Defendant-Appellant Douglass Ray Patterson appeals the sentence imposed after he pled guilty to unlawfully, knowingly and intentionally possessing with intent to distribute 53.6 grams of cocaine base, in violation 21 U.S.C. § 841(a)(1). Specifically, while Patterson does not appeal the district court’s decision to impose a two-level sentencing enhancement for possession of a firearm pursuant to U.S.S.G. § 2Dl.l(b)(l), he claims that the district court erroneously applied the “clearly improbable” standard of § 2Dl.l(b)(l) in denying his application for a “safety valve” reduction under U.S.S.G. § 5C1.2(a). Patterson also argues that using his possession of a firearm to enhance his sentence and also to deny application of the safety valve provision amounts to an unfair double counting. For the reasons set forth below, we find no error in the district court’s application of the Sentencing Guidelines.

I.

On March 5, 2001, agents of the West Tennessee Violent Crimes and Drug Task Force executed a search warrant at Patterson’s residence. Upon arriving, the agents discovered Patterson and other individuals in front of the residence and proceeded to serve the warrant on him. Patterson tried to flee the scene, but he was tackled and restrained by the officers. While the officers were securing the residence, Yolanda Sharp exited the front door, and before she could be stopped, she reached into Patterson’s front pocket and pulled out a large bag of crack cocaine which fell to the ground. Sharp then attempted to flee, but she was also restrained by the officers.

In the ensuing search of Patterson’s residence, the officers located a bag of crack cocaine and a bag of marijuana in the living room. A set of digital scales, a calculator, small plastic bags, and a gun holster were found in the kitchen, while a small bag of marijuana was found in the northwest bedroom of the residence. The total quantity of crack found on Patterson and in his residence amounted to 53.6 grams. Agents also found $915 in cash on Patterson, and $768 in cash on Sharp. Finally, the agents found a .45 caliber pistol loaded with eight rounds of armor-piercing ammunition under a mattress in the southwest bedroom of the residence.

During the sentencing hearing, Probation Officer Mark Escue testified that he assessed a two-level enhancement under § 2Dl.l(b)(l) because the gun was present in Patterson’s residence at the time that Patterson’s drug-trafficking activities occurred. Escue also testified, without objection, that Sharp made a statement that she had witnessed Patterson in possession of a gun on several occasions when Patterson was conducting drug transactions. In an attempt to explain the presence of the gun, Patterson testified he had previously *990been the victim of a home invasion when two intruders, one carrying a gun and the other a knife, broke into his home. He stated that he was stabbed by one intruder while wresting the gun away from the other, and that once he had obtained the gun the intruders fled. Patterson testified that he then kept the gun loaded for his protection and that he placed it under his mattress because he had been attacked in his bedroom. Patterson admitted that the .45 caliber pistol seized by the police during the search of his home was the same gun that he had taken from his alleged attacker, and he stated that it was now his gun. He did not deny possessing the gun on March 5, 2001, when he was arrested for engaging in drug-trafficking activities.

The applicable sentencing guideline for a violation of 21 U.S.C. § 841(a)(1) is found in § 2Dl.l(e)(4) and calls for a base offense level of 32. After argument by counsel at the sentencing hearing, the district court found that Patterson had possessed a gun in connection with his drug activities and that the two-level enhancement under § 2Dl.l(b)(l) was appropriate. Because of the finding that Patterson possessed a firearm in connection with his offense, the district court also reasoned that he was not entitled to a downward departure under the safety valve provision found in § 5C1.2(a). The district court awarded Patterson a three-level reduction for acceptance of responsibility under U.S.S.G. § 3El.l(a) and (b). Pursuant to U.S.S.G. § 5A, based on a total base offense level of 31 and a criminal history category of I, the guideline range for imprisonment is 108 to 135 months. Because Patterson admitted to a quantity of cocaine base in excess of 50 grams, however, the statutorily required minimum sentence is 10 years, or 120 months. 21 U.S.C. § 841(b)(l)(A)(iii). The guideline range is therefore restricted to 120 to 135 months imprisonment under U.S.S.G. § 5Gl.l(b). Consequently, the district court sentenced Patterson to the mandatory minimum of 120 months’ imprisonment.

II.

Patterson’s main contention on appeal is that while he had the burden of proof under § 5C1.2(a) of demonstrating by a preponderance of the evidence that the safety valve provision applied, the district court erroneously applied the “clearly improbable” standard of § 2Dl.l(b)(l) in denying his application for a safety valve reduction. Patterson never raised a challenge to his sentence in light of the Supreme Court’s recent decision in United States v. Booker, - U.S. -, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), and he does not challenge on appeal the imposition of the § 2Dl.l(b)(l) sentencing enhancement. He challenges only the district court’s refusal to apply the safety valve in order to permit a sentence below the 10-year statutory minimum. However, because under the current state of the law it is difficult at best to address any challenge to a sentence without addressing the impact of Booker, we will address Patterson’s challenge in light of Booker and its progeny in this circuit.

