BIRCH, Circuit Judge:

We determine in this case whether the doctrine of collateral estoppel bars the government from prosecuting an individual for perjured testimony given by that individual as a defendant in a previous trial. The district court held that the government may prosecute the defendant for perjury because the jury, in reaching its verdict, did not necessarily find that the defendant’s statements were true. We AFFIRM.

I. BACKGROUND

Defendant-appellant, Clayton Carter, is a former member of the United States Coast Guard (“Coast Guard”). On the morning of August 6,1986, Carter and three other Coast Guard personnel, Loretta Santos, Kathleen Mahood, and Servando Iglesias, travelled with a civilian photographer to a point in or near Biscayne Bay aboard a Coast Guard vessel to retrieve duffel bags of cocaine floating in the water. During the return trip to the Coast Guard station at Miami Beach (the “Base”), Carter and Santos allegedly took four one-kilogram packages of cocaine from the duffel bags and hid them in air duets which led to the engine compartment below. *1534 Santos, Mahood, Iglesias, and Carter turned over the remaining cocaine to authorities upon their return to the Base.

Between 2:00 p.m. and 3:30 p.m. that afternoon, Carter, Santos, Mahood, and Iglesias, this time accompanied by a television news cameraman, allegedly departed from the Base on the same vessel to collect more drugs floating in the bay. During that trip, Carter and Santos supposedly went into the engine compartment, removed the cocaine hidden in the air ducts, and put it in a flight bag that they deposited at a local marina, where they ostensibly had stopped so either Iglesias or Mahood could use the restroom. Santos’s roommate then collected the flight bag from the marina.

In 1991, a federal grand jury indicted Carter, Iglesias, Mahood, and Santos on charges of possession with intent to distribute cocaine and conspiracy to possess cocaine in violation of 21 U.S.C. §§ 841(a)(1) and 846. Santos and Mahood pled guilty to the conspiracy charge. Carter and Iglesias were tried together. The jury acquitted both defendants on the possession charge and failed to reach verdicts on the conspiracy charge. Subsequently, Carter was reindicted for conspiracy as well as for perjury in violation of 18 U.S.C. § 1623 for testimony Carter gave at trial. After the court suppressed certain evidence, the government dropped the conspiracy charges and pursued the perjury charges solely.

Of the five counts of perjury brought against Carter, the magistrate judge recommended that three of the counts be dismissed on the ground of double jeopardy, and that two of the counts of perjury proceed. One of these two counts, Count III of the indictment, charged that Carter

knowingly, willfully, and contrary to his oath declared that he had only been on assignment with the boat crew consisting of Servando Iglesias, Loretta Santos and Kathleen Mahood, maybe one time, when in truth and in fact and as the defendant then and there knew, he had been on assignment with the boat crew consisting of Iglesias, Santos and Mahood on several occasions.

Rl-29-3 (emphasis added). The other count, Count IV, charged that Carter

knowingly, willfully, and contrary to his oath declared that in August 1986, he worked the 7:00 a.m. to 3:00 p.m. shift schedule, when in truth and in fact and as the defendant then and there knew, that in August 1986, he worked on a crew for straight 32 hour shifts.

Id. at 3-4. Carter objected to the magistrate judge’s supplemental report and recommendation as they related to Counts III and IV; the district court denied Carter’s objections and adopted the report and recommendation. 1 Carter appeals.

II. DISCUSSION

The denial of a pretrial motion to dismiss on the ground of double jeopardy is a final judgment that can be appealed to a circuit court of appeals. Abney v. United States, 431 U.S. 651, 662-63, 97 S.Ct. 2034, 2042, 52 L.Ed.2d 651 (1977); see 28 U.S.C. § 1291. Although acquitted of substantive criminal charges at trial, a defendant later may be tried for perjury for false statements made during that trial. See United States v. Williams, 341 U.S. 58, 62, 71 S.Ct. 595, 597, 95 L.Ed. 747 (1951) (“It would be of no service to the administration of justice to enlarge the conception of former jeopardy to afford a defendant immunity from prosecution for perjury while giving testimony in his own defense.”).

Carter, however, asserts that Counts III and IV of the perjury indictment should be dismissed because of the collateral estoppel element of the double jeopardy clause. It is well established that “the doctrine of collateral estoppel applies to criminal cases as part of the constitutional protection against double jeopardy.” United States v. Giarratano, 622 F.2d 153, 155 (5th Cir.1980); *1535 accord Ashe v. Swenson, 397 U.S. 436, 445-46, 90 S.Ct. 1189, 1195, 25 L.Ed.2d 469 (1970). Collateral estoppel “simply forbids the government from relitigating certain facts in order to establish the fact of the crime.” United States v. Mock, 604 F.2d 341, 344 (5th Cir.1979).

In order to successfully invoke collateral estoppel, a party must demonstrate: (1) that the issue in question was actually raised and litigated in the prior proceeding; (2) that the determination was a critical and necessary part of the final judgment in the earlier litigation; and (3) that the issue in the later proceeding is the same as that involved in the prior action. Collateral estoppel applies to “ultimate” as well as “evidentiary” facts.

Delap v. Dugger, 890 F.2d 285, 314 (11th Cir.1989) (citations omitted) (emphasis added), ce rt. denied, 496 U.S. 929, 110 S.Ct. 2628, 110 L.Ed.2d 648 (1990).

