Fredderick D. Jones was convicted in the district court of seven counts of distribution of cocaine base in violation of 21 U.S.C. Sec. 841(a)(1). He challenges his conviction on the ground that the evidence was legally insufficient to support his convictions. He also contests the district court's denial of his motion to suppress evidence as well as its denial of his motion for a mistrial. Finally, he also raises several challenges to the legality of his sentence. For the reasons set forth in the following opinion, we affirm the judgment of the district court.

* BACKGROUND

The charges against Mr. Jones arose out of an investigation conducted by the St. Clair County Sheriff's Department. Deputy Singleton of that department testified that, while operating as an undercover agent, he purchased, on seven occasions between August 2, 1993 and September 15, 1993, crack cocaine from Mr. Jones. Each transaction was witnessed by other law enforcement officers. In the final transaction, Deputy Singleton had used one fifty-dollar bill, two twenty-dollar bills, and one ten-dollar bill. The serial numbers of those bills had been recorded prior to the transaction.

After this final purchase, Captain Terrence Delaney of the St. Clair County Sheriff's Department applied for a warrant to search the house where the transactions had occurred. The application and affidavit for the search warrant listed the serial numbers of the bills used for the final drug purchase. It also recited that this currency was the object of the search. On the basis of this affidavit, a search warrant was authorized by a United States magistrate judge. Although the affidavit listed the serial numbers of each of the bills, the warrant itself simply described the property to be seized as "United States Currency."

On the same day, September 15, 1993, the warrant was executed. Approximately six officers of the St. Clair County Sheriff's Department conducted the search of the residence. These officers were under the supervision of Captain Delaney. Prior to the execution of the warrant, Captain Delaney held a meeting and instructed the officers that the warrant had been issued for specific currency only and that they were to seize no other property. He further ordered them to cease all searching once the currency was found. During the execution of the warrant, the members of the search team conducted simultaneously a search of three bedrooms. Captain Delaney acted as supervisor. When an officer located a quantity of currency, he brought it to Captain Delaney. The Captain then examined the currency and compared the serial numbers with the numbers he had listed on the application for the warrant. Once he determined that the numbers on the currency matched the numbers on the application, Captain Delaney ordered the officers to cease their search.

During the execution of the search warrant, the officers observed other items of evidence. However, in accordance with Captain Delaney's previous order, none of this evidence was seized. Captain Delaney then applied for a second search warrant which would permit the seizure of the evidence that had been found during the earlier search but had not been seized. This evidence included a file cabinet, crack cocaine, additional United States currency, a triple beam scale, two police scanners, four firearms, and a quantity of marijuana.

Mr. Jones was charged with seven counts of distributing cocaine base. He was also charged with single counts of possession with intent to distribute cocaine base, using or carrying a firearm during and in relation to a drug trafficking offense, and possession of a firearm by a felon. After a hearing, the district court denied the motion to suppress the evidence seized during the first search. At the trial, held January 18-20, 1994, Captain Delaney, Deputy Sheriff Singleton, and various expert witnesses testified. Another witness was Felicia Brown, a girlfriend of the defendant, who was present at the residence when the warrant was executed. She testified that, during the period she lived with Mr. Jones, he had sold drugs and she had witnessed the transactions. According to her testimony, he had sold crack cocaine to at least twenty people a day. She also testified that he would hold a gun behind his back when he answered the door of the residence and then would place the gun under a couch if he recognized the customer. She identified the weapon exhibited by the government as one that resembled the firearm that she had seen Mr. Jones possess at the residence.

At the end of trial, the jury began its deliberations. In the first hour of deliberation, one juror sent a note to the court complaining of a headache. The court instructed the jury to cease temporarily its deliberations and to have lunch. It then interviewed the juror who had sent the note. She explained that she had a headache caused by asthma and sinus problems. While she rested, the court and the attorneys discussed the available options. After lunch, the juror advised the court that she was feeling better and that she could continue with the deliberations. When the court informed her that it had decided that it would suspend deliberations for the remainder of the day to allow her to recuperate, the juror responded: "Well, I feel that we might as well just go on with it and get it over with, because I drank a pop. And it kind of helped." (Tr.Vol. III, p. 47). The court then denied Mr. Jones' motion for a mistrial and allowed the jury deliberations to proceed. The jury returned a verdict of guilty with respect to Counts I through VIII. The court, however, later determined that the verdict form on Count VIII was defective and therefore dismissed that count. The jury found Mr. Jones not guilty of the firearm counts.

