
519 F.3d 310 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Marvin GOODMAN, Defendant-Appellant.
No. 06-5513.
United States Court of Appeals, Sixth Circuit.
Submitted: March 14, 2008.
Decided and Filed: March 17, 2008.
*311 *312 *313 ON BRIEF: James E. Thomas, Law Office of James E. Thomas, Memphis, Tennessee, for Appellant. Steven S. Neff, Assistant United States Attorney, Chattanooga, Tennessee, for Appellee.
Before MOORE, GILMAN, and SUTTON, Circuit Judges.

OPINION
KAREN NELSON MOORE, Circuit Judge.
In this case the defendant, Marvin Goodman ("Goodman"), challenges the district court's use of a 1993 Tennessee escape conviction for an enhancement to his sentence under the Armed Career Criminal Act ("ACCA"). Although it is possible that a Tennessee court might no longer consider a violation of house arrest to qualify as an escape under Tennessee law, precedent binds us to consider that conviction a violent felony until such time that Goodman can overturn or expunge that conviction. Goodman also challenges the district court's decision to give him a one-level enhancement for possessing a firearm in connection with a controlled-substance offense. The evidence before the district court did not establish that the firearm was possessed in connection with a controlled-substance offense. We therefore VACATE Goodman's sentence and REMAND to the district court for resentencing consistent with this opinion.

I. BACKGROUND
According to the government's April 20, 2005 statement of factual basis in support of the proposed guilty plea, to which defendant Goodman agreed, the Athens Police Department responded to a 9-1-1 call on August 2, 2004, which reported the firing of shots. When the police arrived, they found one person lying dead on the property and Goodman inside the residence with the victim's girlfriend, Kim Arnwine ("Arnwine"). In addition, the "[o]fficers found a pistol on the couch inside the residence." Joint Appendix ("J.A.") at 19 (Guilty Plea Factual Basis ¶ a).
According to Goodman, he and the victim left the residence and were heading outside to a parked van, but after Goodman reached the van, "he heard several shots fired." Id. Goodman searched for his compatriot and discovered the victim's body lying on the ground. Goodman stated that "he thought he saw someone and while jumping up to run, slipped on a gun. . . . [Goodman] picked up the gun, put it under his arm and then in his waistband, and went inside the house, where he dropped the gun onto the sofa. . . ." J.A. at 19-20 (Guilty Plea Factual Basis ¶ a). "The weapon [officers] found which the defendant admitted to possessing was not the murder weapon." J.A. at 20 (Guilty Plea Factual Basis ¶ a).
The government-filed factual basis also states that Arnwine told police that she had observed the victim with a gun earlier in the day. Furthermore, the factual basis reports that Arnwine stated to the police that the gun was gone when Goodman and the victim left to sell crack cocaine. J.A. at 20 (Guilty Plea Factual Basis ¶ b). In *314 addition, the factual basis asserts that "[h]ad this case proceeded to trial, the United States would have called multiple witnesses who would have testified that [Goodman and the victim] had been selling crack cocaine together in a nearby park and were engaged in an argument with some other narcotics traffickers from Athens immediately prior to the shooting." J.A. at 20 (Guilty Plea Factual Basis ¶ c).
On October 26, 2004, a grand jury indicted Goodman for being a felon in possession of a firearm in violation of 18 U.S.C. § 922(g)(1). J.A. at 7 (Indictment at 1). The indictment further alleged that Goodman had at least three prior felony convictions that satisfied the ACCA under 18 U.S.C. § 924(e). J.A. at 7 (Indictment at 1).
Goodman agreed to plead guilty, and on October 6, 2005, the district court held a hearing where Goodman revoked his initial not-guilty plea. At the rearraignment hearing, the district court asked Goodman whether the government's guilty-plea factual basis was accurate, to which Goodman responded "[m]ostly, sir." J.A. at 32 (Oct. 6, 2005, Rearraignment Hr'g Tr. at 9:7). Goodman apparently disagreed with Arnwine and wished to state that he had not been selling drugs prior to the shooting. See J.A. at 32-33 (Hr'g at 9:2-10:13). The district court, however, explained to Goodman that the factual basis stated only that Arnwine had given that statement to officers, not that Arnwine's statement was true. J.A. at 33-34 (Hr'g at 10:16-11:12). After the district court clarified that point, Goodman agreed to the factual basis. J.A. at 36 (Hr'g at 13:2-8).
