OPINION
McKEAGUE, Circuit Judge.Defendant-Appellant Tyrone Davenport and twenty-eight codefendants were charged in a 147-count superseding indictment. Although Davenport initially faced thirteen counts, he entered into a plea agreement where he pleaded guilty to three counts in exchange for the Government dismissing the remaining counts against him. Davenport’s plea agreement did not include a provision for the Government to make a motion for downward departure from the federal sentencing guide*501lines, and prior to sentencing, Davenport challenged the Government’s “refusal to hear defendant’s proffer and its consequent refusal to make a substantial assistance motion” as a violation of his right to equal protection. On appeal, Davenport argues that the district court erred in finding that the Government’s refusal to accept Davenport’s proffer did not violate the Constitution. We AFFIRM.
I. BACKGROUND
From 2003 to 2008, Davenport worked for a drug-trafficking organization operating in the Columbus, Ohio, area. R. 1225, Change of Plea Tr. at 24; 28. Davenport’s duties included selling and accepting shipments of cocaine and marijuana as well as selling kilogram quantities of both drugs. Id. at 25-26. On December 4, 2008, the Federal Bureau of Investigation executed a search warrant at Davenport’s residence and seized $498 in illegal narcotics proceeds, approximately 21 grams of cocaine, scales with residue, a vice, a gram of marijuana, and a heat lamp. Id. at 26.
On February 26, 2009, the Grand Jury returned a superseding indictment against Davenport and twenty-eight co-defendants. R. 33, Superseding Indictment. On July 2, 2009, Davenport pleaded guilty to the forfeiture count as well as two drug counts in violation of 21 U.S.C. §§ 841(a)(1), 841(b)(1)(A)(ii), and 846. In exchange, the Government dismissed the other counts against him. R. 554, Plea Agreement. The plea agreement did not include a provision for “any type of motion for downward departure pursuant to 18 U.S.C. § 3553(e), U.S.S.G. § 5K1.1, or Rule 35 of the Federal Rules of Criminal Procedure-” Appellee Br. at 2; see also R. 1225 at 22.
Prior to sentencing, Davenport filed a sentencing memorandum. R. 1069, Sentencing Memorandum. In his sentencing memorandum, Davenport asserted that “[pjrior ro [sic] his guilty pleas, Tyrone entered into a plea agreement which, among other items, addressed a potential § 5K1.1 Motion if he provided information of substance and assistance to the government,” but “the government decided not to even speak with Tyrone Davenport.” Id. at 3. Further, Davenport noted that several of his co-defendants had already been sentenced, and “[t]he majority of those similarly situated were given the benefit of § 5K1.1 Motions....” Id. Davenport claimed that the Government refused his proffer because one of the prosecutors, Assistant United States Attorney (“AUSA”) David DeVillers, had a “personal vendetta” against him. According to Davenport:
Subsequent to signing the plea agreement, it was discovered that AUSA De-Villers had no intention of permitting Davenport to proffer and thus avail himself to a possible § 5K1.1 Motion.... The AUSA’s position arose from his pri- or contact with Mr. Davenport in 2002 while an assistant Franklin County Prosecutor. In 2002 Tyrone, along with two (2) other individuals, was indicted for Aggravated Murder. The case was prosecuted by David De[V]illers. As a result of the severance motion, one of the co-defendants was tried first and acquitted of the crime. Tyrone’s case was subsequently dismissed and refiled. AUSA DeViller[s’s] refusal to allow Davenport to proffer was based on his personal animosity toward Mr. Davenport. Defendant believes that it is a violation of his right to equal protection because of a personal vendetta by a AUSA [sic].... Tyrone Davenport was denied his right to be treated as other similarly situated defendants.... As a result, the Court’s hands are tied by the mandatory minimum ten (10) year prison sentence.
Id. at 6-7.