At the sentencing proceeding, the district court determined that a total offense level of 28 was appropriate and that Mr. Jones' prior criminal history warranted a category of III. The court sentenced Mr. Jones to a term of 121 months' imprisonment.

We address first Mr. Jones' contentions with respect to the finding of guilt. His claim that the evidence submitted by the government was legally insufficient to support a finding of guilt need not detain us long. By bringing such a challenge, a defendant bears a "heavy burden." United States v. Scroggins, 939 F.2d 416, 421 (7th Cir.1991). The legal standard by which we measure such a claim is well established. We shall affirm the judgment of conviction if the evidence of record, taken in the light most favorable to the government, will support a rational determination of guilt beyond a reasonable doubt. United States v. Dortch, 5 F.3d 1056, 1065 (7th Cir.1993), cert. denied, --- U.S. ----, 114 S. Ct. 1077, 127 L. Ed. 2d 394 (1994). Mr. Jones' claim that the testimony of the undercover agent was inconsistent in some of its details and his claim that Felicia Brown's testimony was not believed by the jury merely invite us to review the credibility determinations of the jury. It was also for the jury to weigh the fact that Mr. Jones' statement was never reduced to writing.

We also note that the evidence supporting the conviction of Mr. Jones was substantial. The record shows that all seven drug transactions were observed by other officers, that the currency which Deputy Singleton used to purchase the cocaine on the seventh and last occasion was recovered from the defendant's residence, and that the defendant orally confessed to being a drug dealer. Mr. Jones' claim that the evidence of record does not support the jury's verdict is without merit.

Mr. Jones also presents two claims grounded in the Fourth Amendment. First, he submits that the first search warrant was overly broad because it described the object of the search as simply "United States currency, which is property that constitutes evidence of a criminal offense, in violation of Title 21, United States Code, Section 841(a)(1)." Second, he contends that the search, as executed, violated the Fourth Amendment because only the supervising officer, one of approximately six officers involved in the search, knew the serial numbers of the currency sought. Consequently, the other officers continued to search while the supervising officer checked the serial numbers on discovered bills. This procedure, he submits, extended the period of time in which the officers were free to rummage among the property in the residence and to identify other items of evidentiary value.

We turn first to the contention that the warrant was overbroad because it did not contain the serial numbers of the bills sought as evidence. In analyzing this claim, we begin with the well-established proposition that "[t]he proceeding by search warrant is a drastic one, and must be carefully circumscribed so as to prevent unauthorized invasions of the sanctity of a man's home and the privacies of life." Berger v. New York, 388 U.S. 41, 58, 87 S. Ct. 1873, 1883, 18 L. Ed. 2d 1040 (1967) (quotations and citations omitted). General warrants do not satisfy the requirement of the Fourth Amendment that the warrant contain a description of the place to be searched and the persons or things to be seized. U.S. Constitution amend. IV; see Dalia v. United States, 441 U.S. 238, 255, 99 S. Ct. 1682, 1692, 60 L. Ed. 2d 177 (1979). This particularity requirement protects persons against the government's indiscriminate rummaging through their property. See Coolidge v. New Hampshire, 403 U.S. 443, 467, 91 S. Ct. 2022, 2038-39, 29 L. Ed. 2d 564 (1971). Its roots are embedded deeply in the history of the Fourth Amendment. "Vivid in the memory of the newly independent Americans were those general warrants known as writs of assistance under which officers of the Crown had so bedeviled the colonists.... They were denounced by James Otis as 'the worst instrument of arbitrary power, the most destructive of English liberty, and the fundamental principles of law, that ever was found in an English law book,' because they placed 'the liberty of every man in the hands of every petty officer.' " Stanford v. Texas, 379 U.S. 476, 481, 85 S. Ct. 506, 510, 13 L. Ed. 2d 431 (1965). "The requirement that warrants shall particularly describe the things to be seized makes general searches under them impossible and prevents the seizure of one thing under a warrant describing another. As to what is to be taken, nothing is to be left to the discretion of the officer executing the warrant." Marron v. United States, 275 U.S. 192, 196, 48 S. Ct. 74, 76, 72 L. Ed. 231 (1927). "In practice, courts have therefore demanded that the executing officers be able to identify the things to be seized with reasonable certainty and that the warrant description must be as particular as circumstances permit." United States v. Brown, 832 F.2d 991, 996 (7th Cir.1987), cert. denied, 485 U.S. 908, 108 S. Ct. 1084, 99 L. Ed. 2d 243 (1988).