The parties do not dispute that the issues of whether Carter worked with this crew of Santos, Mahood and Iglesias previously, and whether Carter was a day or duty worker were addressed and litigated at trial. They also agree that the truth of these statements was in issue in the first proceeding as eviden-tiary facts. Because the jury returned a general verdict, we must determine by reviewing the record whether, in acquitting Carter of possession with intent to distribute, the jury necessarily concluded that he worked with the Santos, Mahood and Iglesias crew on only one prior occasion and worked until only 3:00 p.m. on August 6, 1986. 2

The necessary elements that must be proved to convict a person of violating 21 U.S.C. § 841(a)(1) for possession of cocaine with intent to distribute are: (1) knowing or willful (2) actual or constructive possession of the cocaine, and (3) an intent to distribute it. See United States v. Poole, 878 F.2d 1389, 1391 (11th Cir.1989) (per curiam). To acquit Carter, the jury had to find that the government did not prove one of the three elements beyond a reasonable doubt. Carter argues that, to acquit him, the jury necessarily found that he was not present on the second trip of that crew, when the cocaine was removed from the boat became his shift was over and he had gone home and because he had not worked with that crew previously.

This contention lacks merit. The evidence at trial against Carter consisted mainly of testimony by Santos and Mahood, who had entered into plea agreements with the government. Testimony showed that Santos and Mahood were good friends both at the time of the incident and thereafter, and that, prior to this incident, they had discussed the possibility of stealing cocaine. Both defendants’ attorneys questioned the credibility of Santos and Mahood’s testimony throughout the trial, and Carter’s attorney emphasized their lack of veracity in his closing argument. The defense suggested in particular that Santos had pled guilty and had agreed to testify to prevent even greater charges being brought against her.

Moreover, the strength of the other witnesses’ testimony was weakened by the six-year hiatus between the incident and the trial. There also were suggestions that no cocaine was ever stolen or hidden on the boat. 3 Carter testified that he could not have helped retrieve the cocaine from the air *1536 ducts because the cocaine was accessible only from the engine compartment which was not large enough to accommodate Santos and him simultaneously. The presence of a civilian on both excursions supported his argument that he lacked the opportunity to complete the crime.

Carter’s attorney also implied that Santos and Mahood concocted this story against Carter to gain revenge. Carter became a confidential informant for the Coast Guard and for the Federal Bureau of Investigation after Santos had left the Base in 1987. Carter, however, informed Coast Guard intelligence officers that Santos used cocaine while on duty and while underway on a boat. Carter also knew that the Coast Guard suspected Santos of larger involvement with illegal drug activities at the Base. He further provided intelligence officers with information regarding drug transactions on the Base involving Santos’s friends.

The jury may have acquitted Carter not because of his alibi, but because one of these defenses created a reasonable doubt as to one of the elements of the crime. 4 Consequently, we conclude that the statements that Carter had worked with this crew previously “one time maybe,” SR5-155-577, and that he worked only the day shift rather than the duty shift, were not decided necessarily by the jury in Carter’s favor. Accordingly, we affirm the district court’s conclusion that these two counts of perjury should not be dismissed.

III. CONCLUSION

Carter appealed the district court’s denial of his pretrial motion to dismiss perjury charges on the grounds of double jeopardy and collateral estoppel. If the statements charged as being false now were necessarily found by the jury to be true, then the charges as to those statements would be barred by double jeopardy. Because we conclude that, in reaching its verdict, the jury did not necessarily find those statements to be true, we AFFIRM.

. The government did not object to the dismissal of the other three counts.

. Where a previous judgment of acquittal was based upon a general verdict, as is usually the case, this approach requires a court to "examine the record of a prior proceeding, taking into account the pleadings, evidence, charge, and other relevant matter, and conclude whether a rational jury could have grounded its verdict upon an issue other than that which the defendant seeks to foreclose from consideration.” The inquiry "must be set in a practical frame and viewed with an eye to all the circumstances of the proceedings.”

Ashe, 397 U.S. at 444, 90 S.Ct. at 1194 (footnote omitted) (citation omitted).

. Although these suggestions were emphasized by Iglesias's counsel, he and Carter's counsel worked in tandem throughout the trial. Carter's counsel also made the inference that Santos and Mahood plotted to involve Carter. Moreover, the jury treated Iglesias and Carter similarly: both were acquitted of the possession count, and both received no verdict on the conspiracy count. It is highly unlikely that arguments made by either *1536 defendant were segregated by the jury in its deliberations.

. After the jury returned the verdict of not guilty on the possession charge and reported that it was unable to reach a verdict on the conspiracy charge, the district court questioned the jury concerning why it failed to reach a verdict on the conspiracy charge. While these answers do not address precisely why the jury acquitted Carter, the answers certainly show that they were not convinced specifically that Carter worked only days or that he did not work regularly with this crew. The district court questioned a juror regarding his thoughts on the case. The juror reported:

I would have liked to have more information. I think we all would have liked to have more information.

Because the bottom line was like, it was who is lying and who is not. Where was the concrete evidence? No mention of anything more — it was brought up just four kilos. Is it worth six years and the expense that the government — no, there had to be a lot more than [four], we assumed, but we don't know.... I mean no information, there was nothing to substantiate whether the man was working second shift. Was he there?

This was hard for us not having the evidence to say, well, you know, couldn't prove that, you know, from what they had to offer. It was like we had to take just the testimony of the witnesses, which I don’t think the government proved or had enough hard evidence.

SR8-157-798-99 (emphasis added). These reflections show only that the jury did not find conclusively either of the disputed facts.