
582 F.3d 641 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Kenta Raynard MOORE, Defendant-Appellant.
No. 08-1699.
United States Court of Appeals, Sixth Circuit.
Argued: August 6, 2009.
Decided and Filed: October 5, 2009.
*642 ARGUED: Paul L. Nelson, Federal Public Defender's Office, Grand Rapids, Michigan, for Appellant. Nils R. Kessler, Assistant United States Attorney, Grand Rapids, Michigan, for Appellee. ON BRIEF: Sharon A. Turek, Federal Public Defender's Office, Grand Rapids, Michigan, for Appellant. B. René Shekmer, Assistant United States Attorney, Grand Rapids, Michigan, for Appellee.
Before: CLAY, COOK, and KETHLEDGE, Circuit Judges.

OPINION
CLAY, Circuit Judge.
Defendant Kenta Raynard Moore ("Moore") appeals the order of the United States District Court for the Western District of Michigan denying his motion for a sentence reduction pursuant to 18 U.S.C. § 3582(c)(2). On appeal, Moore contends that the district court improperly found that he had distributed at least 4.5 kilograms of cocaine base, thus making him ineligible for a reduction. For the following reasons, the district court's denial of a sentence reduction for Moore is REVERSED, and the case is REMANDED so that the district court may reconsider the merits of Moore's motion.

BACKGROUND
According to Moore's Presentence Investigation Report ("PSR"), a confidential informant for the Drug Enforcement Administration made a controlled purchase of 23.4 grams of crack cocaine from Moore on May 11, 1999. On September 13, 1999, a grand jury charged Moore in an indictment with one count of knowingly and intentionally distributing cocaine base in violation of 21 U.S.C. § 841(a)(1). On November 18, 1999, Moore pled guilty to the single count.
Moore's PSR noted as part of its description of Moore's offense conduct that two other individuals who pled guilty to drug distribution gave statements to the DEA that they and Moore pooled money to purchase crack cocaine and powder cocaine "in kilogram quantities" from a supplier in Chicago. The PSR advised that "[the three defendants] paid anywhere from $20,500.00 to $24,000.00 per kilogram, and would purchase anywhere from two to three kilograms per month, sometimes as often as two to three times per month." The PSR also stated that in total, the two proffering defendants "estimated the group purchased between 180 to 300 kilograms of cocaine." (PSR at 4.) The PSR also stated that "[f]or computation purposes, Mr. Moore is being held responsible for at least 1.5 kilograms of cocaine base." (PSR at 5.) At the time of Moore's sentence, under the United States Sentencing Guidelines ("Guidelines"), the highest base offense level of 38 applied to a defendant distributing "1.5 KG or more of cocaine base." U.S.S.G. § 2D1.1(c) (1999).[1]
The PSR recommended a three-level reduction for acceptance of responsibility, *643 noting that Moore "has provided complete information to the government and entered a timely plea of guilty." (PSR at 6.) Moore admitted to the probation officer preparing the PSR that "his overall involvement in the distribution of drugs exceeded 1.5 kilograms of crack cocaine, although he could not be more specific." (PSR at 5-6.) After factoring in a three-level reduction for acceptance of responsibility, the PSR advised that Moore's base offense level was 35, and, stating that Moore had a Criminal History Category of III, recommended a Guidelines range of 210 to 262 months. On April 25, 2000, the government moved the court for a two-level downward departure pursuant to U.S.S.G. § 5K1.1, because Moore had provided substantial assistance to the government.
At Moore's sentencing hearing on May 1, 2000, his counsel informed the court that there were no factual inaccuracies in the PSR. The court found that "at least 1.5 kilograms of base cocaine are attributable to Mr. Moore[.]" Appellant's Br. Ex 4 at 5. The court granted the government's motion for a two-level downward departure, noting that Moore's recommended Guidelines range was now 168 to 210 months. The court then sentenced Moore to 168 months of imprisonment. On February 23, 2004, the district court granted the government's motion pursuant to Federal Rule of Criminal Procedure 35(b) to reduce Moore's sentence because he had testified in the trial of his drug supplier. Accordingly, the court reduced Moore's sentence to 135 months of imprisonment.