The Federal Sentencing Act (the “Act”), 18 U.S.C. § 3551 et seq., 28 U.S.C. § 991 et seq., permits the imposition of a sentence below the relevant statutory minimum sentence in only two circumstances: on motion of the Government because of a defendant’s having provided substantial assistance in the investigation or prosecution of another person who has committed an offense, 18 U.S.C. §§ 3553(e) and 3559(d)(2); and where the defendant meets all of the requirements of the “safety valve,” 18 U.S.C. § 3553(f). Both the statute creating the safety valve and the safety valve provision in the sentencing guidelines, U.S.S.G. § 5C1.2(a), are mandatory; that is, they both require that a *991district court sentence a defendant within the applicable guideline range without regard to the statutory minimum sentence if the defendant meets all five criteria for safety valve relief. 18 U.S.C. § 3553(f); U.S.S.G. § 5C1.2(a). Prior to Booker, that meant that a defendant had a right to be sentenced below the statutory minimum if he met the safety valve criteria. Booker then held — in essence — that the top of each guideline range was a statutory maximum, and that any sentence over that maximum based on facts not pled to or found by the jury violated the Sixth Amendment. See Booker, 125 S.Ct. at 756. Booker also held that the way to remedy the problem was to sever those parts of the Act making the guidelines mandatory, without regard to whether any given sentence actually violated the Sixth Amendment. Id. at 764. The result is advisory, non-mandatory guidelines, id. at 757, which the district courts “must consult ... and take ... into account when sentencing.” Id. at 767.

The Supreme Court explicitly held in Booker that it must excise only those parts of the sentencing statute that were invalid — namely, § 3553(b)(1), the section that makes the guidelines mandatory, and § 3742(e), the section setting forth standards of review on appeal. Booker, 125 S.Ct. at 764. “With these two sections excised (and statutory cross-references to the two sections consequently invalidated), the remainder of the Act satisfies the Court’s constitutional requirements.” Booker did not strike down the statutory safety valve, 18 U.S.C. § 3553(f). That provision, therefore, still requires the district court to “impose a sentence pursuant to guidelines promulgated by the United States Sentencing Commission ... without regard to any statutory minimum sentence, if the court finds at sentencing” that the defendant meets the five criteria. 18 U.S.C. § 3553(f) (emphasis added). We note that this statute, which the Court has explicitly held to be constitutional, unequivocally puts the fact-finding on the court at sentencing, not on the jury. Id. Clearly, then, the judge is to determine the facts upon which eligibility for the safety valve depends under § 3553(f), and the Sixth Amendment is not implicated.

To apply the statutory safety valve provision, the sentencing court must calculate the defendant’s guideline sentence, determine whether the defendant seeking the benefit of the safety valve meets the five requirements for the application of that provision, and, if he does, sentence the defendant “pursuant to the guidelines promulgated” by the Sentencing Commission. 18 U.S.C. § 3553(f); U.S.S.G. § 5C1.2(a). The “guidelines promulgated” by the Sentencing Commission are exactly the same in all respects as they were pre-Booker except that they are now only advisory. The calculations themselves and the case law governing these calculations have not changed. Moreover, because with the exception of those provisions specifically invalidated in Booker, all of the Act is constitutional, § 3553(f) still specifically requires that the sentencing court find at sentencing the facts on which the safety valve depends.

In Patterson’s case, the pertinent safety valve requirement is that the defendant not “possess a firearm or other dangerous weapon ... in connection with the offense.” 18 U.S.C. § 3553(f)(2); U.S.S.G. § 5C1.2(a)(2). A district court’s determination that a defendant possessed a firearm during or in connection with an offense is a factual finding. “[T]he ‘clearly erroneous’ standard of review long has been applied to nonguilt findings of fact by district courts in criminal cases.” Maine v. Taylor, 477 U.S. 131, 145, 106 S.Ct. 2440, 91 L.Ed.2d 110 (1986).