When the situation is evaluated in light of the purposes of the warrant requirement, we believe that the warrant in this case complied with the mandate of the Constitution that the items to be seized be described with particularity. "Although the fourth amendment requires that a search warrant describe the objects of the search with reasonable specificity, it need not be elaborately detailed." United States v. Somers, 950 F.2d 1279, 1285 (7th Cir.1991), cert. denied, 504 U.S. 917, 112 S. Ct. 1959, 118 L. Ed. 2d 561 (1992). "The level of specificity must be such ... that the officers executing the warrant are 'able to identify the things to be seized with reasonable certainty.' " United States v. Sleet, 54 F.3d 303, 307 n. 1 (7th Cir.1995) (quoting United States v. Spears, 965 F.2d 262, 277 (7th Cir.), cert. denied, --- U.S. ----, 113 S. Ct. 502, 121 L. Ed. 2d 438 (1992)). Here, the text of the warrant itself described the object of the search: "U.S. Currency." Although such generalized descriptions have often been deemed insufficient, see 2 Wayne R. LaFave, Search & Seizure Sec. 4.6(c) (2d ed. 1987), we have, in specific circumstances, upheld warrants authorizing the seizure of United States currency. Somers, 950 F.2d at 1285 (citing cases). However, we need not rest solely upon such a proposition today. The warrant incorporated the affidavit by reference. The affidavit submitted in support of this search warrant contained the serial numbers of the currency sought. Although the numbers were not repeated in the warrant, when the two documents are read together, it is apparent that the search was intended to uncover specific bills, the ones used to purchase the cocaine sold by Mr. Jones. Such supporting affidavits have been held capable of supplying by incorporation the particularity required by the Fourth Amendment.1 They perform the dual function of limiting the discretion of the officer executing the warrant and also of informing the person who is subjected to an intrusion of his privacy of the identity of the items that the officer is authorized to seize. See United States v. Hayes, 794 F.2d 1348, 1355 (9th Cir.1986), cert. denied, 479 U.S. 1086, 107 S. Ct. 1289, 94 L. Ed. 2d 146 (1987).

If the affidavit submitted in support of the warrant had been appended physically to the affidavit by the magistrate judge, our inquiry into this matter could end here. Although Mr. Jones' imprecise reference to this specific problem barely preserves the issue for appellate review, an ambiguity in the record requires that we deal with a related matter that bears on the issue of particularity. On this record, we cannot be sure that the affidavit submitted in support of the search was in fact appended to the warrant and was served along with the warrant. Although the warrant acknowledges the existence of the affidavit, it does not explicitly recite that the affidavit is incorporated by reference or that it was attached to the copy served upon execution.

The case law is not in agreement with respect to whether the affidavit supplying the requisite specificity must be appended physically to the warrant. See United States v. Towne, 997 F.2d 537, 547 n. 5 (9th Cir.1993) (collecting cases); see also 2 Wayne R. LaFave, Search & Seizure Sec. 4.6 (2d ed. Supp.1995). Although our own cases have been somewhat less than precise on the matter,2 it is clear that we have upheld a warrant against a challenge to its particularity when an affidavit attached to the warrant or incorporated into it provides the necessary specificity. This standard is the one that we expect to apply in our cases and, when these circumstances are absent, the burden to show that the existing circumstances were the functional equivalent is significant. We believe it is clear, however, that an artificial rigidity in this area would not be compatible with the purpose of the particularity requirement. The particularity requirement traditionally has been applied in a pragmatic matter designed both to protect the subject of the search from the abuses of a generalized search and, at the same time, to recognize realistically the needs of law enforcement authorities. Due regard for the practicalities of the situation always has been an integral part of adjudication of the particularity requirement. For instance, as we noted in Brown, 832 F.2d at 996, "[i]n practice, courts have ... demanded that the executing officers be able to identify the things to be seized with reasonable certainty and that the warrant description must be as particular as circumstances permit." Id. (emphasis supplied).3 More importantly, we recognized these pragmatic considerations in United States v. Nafzger, 965 F.2d 213 (7th Cir.1992). At issue in that case was a specific description of the place to be searched, a matter also addressed by the particularity requirement. In that case, we stated that the "particularity requirement is satisfied if 'the description is such that the officers with a search warrant can with reasonable effort ascertain and identify the place intended.' " 965 F.2d at 215 (quoting Steele v. United States, 267 U.S. 498, 503, 45 S. Ct. 414, 416, 69 L. Ed. 757 (1925)). After noting that particularity is normally shown on the face of the warrant or in an affidavit "properly incorporated" in the warrant, we commented that "in limited cases" the particularity could be supplied by "the executing officer's knowledge that there was a particular place to be searched, known to both him and the magistrate judge at the time the warrant was issued." Id. at 215 (citing United States v. Gahagan, 865 F.2d 1490, 1497-98 (6th Cir.), cert. denied, 492 U.S. 918, 109 S. Ct. 3242, 106 L. Ed. 2d 590 (1989)).