Prior to sentencing, Goodman's Presentence Report ("PSR") recommended that the district court conclude that Goodman was an armed career criminal on the basis of four prior offenses, including a 1993 escape conviction. J.A. at 81 (PSR ¶ 27). In addition, the PSR recommended that the district court conclude that the firearm was possessed "in connection with . . . a controlled substance offense," which would yield a base offense level of 34. 2004 U.S. Sentencing Guidelines Manual ("U.S.S.G.") § 4B1.4(b)(3)(A); J.A. at 81-82 (PSR ¶ 27). Had the PSR not recommended that the district court conclude that the firearm was possessed in connection with a controlled-substance offense, then Goodman's base offense level would have been 33, not 34. U.S.S.G. § 4B1.4(b)(3)(B). The PSR also recommended a three-level deduction for acceptance of responsibility. J.A. at 82 (PSR ¶ 28). Thus, the PSR recommended a Guideline range of 188 to 235 months of imprisonment. J.A. at 91 (PSR ¶ 66).
Goodman filed several objections to his PSR. Goodman objected to the predicate offenses used to establish his eligibility for a sentence as an armed career criminal. J.A. at 94-106 (Objections to PSR at 1-13). In response, the probation officer accepted one of the objections, removing reference to a conviction for attempting to sell cocaine. J.A. at 127 (Supp. Addendum to PSR at 2). Goodman also objected to the PSR's reference to the alleged drug trafficking that appeared in paragraph c of Goodman's factual basis, claiming that it was not relevant to the felon-in-possession conviction. J.A. at 106 (Objections to PSR at 13). The probation officer, however, concluded that the reference to the alleged drug trafficking was appropriate because Goodman agreed to the factual basis, which mentioned the alleged trafficking. J.A. at 127 (Supp. Addendum to PSR at 2). Goodman also objected to the PSR's alternative calculation that would apply only if the district court did not sentence Goodman under the ACCA. J.A. at 107 (Objections to PSR at 14).
On March 24, 2006, the district court held Goodman's sentencing hearing. At *315 the hearing, Goodman objected to the use of his 1993 conviction for escape as a prior violent felony for purposes of the ACCA. J.A. at 48 (Mar. 24, 2006, Sent. Hr'g Tr. at 11:9-22). Although he conceded that the district court was not allowed to pry into the factual details of the 1993 conviction, Goodman claimed that the district court could still consider some records from that conviction, such as the charging document, the plea colloquy, and other factual findings. See J.A. at 46 (Sent. Hr'g Tr. at 9:13-20). Because the escape conviction was for violating house arrest, J.A. at 44 (Sent. Hr'g Tr. at 7:4-7), Goodman argued that the district court should not consider the conviction to be a violent felony. The government responded by saying that "escape constitutes a violent felony, regardless of what the circumstances were in terms of how he escaped or what he had to do in order to escape. None of that matters." J.A. at 51 (Sent. Hr'g Tr. at 14:2-4).
At the hearing, Goodman did not initially mention his objection regarding the PSR's non-ACCA calculation, but the government did offer its own gloss on that objection. The government believed that even if the district court concluded that Goodman was eligible for sentencing under the ACCA, Goodman's objection was relevant to the PSR's use of § 4B1.4(b)(3)(A), which gave a base offense level of 34, as opposed to 33, for Goodman's alleged possession of the firearm in connection with a controlled-substance offense. J.A. at 59 (Sent. Hr'g Tr. at 22:3-7) ("I think that that is still a relevant objection even if the defendant is determined to be an armed career criminal, because I believe it would make the difference between whether he's a Level 34 or a Level 33."). The district court then restated the government's interpretation of the argument, to which Goodman's counsel responded "Judge, that's basically correct." J.A. at 61 (Sent. Hr'g Tr. at 24:1-9).