Patterson admitted to having a gun. Therefore, in order to calculate his guide*992line range, the district court had to determine whether to increase his offense level under § 2D1.1(b)(1). That sentencing guideline provides that a defendant’s base offense level should be increased by two levels, if during the commission of a drug offense, “a dangerous weapon (including a firearm) was possessed.” U.S.S.G. § 2D1.1(b)(1). The comments to the section indicate that “the adjustment should be applied if the weapon was present, unless it is clearly improbable that the weapon was connected with the offense.” U.S.S.G. § 2D1.1 Application Note 3. We have held that for the enhancement to apply, the government must establish by a preponderance of the evidence that the defendant actually or constructively possessed the weapon during the commission of the offense, thereby raising a presumption that such possession was connected to the offense. United States v. Moses, 289 F.3d 847, 850 (6th Cir. 2002). Once the government establishes that the defendant was in possession of a firearm, the burden shifts to the defendant to show that “it was clearly improbable that the weapon was connected to the offense.” Id. (citing U.S.S.G. § 2D1.1 Application Note 3).

In this case, the district court found that the government carried its initial burden of proving by a preponderance of the evidence that Patterson possessed a firearm during his drug offense, raising a presumption that such possession was connected to the offense. Moses, 289 F.3d at 850. The district court concluded, and the record supports the conclusion, that Patterson did not rebut the presumption that the gun was connected to the offense; i.e., he did not show that it was clearly improbable that the gun was connected to the offense. The district court therefore imposed the two-level offense increase called for under § 2Dl.l(b)(l), and the resulting guidelines range straddled the statutory minimum sentence of ten years’ imprisonment.

In order to receive a sentence below the statutory minimum, Patterson has the burden of proving by a preponderance of the evidence that he satisfies the safety valve criteria, and specifically, that he did not possess a firearm in connection with his drug offense. See United States v. Salgado, 250 F.3d 438, 459 (6th Cir. 2001). The district court ruled that Patterson failed to carry his burden of demonstrating his entitlement to safety valve relief. Patterson appeals that decision, essentially contending that the firearm enhancement does not preclude the application of the safety valve.

In addressing this issue, we are faced with what appears to be conflicting precedent in this circuit, and we are called upon to determine whether the law of this circuit is that a defendant who has failed to rebut the § 2D1.1(b)(1) presumption is ineligible for the safety valve. In United States v. Johnson, we made clear that a district court’s determination that certain defendants possessed a firearm for purposes of the firearm enhancement provision of the Sentencing Guidelines rendered them ineligible to receive safety valve relief. 344 F.3d 562, 565 (6th Cir. 2003). Indeed, in Johnson, we explicitly held that as “the two-level enhancement applied pursuant to § 2D1.1(b)(1) was properly applied to both defendants, both are ineligible for ‘safety-valve’ status.” Id. at 567. Nevertheless, while admitting that “one could reasonably construe [Johnson] as implicitly holding that the proper application of a § 2Dl.l(b)(l) enhancement automatically precludes the application of a § 501.2(a) reduction,” a later panel of this court used a footnote to opine that there is in this circuit no binding precedent holding that a § 2Dl.l(b)(l) sentence enhancement “necessarily forecloses” a safety valve reduction in a sentence, and that the Johnson holding “is better understood” as limited to its particular facts. United States v. *993Bolka, 355 F.3d 909, 913 n. 5 (6th Cir. 2004). The Bolka court stated that “the implicit determinations [in Johnson] underlying the application of the § 2D1.1(b)(1) enhancements-not the application of those enhancements in and of themselves-precluded the application of the § 5C1.2(a) ‘safety valve’ reductions.” Id. Citing Johnson, the Bolka court apparently likened the “clearly improbable” standard of § 2Dl.l(b)(l) to the equivalent of proving improbability by clear and convincing evidence. See id. at 914. Based on that conclusion, the court announced that since the “ ‘clearly improbable’ standard is a higher quantum of proof than that of the ‘preponderance of the evidence’ standard,” it “does not deductively follow from a defendant’s failure to satisfy a higher quantum of proof on a particular issue that he cannot satisfy a lower quantum of proof on that same issue.” Id.

The Bolka court’s conclusion is not supported by the Sentencing Guidelines or the language in Johnson. When, as here, a defendant cannot rebut the presumption that he possessed a firearm during the commission of an offense by showing that it was clearly improbable that the weapon was connected to the offense, then that defendant is “ineligible for ‘safety-valve’ status.” Johnson, 344 F.3d at 567. This is so, because if the government carries its burden — as it did here and as it did in Johnson-oi proving that the defendant possessed a firearm during the commission of a drug offense, “the weapon is presumed to have been connected to the defendant’s offense.” Moses, 289 F.3d at 850 (emphasis added). Once that presumption is established, it falls to the defendant to rebut it by showing that it is “clearly improbable” that the gun was connected to the offense. Id. If the defendant can make that showing, the increase of offense level for possession of a weapon will not be imposed. But if the defendant does not make that showing, then he possessed a weapon in connection with the offense. In Johnson, the district court imposed the two-level increase required by U.S.S.G. § 2Dl.l(b)(l) for possession of a gun; that determination, we held, rendered the defendants “ineligible to receive [the benefit of the safety valve] because they did not meet the conditions of § 501.2(a)(2) (‘the defendant did not use violence or credible threats of violence or possess a firearm or other dangerous weapon (or induce another participant to do so) in connection with the offense.’).” As we have heretofore noted, the safety valve criteria set forth in § 501.2(a) are identical to those set out in 18 U.S.C. § 3553(f), the statutory safety valve provision.

