HOLLOWAY, Circuit Judge.

After defendant-appellant Brandon Smith's motions for a judgment of acquittal on a charge under 18 U.S.C. § 924(c)(1) were denied, Smith was convicted on one count of possession of cocaine base with intent to distribute, and on one count under Section(s) 924(c)(1) of using or carrying a firearm during and in relation to a drug trafficking offense. A charge of conspiracy to possess cocaine base with intent to distribute was dismissed by the trial judge at the close of the prosecution's case. United States v. Smith, 857 F. Supp. 1466, 1467 (D. Kan. 1994). On his direct appeal we affirmed the convictions. United States v. Smith, 63 F.3d 956 (1995), vacated, 116 S.Ct. 900 (1996).

Smith petitioned the Supreme Court for certiorari. On February 20, 1996, the Court granted the writ, vacated the judgment and remanded the case to us for reconsideration in light of Bailey v. United States, 116 S.Ct. 501 (1995). We requested and received supplemental briefs from the parties on the application of Bailey, which have been considered. We now reverse the district court's judgment of conviction on the firearms count, the conviction and sentence for possession of cocaine base with intent to distribute remaining undisturbed.

I

Smith was arrested during the execution of a search warrant at his residence. His cocaine conviction was based on evidence of cocaine base seized during the execution of the search warrant, and the firearms conviction was based on evidence of weapons found during the search, including a pistol which was found in plain view on a dresser in the bedroom where Smith was when the police entered the residence. Smith admitted at trial that he owned that pistol and two others which had been found in other rooms of his house. Smith, 63 F.3d at 959-60.

Prior to Bailey we had employed a broad definition of the term "uses" in section 924(c)(1). See Smith, 63 F.3d at 964-65. The Court in Bailey held that the term must be given a narrower construction. In response to the Court's holding, the government has conceded that the evidence in this case was insufficient to support a conviction for use of a firearm. In its brief in the Supreme Court in response to the petition for certiorari in this case, the government stated that under the standard for proof of "uses" adopted in Bailey, as to Brandon Smith "the evidence was insufficient to support petitioner's conviction for `use' under Section 924(c)(1)." Brief for the United States at 12. The concession is also made in the Memorandum Brief of Appellee at 7, filed April 19, 1996, with this court.

II

The government argues, however, that the evidence was sufficient to support a conviction for carrying a firearm in relation to the drug trafficking offense and urges that we therefore reaffirm Smith's conviction on the firearms count on that basis. We conclude that we may not do so. We are convinced that the evidence at trial was not sufficient to support a conclusion that Smith carried a firearm during and in relation to his drug trafficking offense. Thus the Section(s) 924(c)(1) conviction must be reversed and, because on this record double jeopardy principles bar a retrial for the government to attempt to prove a charge under the carrying prong of Section(s) 924(c)(1), no new trial may be had on the firearms charge.

The indictment charged Smith in the disjunctive, alleging that he "did knowingly use or carry firearms. . . ." I R. Doc. 1 at 1. The instructions given on the firearms count were similarly worded in the disjunctive, Instructions 17 18, id. at Doc. 83, and they defined the offense as follows:

In determining whether . . . the defendant used or carried a firearm, you may consider all of the factors received in evidence in the case including the nature of the underlying crime of drug trafficking alleged, the proximity of the defendant to the firearms in question, the usefulness of the firearms to the crime alleged, and the circumstances surrounding the presence of the firearms.

A defendant "uses" a firearm when it (1) is readily accessible, (2) is an integral part of the criminal undertaking, and (3) increases the likelihood of success for that undertaking. The government is not required to show that a defendant actually displayed or fired the weapon to prove "use." However, you must be convinced beyond a reasonable doubt that the firearm played a role in or facilitated the commission of the drug offense charged.

Id., Instruction 20. As we have noted above, it is clear that the definition of "uses" in the above instruction, although in accordance with our case law at the time, is incorrect under Bailey. See United States v. Spring, ___ F.3d ___, 1996 WL 148539, at *13 (10th Cir. 1996).

When a defendant is charged in the disjunctive and one charge is unsupported by any evidence whatsoever, a conviction may be affirmed on the assumption that the jury rejected the "factually insufficient theory" and convicted on the alternative ground for which the evidence was sufficient. United States v. Pace, 981 F.2d 1123, 1130 (10th Cir. 1992) (citing and quoting Griffin v. United States, 502 U.S. 46, 59 (1991), and United States v. Townsend, 924 F.2d 1385, 1414 (7th Cir. 1991)), cert. denied sub nom. Leonard v. United States, 507 U.S. 966 (1993); accord United States v. Linn, 31 F.3d 987, 990-91 (10th Cir. 1994). In Pace, however, we adopted the reasoning of Townsend, which had been cited with approval in Griffin, recognizing "a distinction between legal and factual sufficiency." 981 F.2d at 1130. Where, as here, the evidence was legally insufficient to prove the "use" of a firearm, because of the change in the legal definition announced in Bailey, we cannot assume that the jury did not convict on this legally erroneous basis, premised on the invalid instruction on "uses." See United States v. Self, 2 F.3d 1071, 1092-94 (10th Cir. 1993).