At Davenport’s sentencing hearing, his sentencing memorandum was discussed at *502length. Davenport’s counsel began by apologizing to AUSA DeVillers and stating that “[t]here was no intent in that sentencing memorandum of indicating at all that Mr. DeVillers in any way acted unethically.” R. 1226, Sentencing Tr. at 15-17. Rather, the sentencing memorandum’s goal was simply to “point[ ] out ... the problems with 5K and the unrestrained discretion that it gives the government. ...” Id. Davenport’s counsel then opined that the mandatory minimum is “a problem. It’s unfortunately a statutory problem, and that’s not the Court’s problem, but it still is a problem.” Id. at 17.
The district court noted that whether the government files a “motion under 3553(e) as the guideline 5K1.1 ... [is] a matter committed to the discretion of the government,” and asked: “What authority, if any, would I even have here to pursue a hearing on this if I were so inclined?” Id. at 18. Davenport’s counsel responded: ‘Tour Honor, I’m not saying that the Court has [that authority]. I think it’s important for the Court to know in terms of the global look at Mr. Davenport and his willingness, you know, part of the willingness to proffer goes far and beyond the normal acceptance of responsibility.” Id. Davenport’s counsel further stated that “when you look at him [Davenport] under the various considerations of 3553(a), I think Mr. Davenport is one who is salvageable. ... However, I do realize the Court’s hands are tied by the statute at this point in time.” Id. at 19.
In response, AUSA DeVillers made clear that Davenport’s allegations were false. Davenport’s 2002 case was prosecuted in Franklin County, Ohio; although AUSA DeVillers once worked in the Franklin County prosecutor’s office, DeVil-lers was working with the U.S. Attorney’s office as of 2000. Id. at 20. AUSA DeVil-lers also explained that, even though he was not involved in Davenport’s 2002 prosecution, the prior homicide was one of the reasons the United States did not seek cooperation from Davenport. That is, because the prior homicide investigation remained open and Davenport’s homicide charges were dismissed before the trial began, Davenport could still be re-charged with that offense. Id. Before Davenport entered his plea agreement, the Government made clear that the homicide would be discussed should Davenport be debriefed, and Davenport indicated that he was unwilling to be questioned about the homicide. Id. Therefore, the United States decided not to pursue a proffer and informed Davenport of its decision before he entered the plea agreement. Id. at 21. Finally, the Government noted that Davenport “has a prior aggravated trafficking conviction.” Id. Accordingly, if Davenport “chose not to plead guilty and go to trial, we would file that enhancement, and the defendant would be facing a mandatory minimum of 20 years as opposed to 10 years. So that was, I guess, our stick, if you will, to induce a plea....” Id.
The district court then computed Davenport’s sentencing guideline range. Given Davenport’s final offense level of 29 and criminal history category of IV, the district court found that the guideline range was 120 to 150 months, coupled with the mandatory minimum of a 120-month sentence for violating 21 U.S.C. § 846. Id. at 22. After finding no appropriate departure basis, the district court then reviewed the section 3553(a) factors. Id. In particular, the district court highlighted “the need to avoid unwarranted sentencing disparities involving defendants with similar records and similar pasts.” Id. at 24. The district court found that “[t]he degree of cooperation, of course, is a major factor. In this case there was not cooperation sufficient to obtain a motion from the government to reduce the sentence.” Id. The district court also stated:
*503I do want to spend a moment talking about the issue [regarding] whether or not the defendant had an opportunity to cooperate. As a starting matter, of course, the government’s decision whether to file such a motion is something that Congress has given to the government and the government alone. It is not reviewable by me unless there is some unconstitutional type of deprivation taking place, which I don’t have any sense has occurred in this case. How the government uses the authority, of course, is a very important decision for it to make. But I find nothing in this case that would indicate to me that there was any sort of matter ... that I can consider or would wish to consider regarding Mr. DeVillers’s conduct or involving the way the defendant was either given or denied an opportunity to cooperate. So I don’t find that ... factor would affect the sentence.
Id. at 25. The district court then imposed the ten-year mandatory minimum sentence. Id.
Davenport timely appealed. On appeal, Davenport argues:
The sole issue presented is whether defendant is entitled to remand for an evidentiary hearing to show that the government, in its refusal to hear defendant’s proffer and its consequent refusal to make a substantial assistance motion on defendant’s behalf, treated the defendant dissimilarly from similarly situated co-defendants for no reason rationally related to legitimate government ends.