It is not clear whether the district court proceeded to address Goodman's non-ACCA objection or instead addressed the government's ACCA-based gloss on the original objection. In any event, the district court first restated the government's position that Goodman did not dispute the facts underlying the conviction, J.A. at 61 (Sent. Hr'g Tr. at 24:1-4), but Goodman then indicated that he wanted to make a statement. J.A. at 61 (Sent. Hr'g Tr. at 24:8-19). Goodman attempted to take the stand to explain his factual disagreement, but as he did so the district court reminded Goodman that he was under oath when he made his guilty plea. J.A. at 61 (Sent. Hr'g Tr. at 24:23-24). The district court reiterated the agreed-upon factual basis, stating "[l]ater on it indicates that the United States would have put on evidence through the use of multiple witnesses who would have testified that you and the shooting victim had been selling crack cocaine together in a nearby park and were engaged in an argument with some other narcotics traffickers from Athens immediately prior to the shooting." J.A. at 62 (Sent. Hr'g Tr. at 25:7-13). The district court then warned Goodman that "[s]ometimes defendants, once they come to sentencing, will make some statements that are contrary to either what's in the factual basis or to the facts the Court has found." J.A. at 62-63 (Sent. Hr'g Tr. at 25:24-26:1). The district court noted that if Goodman told a contradictory story, then he might lose his acceptance-of-responsibility credit, J.A. at 63 (Sent. Hr'g Tr. at 26:3-6), and the district court might also punish Goodman for obstruction of justice, J.A. at 63 (Sent. Hr'g Tr. at 26:7-12). The district court told Goodman that "[i]f you want to say something about the facts in your heart of hearts you know to be true, then go ahead and do it. . . . Unfortunately *316 this is not a risk-free environment." J.A. at 63-64 (Sent. Hr'g Tr. at 26:22-27:2).
This lecture prompted Goodman to step off the stand, and neither he nor his attorney made any assertions of fact contradicting the evidence that the government would have presented at a trial. When the district court asked if there were any further arguments concerning the issue of whether Goodman possessed the firearm in connection with drug-distribution activities, Goodman's attorney said "[o]ther than take exception with that, Judge, we have no further argument." J.A. at 65 (Sent. Hr'g Tr. at 28:12-13). The district court then concluded that Goodman possessed the firearm in connection with a controlled-substance offense and applied the one-level increase authorized in § 4B1.4(b)(3)(A): "Based upon the facts as the Court understands them, that is, that on the day in question, the defendant and Mr. Ware were involved in selling drugs; taking into account, also, the defendant's prior history of drug-trafficking activitiesand I believe the last conviction that the Court mentioned also had a gun charge associated with that, alsothe Court, by a preponderance of the evidence, makes a finding that that part of the presentence report is also correct, and the Court will deny the defendant's objection on that ground." J.A. at 65 (Sent. Hr'g Tr. at 28:14-23).
After hearing argument from defense counsel and Goodman regarding sentencing factors, the district court sentenced Goodman to a term of imprisonment of 200 months and three years of supervised release. Goodman filed a timely appeal.

II. ANALYSIS
A. Applicability of the 1993 Escape Conviction
1. Standard of Review
"We review de novo the district court's ruling that [Goodman] is eligible to be sentenced as an armed career criminal. . . . The government bears the burden of establishing that a conviction qualifies for an ACCA sentence enhancement." United States v. Lancaster, 501 F.3d 673, 675 (6th Cir.2007); see also United States v. Hargrove, 416 F.3d 486, 494 (6th Cir. 2005) ("This Court reviews a district court's conclusion that a crime constitutes a violent felony under the ACCA or a crime of violence under the ACCA's parallel provision in the Guidelines de novo.").
2. ACCA and the Categorical Approach
The district court determined that Goodman's 1993 house-arrest violation was a violent felony and, when combined with two other qualifying offenses, triggered the applicability of the ACCA. According to the ACCA, "[i]n the case of a person who violates section 922(g) of this title[, the felon-in-possession provision,] and has three previous convictions by any court referred to in section 922(g)(1) of this title for a violent felony or a serious drug offense, or both, committed on occasions different from one another, such person shall be fined under this title and imprisoned not less than fifteen years, and, notwithstanding any other provision of law, the court shall not suspend the sentence of, or grant a probationary sentence to, such person with respect to the conviction under section 922(g)." 18 U.S.C. § 924(e)(1). Congress then defined "violent felony" to mean "any crime punishable by imprisonment for a term exceeding one year . . . that . . . is burglary, arson, or extortion, involves use of explosives, or otherwise involves conduct that presents a serious potential risk of physical injury to another. . . ." 18 U.S.C. § 924(e)(2)(B).