As Justice Scalia has observed:

Jurors are not generally equipped to determine whether a particular theory of conviction submitted to them is contrary to law — whether, for example, the action in question is protected by the Constitution, is time barred, or fails to come within the statutory definition of the crime. When, therefore, jurors have been left the option of relying upon a legally inadequate theory, there is no reason to think that their own intelligence and expertise will save them from that error. Quite the opposite is true, however, when they have been left the option of relying upon a factually inadequate theory, since jurors are well equipped to analyze the evidence. . . .

Griffin, 502 U.S. at 59 (first emphasis added).

Therefore, even if the evidence that Smith "carried" the firearm were sufficient, we could not allow his Section(s) 924(c)(1) conviction to stand on that basis because we have no assurance that the jury did not convict on the legally insufficient evidence and erroneous instruction regarding use of the firearm.

We reached this same conclusion in Spring. Here, as in Spring, the instruction given to the jury included a definition of "use" which is incorrect under Bailey and drew no distinction between "use" and "carry." Accordingly, Smith's conviction on the firearms count must be reversed.

III

The question then arises whether the evidence would have been sufficient to support a conviction for carrying a firearm under a proper instruction. If so, then we can remand for a new trial without violating double jeopardy principles. United States v. Wacker, 72 F.3d 1453, 1464-65 (10th Cir. 1995). However, if the evidence was insufficient so that a directed verdict of acquittal should have been entered, remand would violate the Double Jeopardy Clause. Id. (citing Burks v. United States, 437 U.S. 1 (1978)).

In Spring we concluded that Bailey "`provides some guidance regarding the correct application of the "carry" prong of section 924(c)(1).'" ___ F.3d at ___, 1996 WL 148539, at *15 (quoting United States v. Riascos-Suarez, 73 F.3d 616, 623 (6th Cir. 1996)). We said that Bailey suggests that "neither storage nor possession of a gun, without more, satisfies the `carry' prong of Section(s) 924(c)(1)." Id. We noted that our previous definition of the "carrying" prong required two elements: "`possession of the weapon through the exercise of dominion or control; and transportation of the weapon.'" Id. at *16 (quoting United States v. Martinez, 912 F.2d 419, 420 (10th Cir. 1990)).

The difficulty here is that the government points us to no evidence that this weapon was transported by defendant Smith during and in relation to the drug trafficking crime. The government relies on Smith's post-arrest statement that he possessed the guns for protection of the drugs, a recorded statement which the jury heard at trial. Smith, 63 F.3d at 965. From this premise, the government contends that Smith admitted that he "placed (carried and set down) the firearms to protect the drugs. . . ." Memorandum Brief of Appellee at 9. Thus, the government invites us to assume that at some unknown time during and in relation to the drug trafficking crime, Smith moved the weapon from some unknown previous location to the dresser where it was found. There is no evidence supporting such an inference. Our record shows that there were ten adults (and one infant) in the house when the police entered. In the bedroom where a loaded pistol was found, defendant's girlfriend and her infant were located when the search began. And a number of footsteps had been heard in the house before the officers entered. 63 F.3d at 959. Hence we can only speculate whether defendant Smith, or any one of the several other persons in the house, during and in relation to the drug trafficking offense, moved the firearms or placed them where they were found during the search.

We cannot rest a conviction on mere suspicion. E.g., United States v. Garcia-Emanuel, 14 F.3d 1469, 1472 (10th Cir. 1994) ("`the evidence presented to support the conviction must be substantial; that is, it must do more than raise a mere suspicion of guilt.'" (quoting United States v. Sanders, 928 F.2d 940, 944 (10th Cir.), cert. denied, 502 U.S. 845 (1991))). We hold that the absence of evidence to support a finding that Smith carried the firearms, or caused them to be carried, during and in relation to his drug trafficking crime, is fatal to his conviction under the carrying prong of Section(s) 924(c)(1).

Accordingly, we REVERSE Smith's conviction under 18 U.S.C. § 924(c)(1) on Count III, and REMAND with directions that the conviction and sentence thereon be set aside.