PHILLIPS, Circuit Judge.

Alondo Gay appeals the district court's denial of his motion for a sentence reduction requested under 18 U.S.C. § 3582(c)(2). The district court denied his motion, concluding that Amendment 750 to the sentencing guidelines did not lower his sentencing range because his 1998 conviction involved too much cocaine base for him to qualify for relief. Gay does not contest this ruling. Instead, he attempts to use the § 3582(c)(2) proceeding as a stepping stone to this court to collaterally attack his original sentence under the Fifth and Eighth Amendments. When asked, Gay's counsel acknowledged at oral argument that she had no authority supporting the use of a § 3582(c)(2) remedy to advance new, unrelated constitutional claims on appeal. We affirm the district court's denial of a sentence reduction under § 3582(c)(2). Although we have no authority to grant relief on Gay's constitutional claims, we address them simply to show them meritless.

BACKGROUND

In July 1998, a federal grand jury sitting in Oklahoma returned an eight-count indictment against Gay, charging him with a host of crimes, including having distributed 245.3 grams of cocaine base in violation of 21 U.S.C. § 841(a)(1). Ultimately, Gay pleaded guilty to this distribution charge in exchange for dismissal of the remaining counts. Applying the 1998 sentencing guidelines, the probation office prepared a final presentence report ("PSR"), which held Gay accountable for relevant conduct of 9,636.88 grams of cocaine base. Because this drug weight exceeded 1.5 kilograms of cocaine base,1 Gay qualified for base offense level 38 — the highest base offense level under U.S. Sentencing Guidelines Manual § 2D1.1. The final PSR assessed two additional levels under § 3B1.1(c) for Gay's aggravating role in the offense and two more levels under § 3C1.1 for his obstruction of justice (threatening a witness in the present case). Based on these calculations, the PSR arrived at a total offense level of 42.

Initially, Gay raised several objections to the factual findings in the PSR, including to the assigned weight of cocaine base. But, at the sentencing hearing, Gay withdrew all of his factual objections. As a result, the prosecution did not oppose, and the court granted, a three-level reduction for acceptance of responsibility.2 This decrease left Gay with a total offense level of 39, which led to a guideline range of 262 to 327 months of imprisonment. The district court sentenced Gay to 262 months of imprisonment.

In 2007, frustrated by the sentencing disparity between cocaine powder and cocaine base, the Sentencing Commission got creative and — with Amendment 706 — reduced the base offense level by two for most weights of cocaine base. It could do so given the statutory framework because, even after lowering the sentencing range, the base offense levels still contained within them the statutory mandatory minimum penalties. See U.S. Sentencing Guidelines Manual app. C, Amendment 706 (Nov. 1, 2007). In 2008, with Congress' acquiescence, the Commission made the base offense level reduction retroactive through Amendment 713. U.S. Sentencing Comm'n, Supplement to the 2007 Guidelines Manual 55-56 (2008). Amendment 706 resulted in the cocaine powder-base ratio falling to about 33:1 for base offense level 38.3

Despite this adjustment to the sentencing guidelines, the federal drug statute continued to calculate its 5- and 10-year mandatory minimum sentences on the basis of a 100:1 ratio between cocaine powder and cocaine base.4 21 U.S.C. § 841(b)(1)(A), (b)(1)(B) (2006) (current version at 21 U.S.C. § 841(b)(1)(A), (b)(1)(B) (2013)). It provided two mandatory minimum sentences: (1) 10 years for offenses involving at least 5 kilograms of cocaine powder or 50 grams of cocaine base; and (2) 5 years for offenses involving at least 500 grams of cocaine powder or 5 grams of cocaine base. Id.

This changed in August 2010 when Congress enacted the Fair Sentencing Act, which reduced the statutory penalty disparity between cocaine powder and crack cocaine to an 18:1 ratio. See Fair Sentencing Act, Pub.L. No. 111-220, 124 Stat. 2372 (2010). For the 10-year mandatory minimum sentence, the ratio became 5 kilograms of powder to 280 grams of base; for the 5-year mandatory minimum sentence, 500 grams of powder to 28 grams of base. U.S. Sentencing Guidelines Manual app. C, Amendment 750 (Nov. 1, 2011). As seen, to reduce the disparity, Congress chose to increase the amount of cocaine base needed to meet the mandatory minimum rather than decrease the amount of powder cocaine.

In response to the Fair Sentencing Act, the Sentencing Commission promulgated Amendment 750, which reduced the base offense levels for various weights of crack cocaine. See id. Specifically, as pertains to Gay's case, it reduced from level 38 to level 36 offenses involving between 2.8 and 8.4 kilograms of cocaine base. Offenses involving more than 8.4 kilograms of cocaine base remained at base offense level 38. U.S. Sentencing Guidelines Manual § 2D1.1(c)(1) (2013). With Congress's acquiescence, the Sentencing Commission applied Amendment 750 retroactively. See U.S. Sentencing Guidelines Manual app. C, Amendment 759 (Nov. 1, 2011).

In view of these developments, Gay filed a motion under § 3582(c)(2) to reduce his sentence. The district court denied Gay's motion, concluding that he was ineligible for relief under Amendment 750 because his "sentence was based on a quantity of cocaine base (9.6 kilograms) that far exceeds the maximum amount to which the amendments apply (8.4 kilograms)." R. vol. 2 at 121. Section 3582(c)(2) does not authorize a sentence reduction if a guideline amendment "does not have the effect of lowering the defendant's applicable guideline range." U.S. Sentencing Guidelines Manual § 1B1.10(a)(2)(B) (2013).

