Dederrian Levon Williams appeals his 120-month sentence imposed after pleading guilty to possession with intent to distribute cocaine, in violation of 21 U.S.C. § 841(a)(1).

At sentencing, Williams moved the district court for a guideline downward departure, pursuant to U.S.S.G. § 5H1.4, based on his renal kidney disease, which the court denied. However, the court then varied his sentence down to the statutory minimum sentence pursuant to 18 U.S.C. § 3553(a). On appeal, Williams argues that the district court erred by refusing to impose a sentence lower than the statutory mandatory minimum sentence because such a decision violated the Eighth Amendment. Specifically, he argues that, because he is seriously infirm, the district court should have imposed a lesser sentence or home imprisonment so that he could receive the medical care that he needs.

If the defendant requests a downward departure from the guideline range, and the district court refuses to grant the departure, we have no jurisdiction to review the district court’s decision “unless the district court incorrectly believed that it lacked the statutory authority to depart from the guideline range.” United States v. Norris, 452 F.3d 1275, 1282 (11th Cir. 2006). Furthermore, district courts are governed by the mandatory minimum sentences established by Congress and have “no discretion to depart downward from the relevant statutory mandatory minimum sentences.” United States v. Simpson, 228 F.3d 1294, 1303 (11th Cir. 2000). We have stated that:

There are only two circumstances in which a court can depart downward from a statutorily authorized mandatory minimum sentence. Either the Government must file a motion to recognize the defendant’s “substantial assistance” in the investigation or prosecution of another, see 18 U.S.C. § 3553(e), or, the defendant must fall within the provisions of the “safety valve” embodied in 18 U.S.C. § 3553(f).

Id. at 1304-05.

Additionally, following the Supreme Court’s decision in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), we review sentences under the advisory guideline regime for “unreasonable[ness].” Booker, 543 U.S. at 261, 125 S.Ct. at 765. We have stated that the district court first must correctly calculate the defendant’s guideline range, then, using the 18 U.S.C. § 3553(a) sentencing factors, the court can impose a *865 more severe or more lenient sentence, as long as it is reasonable. United States v. Crawford, 407 F.3d 1174, 1179 (11th Cir. 2005). The relevant § 3553(a) factors are:

(1) the nature and circumstances of the offense and the history and characteristics of the defendant; (2) the need for the sentence imposed (A) to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense; (B) to afford adequate deterrence to criminal conduct; (C) to protect the public from further crimes of the defendant; and (D) to provide the defendant with needed [treatment]; (3) the kinds of sentences available; (4) the kinds of sentence and the sentencing range ...; (6) the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct; and (7) the need to provide restitution to any victims of the offense.

18 U.S.C. § 3553(a); Booker, 543 U.S. at 260-61, 125 S.Ct. at 765-66.

We have held that “[i]n non-capital cases, the Eighth Amendment encompasses, at most, only a narrow proportionality principle.” United States v. Brant, 62 F.3d 367, 368 (11th Cir. 1995). A threshold determination must be made “that a sentence imposed is grossly disproportionate to the offense committed.” United States v. Arias-Izquierdo, 449 F.3d 1168, 1186 (11th Cir. 2006)(internal citation omitted).

Upon review of the record and the sentencing transcripts, and upon consideration of the briefs of the parties, we find no reversible error. To the extent that Williams appeals the district court’s refusal to depart downward, pursuant to § 5H1.4, this Court does not have jurisdiction to hear Williams’s appeal, as the district court recognized its discretionary authority to depart. To the extent, however, that Williams appeals the reasonableness of his sentence, the imposition of the statutory mandatory minimum sentence was reasonable, as the district court did not have any authority to impose a sentence below the statutory minimum sentence. Accordingly, we affirm.

AFFIRMED.