In determining whether a conviction counts as a violent felony for purposes of *317 the ACCA, the Supreme Court has stated that "the language of § 924(e) generally supports the inference that Congress intended the sentencing court to look only to the fact that the defendant had been convicted of crimes falling within certain categories, and not to the facts underlying the prior convictions." Taylor v. United States, 495 U.S. 575, 600, 110 S.Ct. 2143, 109 L.Ed.2d 607 (1990). Thus, in most cases, the question is whether the conviction in question falls within a category determined to contain violent felonies, and beyond that "we are forbidden from conducting a `broad factual inquiry' into the circumstances surrounding a prior conviction." United States v. Bailey, 510 F.3d 562, 565 (6th Cir.2007) (applying career-offender enhancement of § 4B1.1).
Although much of the time, "`only the fact of the prior conviction and the statutory definition of the predicate offense are used to determine whether a prior conviction is a [qualifying] offense,'" there are situations where we can look beyond the statutory definition. United States v. Montanez, 442 F.3d 485, 489 (6th Cir.2006) (citation omitted) (applying career-offender enhancement of § 4B1.1). "If . . . the categorical approach fails to be determinative, a sentencing court may look to the `charging document, written plea agreement, transcript of plea colloquy, and any explicit factual finding by the trial judge to which the defendant assented. . . .'" Id. (quoting Shepard v. United States, 544 U.S. 13, 15, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005)).
Because the categorical approach is not a fact-based approach, the government need not prove that a given offense is always violent in order for the offense to qualify as a violent felony. "Rather, a determination that `most instances of an offense involve a serious potential risk of injury' is sufficient to support the conclusion that the crime constitutes a violent crime under the `otherwise clause.'" United States v. Vanhook, 510 F.3d 569, 575 (6th Cir.2007) (quoting United States v. Johnson, 246 F.3d 330, 333 (4th Cir.2001)). It is this structure that governs our consideration of whether Goodman's 1993 escape conviction for his house-arrest violation counts as a violent felony under the ACCA.
3. ACCA and Escape
Goodman questions the district court's determination that his 1993 escape conviction for his violation of house arrest was a violent felony. According to current Tennessee law, which was applicable at the time of Goodman's 1993 conviction: "It is an offense for any lawfully confined person arrested for, charged with, or found guilty of a civil or criminal offense to escape from a penal institution. . . ." TENN.CODE ANN. § 39-16-605(a). Separately, Tennessee law states that a "`[p]enal institution' includes any institution or facility used to house or detain a person. . . ." TENN.CODE ANN. § 39-16-601(4).
We have previously considered Tennessee's escape statute within the context of the categorical approach. In 1999, we dealt with the similar, non-ACCA question of whether a violation of Tennessee's escape statute[1] was a crime of violence for purposes of determining whether the defendant was a career offender under the Sentencing Guidelines. In that case, we stated that "[e]very escape scenario is a powder keg, which may or may not explode *318 into violence and result in physical injury to someone at any given time, but which always has the serious potential to do so," and we concluded that an escape is a crime of violence under U.S.S.G. §§ 4B1.1 and 4B1.2. United States v. Harris, 165 F.3d 1062, 1068 (6th Cir.1999) (quotation marks omitted). Shortly thereafter, relying upon Harris, we concluded that an escape conviction under Tennessee's escape statute is a violent felony under the ACCA: "Because Harris found an escape statute quite similar to the one in question here to create a `crime of violence,' or a felony `otherwise involv[ing] conduct that presents a serious potential risk of physical injury to another' under USSG § 4B1.2, it would be logically inconsistent for this court to find that escape is not a `violent felony' using identical language from the ACCA." United States v. Houston, 187 F.3d 593, 594-95 (6th Cir. 1999), cert. denied, 528 U.S. 1094, 120 S.Ct. 832, 145 L.Ed.2d 700 (2000). Under our categorical approach, once we have determined that a statute covers a violent felony, as we have with Tennessee's escape statute, our review goes no further than confirming that the defendant has a conviction under that statute. Because Goodman has a conviction under Tennessee's escape statute, the district court did not err in considering it a qualifying offense under the ACCA.