DISCUSSION

A. Gay's Claims and Legal Theories

In his briefing, Gay contends that the "continued enforcement of [his] sentence of confinement derived through the application of the 100-to-1 punishment differential for cocaine base and enforced through the application of the mandatory sentencing guidelines" violates his Due Process rights under the Fifth Amendment. Appellant Br. at 12. Because, he says, his sentence was "derived through a process now recognized as Constitutionally flawed and scientifically untenable," Gay argues that it also violates the Eighth Amendment's prohibition against cruel and unusual punishment.5 Appellant Br. at 4, 16. He claims that his sentence was "derived as a result of a process that both violated the Sixth Amendment and enforced a grossly disproportionate punishment differential subsequently acknowledged as insupportable." Id. at 18-19.

B. No Authority to Hear Constitutional Challenges in § 3582(c)(2) Proceedings

We review de novo the scope of a district court's authority to resentence a defendant in a § 3582(c)(2) proceeding. United States v. Williams, 575 F.3d 1075, 1076 (10th Cir.2009). Nowhere does Gay tie his constitutional challenges to his motion for a sentence reduction under § 3582(c)(2), the matter heard in the district court and supposedly supplying a basis for this appeal. Instead, as noted above, he complains that United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005),6 has not been applied retroactively and that as a result, his sentence continues to reflect the 100:1 sentencing disparity existing at his 1998 sentencing. At the same time, he acknowledges that the Supreme Court itself has recently stated that Booker is not applicable retroactively. See Dillon v. United States, 560 U.S. 817, 828, 130 S.Ct. 2683, 177 L.Ed.2d 271 (2010) (reviewing an appeal from a § 3582(c)(2) proceeding, the Court rejected an argument that, under Booker, the district court should have resentenced the defendant under the advisory guidelines and adjusted his criminal history category). Moreover, Gay can hardly deny that the district court would have been quite willing to give him the benefit of Amendment 750's 18:1 ratio had it in fact served to lower his sentencing range.

Gay's challenge amounts to a collateral attack on his sentence, seeking relief beyond that allowed in a § 3582(c)(2) proceeding. See United States v. Price, 438 F.3d 1005, 1006-07 (10th Cir.2006) (finding no authority to consider Booker relief in a § 3582(c)(2) proceeding after noting that courts may modify a defendant's sentence only when Congress has expressly given jurisdiction to do so); United States v. Smartt, 129 F.3d 539, 542-43 (10th Cir. 1997) (finding no jurisdiction in a § 3582(c)(2) appeal to consider the effect of counsel's failure to request safety-valve relief, because this relief should be addressed in a 28 U.S.C. § 2255 motion). Nothing in the limited congressional grant of authority to modify sentences provided by § 3582(c)(2) allows Gay to challenge the constitutionality of his sentence. He must do so either on direct appeal or in a § 2255 petition.

"A judge's resentencing authority is a creation of statute...." United States v. Pedraza, 550 F.3d 1218, 1220 (10th Cir.2008). "[A] district court is authorized to modify a defendant's sentence only in specified instances where Congress has expressly granted the court jurisdiction to do so." Price, 438 F.3d at 1007 (emphasis in original) (citation omitted) (internal quotation marks omitted). Courts may grant a sentence reduction under § 3582(c)(2) only where the Sentencing Commission has lowered a prisoner's applicable guideline range. See Pedraza, 550 F.3d at 1220. This limited jurisdiction is a "narrow exception to the usual rule of finality of judgments...." Id. Section 3582(c)(2) proceedings are "narrow" in scope and authorize "only a limited adjustment to an otherwise final sentence and not a plenary resentencing proceeding." Dillon, 560 U.S. at 826, 130 S.Ct. 2683; see also United States v. Washington, 759 F.3d 1175, 1181 (10th Cir.2014) ("[W]e begin by recognizing [that] the modification procedure set out in § 3582(c)(2) is carefully constrained.").

C. Fifth and Eighth Amendment Claims

Gay argues that his 1998 sentencing, based on a 100:1 disparity between cocaine powder and cocaine base, violates both his Fifth and Eighth Amendment rights. In fact, at oral argument, his counsel contended that any disparity beyond a 1:1 ratio violates the Eighth Amendment. Because he did not raise these issues in the underlying proceeding, we review these claims for plain error. United States v. Steele, 603 F.3d 803, 808 (10th Cir.2010).

There is no plain error here because, as Gay himself acknowledges, our precedent squarely rejects Gay's argument. See United States v. Brooks, 161 F.3d 1240, 1247 (10th Cir.1998) (applying binding circuit precedent, the court rejected the defendant's argument that the 100:1 disparity for cocaine powder and cocaine base violated the Fifth and Eighth Amendments). Congress has also explicitly rejected this notion: "the sentence imposed for trafficking in a quantity of crack cocaine should generally exceed the sentence imposed for trafficking in a like quantity of powder cocaine." Kimbrough v. United States, 552 U.S. 85, 105, 128 S.Ct. 558, 169 L.Ed.2d 481 (2007) (quoting Pub.L. 104-38, § 2(a)(1)(A), 109 Stat. 334) (internal quotation marks omitted). Nor does Gay's 262-month sentence violate the Eighth Amendment based solely on the length of incarceration. See United States v. Williams, 576 F.3d 1149, 1165 (10th Cir.2009) (affirming life sentences on two counts of distributing more than 50 grams of cocaine base); see also Harmelin v. Michigan, 501 U.S. 957, 1002-05, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991) (holding that a life sentence without parole for possession of 650 grams of cocaine base did not violate the Eighth Amendment).

CONCLUSION

The district court did not err in finding that Gay was ineligible for a sentence modification under § 3582(c)(2). Further, we hold that we lack authority to hear an Eighth or Fifth Amendment challenge to a final sentence in a § 3582(c)(2) proceeding. Accordingly, we affirm the district court's order denying relief under § 3582(c)(2).