In this case, several factors militate in favor of our concluding that this warrant be considered as containing the requisite particularity. At the outset, we note that there is no serious doubt that the magistrate judge considered the affidavit in issuing the warrant. It is clear that he directed that the original of the affidavit be filed with the warrant. It is equally evident from the record that Captain Delaney, the officer in charge of conducting the search, had in his possession the serial numbers of the currency listed in that affidavit, that he limited the search to those items described in the warrant, and that he made a return to the magistrate that conformed to the warrant and affidavit. Under the circumstances presented here, therefore, reliance on the affidavit to supply the requisite specificity is compatible with the values protected by the Fourth Amendment.

We now turn to an examination of whether the search was conducted in a manner that comports with the reasonableness requirement of the Fourth Amendment. The officers were told that they were to search for specific United States currency. There is no suggestion that the officers searched in places where currency could not be found. Once it was verified that they had found the currency in question, the search stopped. Nothing else was seized at that time. The house was sealed, a second warrant obtained, and the other evidence against the defendant was then seized during a second search.

The search methodology employed by the supervising officer is not constitutionally infirm. The Fourth Amendment requires that the officers executing the warrant employ a methodology that is, in light of the values protected by the Fourth Amendment and the exigencies of the situation, a reasonable one.4 The officers no doubt had the obligation to take reasonable steps to minimize the intrusion necessary for the location of the items named in the warrant. The use of several officers certainly increased the chances of identifying the sought bills quickly and therefore minimized, at least temporally, the degree of intrusion caused by the execution of the warrant. With the advantage of hindsight, it is possible to suggest a better approach for the reconciliation of those competing interests. It might have been possible for the supervising officer to have furnished each of the officers with a copy of the serial numbers and therefore to have minimized further the time necessary to locate the currency that was the object of the search. We cannot say, however, that the failure to take that extra step was a lapse of constitutional dimension. Under the circumstances here, the supervisory officer's methodology cannot be called unreasonable. Moreover, Mr. Jones can claim no real harm here. The currency, which was the object of the search, was located in a file folder together with a quantity of crack cocaine. In addition, by the time of the discovery of the currency, the officers had apparently already observed, but not seized, other items of evidence. Whatever items were observed in the minimum time it took the officer who discovered the bills to check the numbers with his supervisor were cumulative in the subsequent determination of probable cause for the second warrant.

Within an hour after the jury had begun deliberations, Juror Hayes sent the court a note which read "My head hurts too badly. I can't think." The court ordered deliberations to cease and Juror Hayes was given the opportunity to rest. After consultation with counsel, the district court tentatively decided to recess further jury deliberations and to resume the next day. When Juror Hayes was informed of this decision, however, she stated: "Well, I feel that we might as well just go on with it and get it over with, because I drank a pop. And it kind of helped." Troubled by Juror Hayes' wish to "get it over with," the defendant moved for a mistrial. The district court denied the motion.

We review the denial of a mistrial under the abuse of discretion standard. United States v. Canino, 949 F.2d 928, 937 (7th Cir.1991), cert. denied, 504 U.S. 910, 112 S. Ct. 1940, 118 L. Ed. 2d 546 (1992). In deciding whether the district court abused its discretion, it is assumed that the trial judge was in the best position to evaluate the seriousness of the incident. Id. In this case, the court questioned the juror before allowing deliberations to resume: "Do you feel that you can do this and fulfill your duties, your oath as a juror to be fair to everyone in this case?" The juror answered affirmatively. Only then did the court allow deliberations to continue. We shall not second-guess the decision of the district court. The stated desire of Juror Hayes to "get it over with" might, as a purely semantic matter, indicate a lack of appreciation of the importance of her duty to give the evidence in the case careful and thorough consideration. But an equally plausible interpretation is possible. Choosing between these two interpretations required an estimation of a human situation by the district court that cannot be reproduced on the cold trial record before us. What the record does show is that the district court reached its conclusions only after noting carefully the options and carefully scrutinizing and assessing the commitment of the juror to live up to the obligations of her oath. Moreover, just as we shall not second-guess the determination of the district court, we shall not presume that the jury did not perform its duty. "[I]t must be assumed that the jury performed its duty." United States v. Fulk, 816 F.2d 1202, 1205 (7th Cir.1987) (citation omitted).