Goodman argues that despite our categorical approach, Tennessee would no longer consider a violation of house arrest to be an escape, so we should not count his escape as a violent felony. The highest criminal court in Tennessee, three years after Tennessee convicted and sentenced Goodman under its escape statute, held that a felon who walked away from his parole officer could not be charged with escape under Tenn.Code Ann. § 39-16-605(a):
We agree with the petitioner that his actions on March 2, 1994 did not constitute the criminal offense of escape from a penal institution. For purposes of the escape statute, § 39-16-601 defines "penal institution" as "any institution used to house or detain a person: (A) [c]onvicted of a crime; or (B) [w]ho is in direct or indirect custody after a lawful arrest." Community Corrections, however, is an alternative to incarceration and is noncustodial in nature. Community Corrections Programs "involve close supervision but . . . do not involve housing of the offender in a jail, workhouse or community facility." From our review of the plain language of the statutory provisions at issue, we conclude that Community Corrections does not qualify as a "penal institution" for the purposes of the escape statute.
Bentley v. Tennessee, 938 S.W.2d 706, 710 (Tenn.Crim.App.1996) (citations omitted), overruled on other grounds by Tenn. Sup. Ct. R. 28 § 3(B) (concerning application for permission to appeal). According to Goodman, if Tennessee places such importance on the term "penal institution," then it is likely that the state courts would also construe a violation of house arrest to be an offense that does not fall within the escape statute.
Goodman may in fact be correct that Tennessee courts would not now consider a violation of house arrest to be an offense under Tennessee's escape statute, but that is a question for the Tennessee courts, not for us. The Supreme Court has instructed that sentencing under the ACCA is not the appropriate place for a defendant to mount a collateral attack on previous convictions. Custis v. United States, 511 U.S. 485, 490, 114 S.Ct. 1732, 128 L.Ed.2d 517 (1994) ("Custis argues that the ACCA should be read to permit defendants to challenge the constitutionality of convictions used for sentencing purposes. Looking to the language *319 of the statute, we do not believe § 924(e) authorizes such collateral attacks."). Until prior convictions are set aside, courts may still count the convictions in relation to the ACCA. Id. at 491, 114 S.Ct. 1732 ("The provision that a court may not count a conviction `which has been . . . set aside' creates a clear negative implication that courts may count a conviction that has not been set aside." (quoting 18 U.S.C. § 921(a)(20))); Turner v. United States, 183 F.3d 474, 477 (6th Cir.1999) ("We read Custis as requiring Turner to challenge the underlying state convictions first in the state court or in an independent habeas corpus proceeding brought pursuant to 28 U.S.C. § 2254. Only after Turner succeeds in such a challenge can he seek to reopen his sentence in this case."), cert. denied, 528 U.S. 1195, 120 S.Ct. 1255, 146 L.Ed.2d 112 (2000). Thus, if Goodman believes that Tennessee courts would no longer uphold his 1993 escape conviction, his first step must be seeking to have Tennessee courts overturn or expunge the conviction.
Therefore, until Goodman gets his 1993 escape conviction overturned or removed from his record, our prior precedent compels us to conclude that the conviction was for a violent felony. Thus the district court did not err when it sentenced Goodman under the ACCA.
B. Use of the Firearm `In Connection With' a Controlled-Substance Offense
The second issue on appeal is whether the district court correctly concluded that Goodman possessed the firearm in connection with a controlled-substance offense under the 2004 Sentencing Guidelines, § 4B1.4(b)(3)(A). The government asks us to hold that Goodman waived any objections to the district court's determination when he agreed to the factual basis. It is true that a defendant may waive objections if he "intentional[ly] relinquish[es] or abandon[s] . . . a known right." United States v. Olano, 507 U.S. 725, 733, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993). In particular, "we agree with the court in United States v. Sloman that `[a]n attorney cannot agree in open court with a judge's proposed course of conduct and then charge the court with error in following that course.'" United States v. Aparco-Centeno, 280 F.3d 1084, 1088 (6th Cir.) (quoting United States v. Sloman, 909 F.2d 176, 182 (6th Cir.1990)), cert. denied, 536 U.S. 948, 122 S.Ct. 2638, 153 L.Ed.2d 818 (2002).
By claiming a broad waiver, the government obscures exactly what arguments Goodman waived when he agreed to the factual basis. Because he agreed to the factual basis, Goodman cannot now dispute either that Arnwine stated to police officers that she saw the victim with the gun before Goodman and the victim left to sell crack cocaine or that the government would have called witnesses who would have testified that Goodman was selling crack cocaine in a nearby park prior to the shooting. Although those two points are unassailable, it is important to note that at no point did Goodman agree that Arnwine or the potential government witnesses were correct; in fact, the district court made it clear to Goodman during his rearraignment that he was specifically not agreeing to the underlying accuracy of the statements. Thus, Goodman is not precluded from arguing that the district court erred in concluding that he possessed the firearm in connection with a controlled-substance offense.