Effective November 1, 2007, the United States Sentencing Commission promulgated "Amendment 706," amending the Guidelines to reduce the base offense level for crack cocaine offenses by two offense levels. United States v. Poole, 538 F.3d 644, 645 (6th Cir.2008). After the enactment of Amendment 706, a defendant now had to be responsible for "4.5 [kilograms] or more of cocaine base," an increase from 1.5 kilograms in 2000, in order to receive an offense level of 38; a finding of "at least 1.5 [kilograms] but less than 4.5 [kilograms] would mandate a Guidelines offense level of 36." U.S.S.G. supp. to app. C, amend. 706 (Nov. 1, 2007), incorporated into U.S.S.G. § 2D1.1(c). Effective March 3, 2008, Amendment 706 was made retroactive. Poole, 538 F.3d at 645-46. On February 25, 2008, Moore filed a pro se motion for a sentence reduction pursuant to 18 U.S.C. § 3582(c)(2), asserting that he was eligible for the reduction under Amendment 706.
On March 19, 2008, the United States Probation Office submitted a Sentence Modification Report ("SMR"). In a section entitled "Original Guideline Calculation as determined by the Court at Sentencing," the SMR states: "The United States Sentencing Commission Guideline for violation of 21 U.S.C. § 841(a)(1) ... calls for a base offense level of 38 for offenses involving at least 1.5 kilograms of cocaine base. According to the Offense Conduct section, this defendant's criminal activity involved at least 1.5 kilograms of cocaine base." (SMR at 1.) In a subsequent section entitled "Amended Guideline Calculation," the SMR states: "The United States Sentencing Commission Guideline for violation of 21 U.S.C. § 841(a)(1) ... calls for a base offense level of 38 for offenses involving at least 4.5 kilograms of cocaine base. According to the Offense Conduct section, this defendant's criminal activity involved at least 4.5 kilograms of cocaine base." (SMR at 2.) Under "Public Safety Factors," the SMR states that "Mr. Moore's involvement in cocaine sales was significant, being responsible for between 180 and 300 kilograms of cocaine." (SMR at 3.) Finally, in a section entitled "The defendant is ineligible for reduction in sentence for the following reason(s)," the *644 SMR includes a checked box next to "Quantity used to drive guideline exceeds 4,500 grams[.]" (SMR at 4.) On April 10, 2008, Moore submitted a response objecting to the SMR.
On April 25, 2008, the district court denied Moore's motion in a two-paragraph order, in which it stated:
... [T]he motion is denied because defendant is ineligible for reduction in sentence because the quantity of drugs used to drive the guidelines exceeds 4,500 grams.
Defendant argues that the amount of drugs in which he was involved in the original offense conduct as reported in the Presentence Report is "not exact," "open to interpretation," and "speculative at best". However, even assuming for sake of argument without conceding the point, that defendant's argument is correct, it is clear that defendant raised no factual or legal objection to the Presentence Report. His collateral challenge to the amount of drugs stated in the Presentence Report almost 8 years after the fact, is too late. His failure to object at the time of sentencing stands as an admission of the fact. United States v. Adkins, 429 F.3d 631, 632-33 (6th Cir.2005).
(ROA at 31.)
Moore timely appealed the denial of his motion for a reduction. (ROA at 32.)

DISCUSSION

Standard of Review
"A motion for modification made under 18 U.S.C. § 3582(c)(2) is reviewed for an abuse of discretion." United States v. Carter, 500 F.3d 486, 490 (6th Cir.2007). "A district court abuses its discretion when it applies the incorrect legal standard, misapplies the correct legal standard, or relies upon clearly erroneous findings of fact." United States v. Pugh, 405 F.3d 390, 397 (6th Cir.2005). This Court should reverse the district court's decision only if it is "firmly convinced that a mistake has been made." McCombs v. Meijer, Inc., 395 F.3d 346, 358 (6th Cir.2005). "When reviewing the district court's application of the Sentencing Guidelines, we review the district court's factual findings for clear error and mixed questions of law and fact de novo." United States v. May, 568 F.3d 597, 604 (6th Cir.2009).