Appellant Br. at 1; see also id. at 16.
II. ANALYSIS
Davenport’s appeal raises the issue of whether the district court erred in refusing to conduct an evidentiary hearing on the Government’s rejection of Davenport’s willingness to proffer as a part of its section 3553(a) analysis before imposing Davenport’s sentence. This Court reviews a district court’s sentence for procedural and substantive unreasonableness under the deferential abuse of discretion standard. See, e.g., United States v. Alexander, 543 F.3d 819, 821-22 (6th Cir.2008). A sentence is procedurally unreasonable if, inter alia, the district court failed to properly calculate the Guidelines range, treated the Guidelines range as mandatory, failed to consider section 3553(a) factors, used clearly erroneous facts in imposing the sentence, or failed to adequately explain the sentence. Id. at 822. A sentence is substantively unreasonable if the district court arrives at a sentence arbitrarily, uses impermissible sentencing factors, fails to consider relevant sentencing factors, or gives unreasonable weight to any one factor. United States v. Baker, 559 F.3d 443, 448 (6th Cir.2009). This Court reviews a constitutional challenge to a defendant’s sentence de novo. See United States v. Crowell 493 F.3d 744, 749 (6th Cir.2007), cert. denied, 552 U.S. 1105, 128 S.Ct. 880, 169 L.Ed.2d 739 (2008).
As the Supreme Court has clearly established, “federal district courts have authority to review a prosecutor’s refusal to file a substantial-assistance motion and to grant a remedy if they find that the refusal was based on an unconstitutional motive. Thus, a defendant would be entitled to relief if a prosecutor refused to file a substantial-assistance motion, say, because of the defendant’s race or religion.” Wade v. United States, 504 U.S. 181, 185-86, 112 S.Ct. 1840, 118 L.Ed.2d 524 (1992). A defendant is also entitled to relief if the prosecutor’s refusal to file a substantial-assistance motion is not rationally related to any legitimate Government end. Chapman v. United States, 500 U.S. 453, 464-65, 111 S.Ct. 1919, 114 L.Ed.2d 524 (1991). However, the defendant has the burden of making a substantial threshold showing: “a claim that a defendant merely provided *504substantial assistance will not entitle a defendant to a remedy or even to discovery or an evidentiary hearing. Nor would additional but generalized allegations of an improper motive.” Wade, 504 U.S. at 186, 112 S.Ct. 1840.
Davenport failed to produce a cognizable allegation that the Government’s refusal to file a substantial-assistance motion was based on an unconstitutional motive. Davenport’s generalized allegations fall short of meeting his burden of making a substantial threshold showing. Further, the Government offered two constitutionally acceptable reasons that distinguished Davenport from his co-defendants. First, when the Government raised the possibility of a proffer, Davenport refused to cooperate with the Government about the 2002 murder. R. 1226, p. 20. Second, the Government chose not to pursue a proffer because of Davenport’s prior convictions. Id. at 21. Consequently, the district court properly exercised its authority under Wade. Accordingly, we find that Davenport’s sentence was procedurally reasonable. See Alexander, 543 F.3d at 822.
We also find no grounds for challenging the substantive reasonableness of Davenport’s sentence. Even though Davenport urged the district court to consider the Government’s rejection of his proffer as a sentencing factor, the district court’s refusal to consider this issue as relevant to Davenport’s acceptance of responsibility does not amount to a “failure] to consider relevant sentencing factors.” See Baker, 559 F.3d at 448. Assuming, without deciding, that a defendant’s inability to proffer constitutes a relevant sentencing factor, the district court thoroughly considered the issue at the sentencing hearing. Indeed, even though the district court ultimately determined that Davenport’s inability to proffer would not affect his sentence, R. 1226 at 25, the district court discussed the situation with both parties at length before analyzing the section 3353(a) factors and sentencing Davenport. In doing so, the district court did not abuse its discretion. Accordingly, we AFFIRM the district court’s sentence.