Goodman attacks in a multitude of ways the district court's conclusion that he possessed a firearm in connection with a controlled-substance offense. We identify three attacks on the validity of the district *320 court's decision: (1) Goodman now claims that he objected at the rearraignment to the factual basis by attempting to deny the underlying accuracy of what Arnwine told the police; (2) in the objections to the PSR Goodman claimed that the district court should not consider the factual basis's statement that the government would have presented at trial the testimony of witnesses regarding Goodman's drug sales in the park; and (3) at the sentencing hearing Goodman's counsel accepted the government's gloss on Goodman's PSR objection as stating that the firearm should not be considered as having been possessed in connection with a controlled-substance offense. The first two of these attacks fail.
At sentencing, the district court correctly considered as ineffective Goodman's attempt at rearraignment to attack the underlying truth of Arnwine's statement in the factual basis. At the rearraignment, after the district court explained to Goodman that by agreeing to the factual basis Goodman was explicitly not accepting the underlying accuracy of Arnwine's claims,[2] Goodman accepted the factual basis upon that understanding. Goodman's only attempt to deny Arnwine's statements was aborted. Furthermore, Goodman never even attempted to question the factual basis's statement regarding the witnesses that the government said it would have presented at trial to testify that Goodman and the victim had sold crack cocaine in the nearby park. Thus, the district court did not err in considering the factual basis during Goodman's sentencing. As we already noted, however, Goodman agreed only that he could not deny that Arnwine made the statement regarding the gun and that the government had witnesses who would have testified that Goodman and the victim were trafficking crack cocaine, not that Arnwine was correct or that Goodman was actually trafficking cocaine. Thus, Goodman could have presented contravening evidence at his sentencing hearing.
Even though Goodman failed to controvert the government's evidence, we agree with Goodman that "[t]he government did not establish a sufficient connection with a felony drug offense for the district court to apply the enhancement for such [an] offense." Appellant Br. at 18. Goodman makes this argument in two ways: (1) he claims that the district court cannot consider unindicted conduct, and (2) he claims that the facts that the district court possessed did not support the one-level enhancement. While we disagree with Goodman on the first point and conclude that unindicted conduct is appropriately considered as part of § 4B1.4(b)(3), we agree that the district court clearly erred in concluding that Goodman possessed a firearm in connection with a controlled-substance offense. In making this determination, we look not only to cases involving § 4B1.4(b)(3), but also to cases involving § 2K2.1(b)(5), which uses the exact same "in connection with" language. See United States v. Rutledge, 33 F.3d 671, 674 (6th Cir.1994) (noting the equivalency in language between §§ 4B1.4(b)(3) and 2K2.1(b)(5)), cert. denied, 513 U.S. 1193, 115 S.Ct. 1258, 131 L.Ed.2d 138 (1995).
We conclude that the district court did not err when it considered unindicted conduct. Section 2K2.1 makes it clear that the "in connection with another felony offense" *321 language refers to "any offense (federal, state, or local) punishable by imprisonment for a term exceeding one year, whether or not a criminal charge was brought, or conviction obtained." U.S.S.G. § 2K2.1, cmt. 4 (emphasis added). Thus, the district court did not err by considering the alleged drug trafficking even though Goodman was never indicted or convicted for that drug trafficking.
In evaluating whether the government's evidence supported the district court's application of the one-level enhancement for possession of a firearm in connection with a controlled-substance offense, we apply a deferential standard of review. See United States v. Ennenga, 263 F.3d 499, 502 (6th Cir.2001); see also United States v. Clay, 346 F.3d 173, 178 (6th Cir.2003) (reviewing for clear error). The government bears the burden of establishing that Goodman possessed the firearm in connection with a controlled-substance offense. Lancaster, 501 F.3d at 675. Under § 2K2.1, and therefore under § 4B1.4 as well, "[t]he full burden of proof on the particular enhancement sought . . . remain[s] with the government." Clay, 346 F.3d at 179. In contrast, the commentary to § 2D1.1, which lacks the "in connection with" language, applies a two-level enhancement when a firearm was possessed, and employs a burden-shifting approach that places on the defendant an obligation to show that "it was clearly improbable that the firearm was connected to the other offense." Id.; U.S.S.G. § 2D1.1 cmt. 3 ("The adjustment should be applied if the weapon was present, unless it is clearly improbably that the weapon was connected with the offense."). Under § § 2K2.1(b)(5) and 4B1.4(b)(3), however, the burden remains with the government to show that the firearm was possessed in connection with a controlled-substance offense.