Analysis
Moore argued before the district court that he was entitled to a reduction in his sentence because the information contained in his initial PSR with respect to the quantity of crack he distributed "is not exact and is open to interpretation." (ROA at 14.) The district court denied Moore's motion for a modified sentence. The district court held that Moore could not contest the SMR's factual finding that he possessed more than 4.5 kilograms of crack cocaine because he did not object to the PSR at his original sentencing, and was therefore bound by its facts. The district court correctly stated that Moore is bound by the factual allegations in the PSR to which he did not object. See United States v. Adkins, 429 F.3d 631, 632-33 (6th Cir.2005). However, Moore's PSR never stated that he was involved in possessing or distributing more than 4.5 kilograms of crack; the PSR stated only that "for computational purposes, Moore is being held responsible for at least 1.5 kilograms of cocaine base." (PSR at 5.)
Moreover, while the facts described in the offense conduct could have allowed the district court to find by a preponderance of the evidence that Moore was responsible for at least 4.5 kilograms of crack, the facts set forth in the PSR do not mandate such a finding. The PSR stated that DEA agents observed Moore carry out one sale of 23.4 grams of crack. The PSR also *645 noted that Moore and two other individuals pooled their money to purchase crack and powder cocaine "in kilogram quantities" from a supplier in Chicago, perhaps as often as two or three times per month. However, the PSR never explains how much of the drugs they purchased was crack and how much was cocaine; the PSR states that the two other individuals "estimated" that they purchased between 180 and 300 kilograms of cocaine, but did not disclose how much crack the team purchased or cooked. Thus, by failing to object to any statement in the PSR at his original sentencing, Moore did not admit that he was responsible for 4.5 kilograms of crack; he could have agreed with all of the PSR's factual allegations, while still believing that the total amount of crack he possessed or distributed was less than 4.5 kilograms. Accordingly, the district court committed legal error by refusing to consider Moore's objection to the SMR.
The only remaining question is whether the error was harmless-i.e., whether we can be certain that the error did not affect the disposition of Moore's motion. In the analogous context of a district court's procedural error at sentencing, the harmless error standard "requires the party who wishes to defend the sentence to `persuade the court of appeals that the district court would have imposed the same sentence absent the erroneous factor.'" United States v. Anderson, 526 F.3d 319, 330 (6th Cir.2008) (quoting Williams v. United States, 503 U.S. 193, 203, 112 S.Ct. 1112, 117 L.Ed.2d 341 (1992)); see also United States v. Vandeberg, 201 F.3d 805, 812 (6th Cir.2000) ("Remand is appropriate unless the appellate court is convinced that the trial court would have imposed the same sentence absent [its] misinterpretation of the guideline.") (quotations and citation omitted). The government cannot make the necessary showing to convince us that the district court would have imposed the same sentence absent its error. The district court did not indicate how it would have responded to Moore's motion if it had understood that Moore's previous admissions did not bind its resolution of his motion. To be sure, the district court could have made findings of fact based upon the PSR that would have provided a basis for rejecting Moore's motion on its merits. Yet the district court never made any such findings, and because it never did so, we cannot know for certain that the district court would have denied the motion.
The Guidelines advise that:
[i]n determining whether, and to what extent, a reduction in the defendant's term of imprisonment under 18 U.S.C. 3582(c)(2) and this policy statement is warranted, the court shall determine the amended guideline range that would have been applicable to the defendant if [Amendment 706] had been in effect at the time the defendant was sentenced. In making such determination, the court shall substitute only [Amendment 706] for the corresponding guideline provisions that were applied when the defendant was sentenced and shall leave all other guideline application decisions unaffected.