Mr. Jones next submits that Sec. 2D1.1(a)(3)5 of the United States Sentencing Guidelines is unconstitutional. The district court found that Mr. Jones' relevant conduct involved 7.7 grams of cocaine base. Under Sec. 2D1.1(a)(3) and (c), the base offense level for this quantity of cocaine base is 26. The base offense level for an identical quantity of cocaine powder, however, is only 12 under Sec. 2D1.1(a)(3) and (c). Mr. Jones claims that this disparity in sentencing violates his right to equal protection because the enhanced penalty for cocaine base has a disproportionate impact on African-Americans. He further submits that this disparity is irrational because no scientific evidence has established that cocaine base is any more dangerous than cocaine powder.

As Mr. Jones frankly recognizes, this court has already squarely addressed and rejected these arguments in United States v. Chandler, 996 F.2d 917, 918 (7th Cir.1993) (per curiam).6 We noted that there was no evidence that the Congress acted with discriminatory intent when it allowed this disparate sentencing scheme of Sec. 2D1.1(a)(3) to take effect. The court also determined that Sec. 2D1.1(a)(3) is related rationally to Congress' concern about the heightened addictiveness and dangerousness of cocaine base as compared to ordinary cocaine. Id. at 918 (citing United States v. Lawrence, 951 F.2d 751, 754-56 (7th Cir.1991)); see also United States v. Smith, 34 F.3d 514, 525 (7th Cir.1994) (rejecting Eighth Amendment argument based on disparate treatment of cocaine and cocaine base). Because Mr. Jones has offered no compelling reason for overturning Chandler here, the doctrines of stare decisis and precedent require that we adhere to the law of the circuit.

Mr. Jones also challenges the district court's decision to increase his base offense level by two levels under Sec. 2D1.1(b)(1) for possessing a firearm during the commission of the drug offenses for which he was convicted. The defendant contests this decision because the jury had found him not guilty of the two firearm possession-related charges for which he had been indicted.7 We believe, however, that the district court's decision is permitted by the law of the circuit.

First, it is clear that there is no automatic bar to the action taken by the district court. As we noted in United States v. Ewing, 979 F.2d 1234, 1237 (7th Cir.1992), an acquittal on a firearms charge does not bar the imposition of an enhanced sentence based on the same conduct. "Nothing in either the Guidelines or the Constitution prevents a judge from taking account of conduct in which the defendant engaged, whether or not an acquittal prevents the imposition of criminal penalties directly on that conduct." United States v. Welch, 945 F.2d 1378, 1385 (7th Cir.1991), cert. denied, 502 U.S. 1118, 112 S. Ct. 1235, 117 L. Ed. 2d 469 (1992) (quoting United States v. Fonner, 920 F.2d 1330, 1332 (7th Cir.1990)). In making this sentencing determination, the district court need be convinced only by a preponderance of the evidence that the defendant engaged in the enhancement-triggering conduct; by contrast, proof beyond a reasonable doubt is necessary to establish a criminal conviction. An acquittal "does not mean that the defendant didn't do it; it means that the prosecution failed to establish culpability beyond a reasonable doubt." Fonner, 920 F.2d at 1332.

We still must review for clear error the district court's factual finding that the defendant possessed a firearm in connection with these drug offenses. See United States v. Brown, 962 F.2d 560, 565 (7th Cir.1992). The district court had before it the testimony of Felicia Brown, a girlfriend of the defendant. She testified that, when the defendant sold drugs from the residence, he held a firearm behind his back as he answered the door. If he recognized the customer, he would place the weapon under a couch and then complete the transaction. Brown's testimony was corroborated by the recovery of a handgun from under the couch in question. Three other handguns were also seized from the residence. We cannot say that the district court committed clear error by concluding that a preponderance of the evidence supported the finding that the defendant did use a firearm in connection with his drug trafficking activities.

The district court committed no reversible error with respect to the adjudication of guilt or the imposition of sentence. Accordingly, the judgment of the district court is affirmed.

AFFIRMED.