To the extent that the opinion in Bolka attempts to overrule Johnson’s holding that imposition of a firearm enhancement necessarily forecloses application of safety valve relief, we decline to follow it. The Sixth Circuit rules dictate that one panel of this court cannot overrule the published opinion of an earlier panel. 6 Cir. R. 206(c) (January 2004).1 In fact, we have long adhered to the venerable principle that a prior published decision remains controlling unless overturned by an inconsistent decision of the Supreme Court or by this court sitting en banc. United States v. Smith, 73 F.3d 1414, 1418 (6th Cir. 1996). We are therefore bound to apply the clear holding of Johnson to the facts of this case, and we conclude that as the two-level enhancement was properly applied to Patterson pursuant to § 2Dl.l.(b)(l), he is necessarily ineligible *994for a safety valve reduction under § 501.2(a). Johnson, 344 F.3d at 567; see also United States v. Likins, 84 Fed.Appx. 504, 511-13 (6th Cir. 2003) (reading Johnson as adopting per se bar); United States v. Mitchell, 63 Fed.Appx. 224, 228-29 (6th Cir. 2003) (noting that district court’s imposition of the § 2D1.1(b)(1) enhancement effectively deprived defendant of the safety valve reduction); United States v. Highsmith, 60 Fed.Appx. 517, 519 (6th Cir. 2003) (reading United States v. Stewart, 306 F.3d 295, 296 (6th Cir. 2002), as adopting a per se bar); United Stated v. Bursey, 2000 WL 712377, at *4 (6th Cir. May 23, 2000) (observing that “constructive or actual possession of a firearm will prevent application of the safety valve”). In short, the holding in Johnson is express and unambiguous and governs our analysis here. And we think it is worth noting that the Bolka footnote purporting to limit Johnson to its facts does so by citing no fewer than five times to the “implicit,” “inherent,” and “essen[tial]” characterizations of the express holding in Johnson. Bolka, 355 F.3d at 913 n. 5.

Even assuming, arguendo, that safety valve relief is not foreclosed by application of a firearm enhancement, the district court did not commit reversible error in denying Patterson application of the safety valve. The district court did not simply hold that because it had concluded that Patterson did not rebut the presumption that the gun found in his house was connected to the offense, Patterson was automatically ineligible for the safety valve. Rather, the court held that Patterson’s testimony that he had the gun for his protection because he feared another home invasion — the only evidence Patterson adduced with regard to his possession of the gun — was probably true, but that the obvious reason for Patterson’s fear of another home invasion was that he kept illegal drugs in his house, and therefore the weapon was connected with the offense. That finding is not clearly erroneous.

We find no error in the district court’s finding that Patterson did not meet the requirements for sentencing under the safety valve provisions of the statute and the Sentencing Guidelines. Because Patterson is ineligible for the safety valve, the district court was required to impose at least the statutory minimum sentence, exactly the sentence the court did impose.

While Patterson was sentenced under the mandatory guidelines system that no longer exists post -Booker, we find that for the reasons explained hereinabove, our holding in United States v. Oliver, 397 F.3d 369 (6th Cir. 2005), is not implicated in this case. Neither is our holding in United States v. Barnett, 398 F.3d 516 (6th Cir. 2005) implicated here. The Barnett question — what would the sentencing court have done had it known that the guidelines were not mandatory — does not arise in this case because the court sentences the defendant to the statutory minimum sentence. It could not have gone any lower. Here, the guidelines calculation, in particular the firearm enhancement, results in Patterson’s being ineligible for the safety valve, and, even if that ineligibility were not automatic, Patterson did not demonstrate that he met the requirements for the safety valve. The latter determination is based on facts that the district court found at sentencing, as it was required to do under § 3553(f).

III.