In carrying its burden, "[s]o long as the government proves by a preponderance of the evidence that the firearm served some purpose with respect to the felonious conduct, section 2K2.1(b)(5)'s `in connection with' requirement is satisfied." United States v. Carter, 355 F.3d 920, 925 (6th Cir.2004) (quotation marks omitted) (quoting United States v. Spurgeon, 117 F.3d 641, 644 (2d Cir.1997)). The government can satisfy its burden by showing that "the weapon facilitated or potentially facilitated the felonious conduct, or emboldened the defendant during the felonious conduct.'" Id. (quotation marks omitted) (quoting United States v. Sanders, 162 F.3d 396, 404 (6th Cir.1998)). However, "possession of firearms that is merely coincidental to the underlying felony offense is insufficient to support the application of § 2K2.1." Ennenga, 263 F.3d at 503; see also United States v. Kolley, 330 F.3d 753, 757 (6th Cir.2003) (same).
In the instant case, we conclude that the government has not carried its burden and that the district court clearly erred in reaching the opposite conclusion. As suggestive as it may have been, the evidence that the government presented to the district court did not establish that Goodman possessed the firearm in connection with the alleged drug-trafficking crime. First, it was agreed in paragraph b of the government's factual basis that Arnwine, while not under oath or making out a sworn statement, had previously told investigators that she saw the victim with a gun and saw that the gun was gone when Goodman and the victim left to sell crack cocaine. This statement, if true, establishes only that Goodman or the victim took the gun when they left. Second, it was agreed in paragraph c of the government's factual basis that the United States would have presented at trial witnesses *322 who would have testified that Goodman and the victim had been selling crack cocaine in a park. The factual basis does not state that these witnesses saw either Goodman or the victim with the gun while they were selling crack cocaine. In summary, the evidence that the government gave to the district court, if true, would establish only the following things: (1) the victim had a gun at Arnwine's residence at some point earlier on the day of the shooting, (2) after Goodman and the victim left, Arnwine did not notice the gun at her residence, (3) Goodman and the victim sold crack cocaine prior to the shooting,[3] and (4) after the victim was shot, Goodman carried a gun, which was not the murder weapon, into Arnwine's residence. It is important to note that the government's factual basis does not state the following: (1) who took the gun from Arnwine's residence, (2) whether either the victim or Goodman had the gun when they went to sell crack cocaine, and (3) whether the gun that Arnwine claimed to observe earlier was the same gun that the police discovered when they arrived at Arnwine's residence. Given these significant factual gaps, the district court clearly erred when it concluded that Goodman possessed a firearm in connection with a controlled-substance offense.
These factual gaps make the district court's application of the one-level enhancement clearly erroneous because the factual basis provides no connection between the possession of the gun and the alleged drug trafficking. Goodman did not admit to possession of every weapon discussed in the factual basis; he admitted to possessing only the weapon that was discovered in Arnwine's residence, that Goodman claimed to have simply carried in from the yard after he tripped on it near the victim's body. The government wanted the district court to believe that Goodman possessed this police-discovered firearm in connection with a controlled-substance offense; the government attempted to imply that Goodman and the victim must have possessed the firearm while drug trafficking. Our precedent requires that there be "a clear connection" between the gun that served as the basis for the conviction for felon in possession of a firearm and the gun possessed during the other offense that triggers the enhancement. United States v. Howse, 478 F.3d 729, 733 (6th Cir.2007). In this case, there must be a "clear connection" between the gun Goodman admitted to possessing and the gun that he allegedly possessed during the controlled-substance offense. The factual basis, however, provides absolutely no evidence establishing that Goodman and the victim were armed during the drug trafficking. Similarly, even if they were armed during the drug trafficking, the factual basis provides no evidence establishing that the firearm they possessed during the trafficking was the same firearm that the police discovered in Arnwine's residence. There is no evidence establishing that the police-discovered firearm was in any way connected to the alleged drug trafficking. In short, the government failed to sustain its burden on the applicability of the one-level enhancement, and the district court's application of the enhancement was clearly erroneous.
