability on Sanders’ ineffective assistance of counsel claim, this Court lacks jurisdiction to consider this argument unless we grant a certificate of appealability on the issue. See Hurel Guerrero v. United States, 186 F.3d 275, 278-79 (2d Cir.1999). We will not grant such a certificate unless we determine that the movant has made a “substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). We find that Sanders has not made a substantial showing that any alleged deficiencies by his counsel rose to constitutional proportions because Sanders is unable to show, as required by the Strickland test, that his counsel’s alleged defects prejudiced his rights. As discussed above, and as the district court found, Sanders’ counsel’s failure to object to the characterization of the drugs as crack cocaine rather than another form of cocaine base would not have meaningfully changed the results of the proceedings because the Government presented substantial evidence that the cocaine base Sanders possessed was crack cocaine.
We have considered appellants’ remaining arguments and find them to be without merit.3 For the reasons discussed, the judgment of the district court is hereby AFFIRMED.
. Sanders had sixty days from the dale of entty of the district court’s order to file an appeal. Fed R.App.P. 4(a)(1)(B). We have held that a motion for a certificate of appeala-bility may be construed as a notice of appeal. See Marmolejo v. United States, 196 F.3d 377, 378 (2d Cir.1999) (per curiam). Sanders’ motion for a certificate of appealability was entered on August 2, 1999, the first business day after the date on which his time to appeal expired. Therefore, Sanders’ appeal is timely. See Fed.R.App.P. 26(a)(3); Fed.R.Crim.P. 45(a).
. Relying on Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), Sanders contends that he would not be subject to the five year statutory minimum under 21 U.S.C. § 841(b)(1)(b) on the narcotics count if this Court vacated his sentence because the grand jury did not find the drug quantity necessary for such punishment. We reject this argument. When Sanders knowingly and voluntarily entered a guilty plea, he waived all non-jurisdictional defects in the prior proceedings. See United States v. Coffin, 76 F.3d 494, 496 (2d Cir.1996). Also relying on Apprendi, Sanders claims that the district court lacked jurisdiction over the narcotics count because the indictment did not allege the quantity of cocaine base he possessed. Because Sanders admitted at his plea allocution and sentencing to the quantity of cocaine base he possessed, any Apprendi error was harmless. See United States v. Champion, 234 F.3d 106, 109-10 (2d Cir.2000) (per cu-riam).
. In a separate per curiam opinion today, we reject Sanders’ contention that the district court lacked jurisdiction over the indictment against him because cocaine base and crack cocaine are not controlled substances.