Patterson also asserts that the district court’s use of the firearm to trigger a two-level enhancement under § 2Dl.l(b)(l) and to deny him the benefit of the safety valve under § 501.2(a) amounts to an unfair double counting. “The established rule in the Sixth Circuit is clear that impermissible double counting *995occurs when precisely the same aspect of a defendant’s conduct factors into his sentence in two separate ways.” United States v. Young, 266 F.3d 468, 485 (6th Cir. 2001) (internal quotations omitted). Patterson has cited to no cases in which, by factoring into the calculation of the sentence conduct giving rise to both a firearm enhancement and the denial of the safety valve, the district court engaged in double counting. On the contrary, the cases we have cited above stand for exactly the opposite proposition, i e. that conduct giving rise to a firearm enhancement prevents application of the safety valve. See, e.g., Johnson, 344 F.3d at 567. The double-counting principle is more properly meant to prevent multiple sentencing enhancements that factor the same conduct negatively into a defendant’s sentence more than once, and even then, we have held, “not all instances of double counting are impermissible.... [W]e allow double counting where it appears that Congress or the Sentencing Commission intended to attach multiple penalties to the same conduct.” United States v. Farrow, 198 F.3d 179, 194 (6th Cir. 1999). Here, the conduct that supported the increase of offense level under U.S.S.G. § 2Dl.l(b)(l) was the possession of a gun in connection with the offense of conviction. That conduct supported no other enhancement, and was further relevant to the sentence only to the extent that, because of the express terms of the safety valve statute, it prevented Patterson from obtaining a reduction of his sentence below the statutory minimum. Accordingly, we find no double counting here.

IV.

For the foregoing reasons, we AFFIRM the judgment of the district court.

concurring.

Because I believe our decision in United States v. Bolka, 355 F.3d 909 (6th Cir. 2004), is not inconsistent with United States v. Johnson, 344 F.3d 562 (6th Cir. 2003), I disagree with the majority’s decision to ignore our precedent in Bolka and therefore write separately.

The majority interprets Johnson as announcing a per se rule that a firearm enhancement always precludes safety-valve relief. The majority then holds that our decision in Bolka is not good law insofar as it states that a firearm enhancement may not always preclude safety-valve relief since the burden of proof for each finding is different. However, the majority’s interpretation of the decision in Johnson is incorrect. The Court in Johnson did not consider or decide whether the imposition of a firearm enhancement always precludes application of safety-valve relief. Rather, the Court, after discussing the facts surrounding the possession of the specific firearm at issue in that case, and noting the “great deference” granted to the district court’s determination that the defendant’s story regarding possession of the firearm was not credible, stated “[a]s we have held that the two-level enhancement applied pursuant to § 2Dl.l(b)(l) was properly applied to both defendants, both are ineligible for ‘safety-valve’ status.” Johnson, 344 F.3d at 567. This conclusion appears in one sentence at the end of the opinion without any legal analysis about the interplay of the two statutes. While one could read Johnson to announce a broad rule that any time a defendant received an enhancement under § 2Dl.l(b)(l) he is ineligible for safety valve relief, a more appropriate interpretation of the extensive discussion surrounding the defendant’s possession of the firearm followed by the brief discussion of the inappropriateness of safety-valve relief is that the Court made a fact-based determination that safety-valve relief was inappropriate in that case, rather than announcing a broad per se rule that safety-valve relief *996is never appropriate when an enhancement is imposed. This is the more reasonable construction since the Johnson Court does not engage in any analysis to create this per se rule, nor did it use terms that might imply such a rule such as “always” or “per se.” Cf. Bey v. Johnson, 407 F.3d 801, 806-07 (6th Cir. 2005). Rather, the language used implies reference back to the discussion of the facts considered by the district court and the deference granted to the district court’s credibility determinations to determine that the enhancement applied, not a per se rule that anytime an enhancement applies the safety-valve cannot apply. Furthermore, an in pari materia interpretation that reads Bolka and Johnson together is most appropriate since the majority’s interpretation would result in a intra-circuit conflict, a practice this Court should avoid when possible. United States v. Humphrey, 287 F.3d 422, 451 (6th Cir. 2002). (“Cases should be construed as to avoid intra-circuit conflicts, not to create them.”).

However, while I believe there may be a case wherein a defendant would be able to qualify for safety-valve relief while still receiving the firearms enhancement, I recognize that such circumstances are rare. I also agree that this is not such a case. The defendant admitted he had a firearm on his person at the time of his arrest. He also admitted that there were drugs and other drug paraphernalia in the vehicle in which he was arrested. These facts, combined with the district court’s determination that the defendant’s story regarding the firearm was not credible, are sufficient to preclude safety-valve relief. As such, I agree with the majority that the district

court did not err in refusing to apply the safety-valve in this case.