*323 In a case where we reached the opposite conclusion in holding that the district court did not clearly err when it found that the defendant possessed a gun in connection with a drug crime under § 2K2.1, we specifically noted the importance of the fact that the defendant's possession "was neither accidental nor coincidental." United States v. Richardson, 510 F.3d 622, 627 (6th Cir.2007). We cannot say, based on the sparse evidence here, that Goodman's possession of the firearm was anything more than accidental or coincidental as it related to the alleged drug trafficking. Although it may be true that Goodman engaged in drug trafficking earlier on the day of the shooting, because there is no evidence connecting the firearm to the drug trafficking, there is no evidence to suggest that Goodman's subsequent possession of a firearm was anything more than an unfortunate coincidence. Thus, the district court's conclusion was clearly erroneous and the district court should not have applied the one-level enhancement for possession of a firearm in connection with a controlled-substance offense.
The government asserts that even if the district court incorrectly applied the one-level enhancement, any error regarding the enhancement is harmless because the Guidelines sentencing range without the one-level enhancement would have yielded a sentencing range of 168 to 210 months (instead of 188 to 235 months with the one-level enhancement), which is inclusive of the 200-month sentence that Goodman received. This argument is without merit. Recently, the Supreme Court stated that "failing to calculate (or improperly calculating) the Guidelines range" was a procedural error. Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 597, 169 L.Ed.2d 445 (2007). Similarly, we recently observed that "we cannot find that a sentencing court has properly considered the § 3553(a) factors if it miscalculated the advisory Guidelines range which it must consider together with the § 3553(a) factors." United States v. Lalonde, 509 F.3d 750, 763 n. 5 (6th Cir.2007). The Third Circuit reached a similar conclusion when it stated that "we conclude that such an `overlap' [of the applicable ranges for the correct and incorrect Guidelines calculations] does not necessarily render an error in the Guidelines calculation harmless." United States v. Langford, 516 F.3d 205, 216 (3rd Cir.2008). Moreover, in this case there is no indication that the district court would have selected the same sentence even without the one-level enhancement. Thus, the miscalculation, even though Goodman's sentence would be within the Guidelines range either with or without the one-level enhancement, was not a harmless error.
Because "[t]he government had the burdens of production and persuasion, . . . we see no reason why it should get a second bite at the apple. No special circumstances justified, or even explained, the government's failure to sustain these burdens." United States v. Leonzo, 50 F.3d 1086, 1088 (D.C.Cir.1995). Thus, "the case must be remanded for resentencing on the present record, since `[t]he government was entitled to only one opportunity to present evidence on this issue.'" United States v. Gill, 348 F.3d 147, 156 (6th Cir.2003) (alteration in original) (quoting United States v. Wyss, 147 F.3d 631, 633 (7th Cir.1998)).

III. CONCLUSION
For the foregoing reasons, we AFFIRM the district court's decision to sentence Goodman under the ACCA. However, we VACATE the district court's application of the one-level enhancement for possession of a firearm in connection with a controlled-substance offense and we REMAND *324 to the district court for resentencing consistent with this opinion.
NOTES
[1]  At issue was an earlier version of Tennessee's escape statute, making it a felony for "any person confined in a county workhouse or jail or city jail or municipal detention facility upon any charge of or conviction of a criminal offense constituting a felony [to] escape or attempt to escape therefrom." TENN. CODE ANN. § 39-5-706 (repealed 1989).
[2]  The district court's point was addressed only to paragraph b of the factual basis, which discusses Arnwine's statement, not paragraph c, which discusses the witnesses that the government would have called during trial. Presumably, the district court's argument regarding the distinction between the truth of the factual basis and the underlying truth of the statements that the factual basis references would be equally applicable to paragraph c.
[3]  It is not clear from the factual basis whether Arnwine's statement indicates that she saw the gun immediately prior to the shooting or immediately prior to the drug sales in the park. Thus, the chronology of the factual basis is uncertain; Goodman and the victim may have been at Arnwine's just once (after the drug sales but prior to the shooting) or twice (once before the drug sales and once before the shooting). This indeterminacy does not affect our conclusion.