U.S.S.G. § 1B1.10(b)(1).
None of the facts contained in Moore's original PSR necessarily render Moore ineligible for a reduction under Amendment 706. The PSR did not specifically link Moore to 4.5 kilograms of crack; Moore never admitted to any facts beyond those in the PSR; and the district court at sentencing did not adopt any more specific factual findings regarding the quantity of crack Moore distributed. Determining whether Moore's Guidelines range would have been amended if Amendment 706 "had been in effect at the time the defendant was sentenced" is impossible. *646 U.S.S.G. § 1B1.10(b)(1).[2] The PSR recommended that "for computational purposes" Moore be held responsible for "at least 1.5 kilograms," tracking the highest offense level at that time. (PSR at 5.) Had Amendment 706 been in place, the PSR would likely have either computed Moore's drug quantity as "at least 4.5 kilograms" or, if the quantity was lower than 4.5 kilograms, would have needed to be more precise than prefacing the stated quantity with "at least." In the absence of any previous factual finding that would have rendered Moore ineligible, nothing in § 3582(c)(2) or the Guidelines precluded the district court from granting Moore's motion for a modification. Because the district court could have granted Moore a sentence reduction by finding that the government never proved that Moore was responsible for a quantity of crack greater than 4.5 kilograms, the district court's error was not harmless and constituted an abuse of discretion. See United States v. Hazelwood, 398 F.3d 792, 801 (6th Cir. 2005).
Having found that the district court's error was not harmless, we remand Moore's case back to the district court for a ruling on his motion. Because the district court barred Moore from objecting to the recommended findings in the SMR, it never considered his argument that the facts in the PSR do not support holding him responsible for 4.5 kilograms of crack. See United States v. Gale, 468 F.3d 929, 940 (6th Cir.2006). ("When, on appeal, a defendant's argument and supporting evidence presents an arguably meritorious claim for a lesser sentence, but there is little to suggest that the district court actually considered it, then remand may be appropriate."). We do not agree with Moore that the district court's previous determination of "more than 1.5 kilograms" means that it cannot also find more than 4.5 kilograms. Unlike the prior sentencing in United States v. Adams, 104 F.3d 1028, 1030 (8th Cir.1997), nothing in the record from Moore's initial sentencing indicates that the district judge made any specific determination other than more than 1.5 kilograms. Since 4.5 kilograms is more than 1.5 kilograms, a new factual finding of the higher quantity is not inconsistent with the court's determination at Moore's original sentencing. Remand is appropriate here not because the district court must apply the reduction, but because no factual finding definitively linked Moore with 4.5 kilograms of cocaine base.

CONCLUSION
For the reasons set forth above, the district court's denial of Moore's sentencing reduction motion is REVERSED, and the case is REMANDED for consideration of Moore's motion on the merits.
NOTES
[1]  Because Moore was sentenced in May 2000, the Guidelines effective November 1999 should have been used. The PSR indicates that its recommendations were based on the Guidelines effective November 1998. Regardless, because the Guidelines provision at issue, U.S.S.G. § 2D 1.1(c), was identical in the 1998 and 1999 editions, the use of the incorrect sentencing guideline is harmless.
[2]  For this reason, we do not believe Moore's subsequent testimony at the trial of his supplier that he had picked up six to eight kilograms of cocaine base in Chicago means Moore is necessarily ineligible for the reduction. Moore was sentenced on May 1, 2000, while his testimony was given in August 2000. The district court should make its decision based on the information that was available at the time of sentencing, although we acknowledge the judge has the discretion to deny Moore's motion even if his Guidelines range is lowered. See United States v. Ursery, 109 F.3d 1129, 1137 (6th Cir.1997) ("[A] district court has the discretion to deny a section 3582(c)(2) motion, even if the retroactive amendment has lowered the guideline range.").
