#### UNITED STATES of America, Plaintiff-Appellee, v. Leonard LLOYD (92-2106); Shawn Huffman (92-2108); Darryl Little (92-2146); and Mario Taylor (92-2175), Defendants-Appellants.

Nos. 92-2106, 92-2108, 92-2146 and 92-2175.

United States Court of Appeals, Sixth Circuit.

Argued Sept. 21, 1993.

Decided Oct. 29, 1993 *.

*1202Jennifer J. Peregord, Office of U.S. Atty., Detroit, MI (argued and briefed), for U.S.

Edward Wishnow, Southfield, MI (argued and briefed), for Leonard Lloyd.

Shawn Huffman, pro se.

F. Randall Karfonta, Mogill, Posner & Cohen, Detroit, MI (argued and briefed), for Shawn Huffman.

Kenneth R. Sasse, Detroit, MI (argued and briefed), for Darryl Little.

David I. Goldstein, Ann Arbor, MI (argued and briefed), for Mario Taylor.

Before: KENNEDY and RYAN, Circuit Judges; and BROWN, Senior Circuit Judge.

*

 This decision was originally issued as an "unpublished decision" filed on October 29, 1993. On November 18, 1993, the court designated the opinion as one recommended for full-text publication.

RYAN, Circuit Judge.

In this consolidated criminal case, the defendants, Leonard Lloyd, Shawn Huffman, Darryl Little, and Mario Taylor, appeal their conviction by a jury on multiple charges arising from a large drug distribution conspiracy. The defendants, separately and in various combinations, raise a number of challenges to their judgments of conviction and sentences. Finding the defendants’ arguments with regard to their convictions to be without merit, we affirm each of their judgments for reasons we shall fully develop. We also affirm the sentences of defendants Lloyd, Huffman, and Taylor. Because Little’s sentence, however, was grounded in part on a mistaken conclusion of law, we vacate and remand for resentencing.

I.

A. The Indictment

The defendants, along with thirteen others, were charged in a February 1991 indictment with a variety of drug and firearm crimes. The case originally proceeded to trial against these four defendants in December 1991, and the outcome was a jury deadlock on all but five counts. Taylor was acquitted on four counts, including the overarching conspiracy count and two counts of aiding and abetting the distribution of cocaine, and Lloyd was acquitted on one count of possession of cocaine with intent to deliver.

The government again prosecuted the same four defendants in April 1992, and that is the trial from which this appeal is taken. The following summaries represent the counts with which the defendants were charged in the Second Amended Superseding Indictment (Redacted) submitted to the jury.

Little was charged with six counts: conspiracy to possess cocaine and crack with intent to distribute, and to distribute cocaine *1203and crack, in violation of 21 U.S.C. §§ 846 & 841 (count 1); possession of cocaine within 1000 feet of a school with intent to distribute, and aiding and abetting thereof, in violation of 21 U.S.C. §§ 841 & 845a(a), 18 U.S.C. § 2 (count 2, relating to events of November 23, 1988); use and carrying of firearms during drug trafficking, and aiding and abetting thereof, in violation of 18 U.S.C. §§ 924(c)(1) & 2 (counts 3 and 6, relating to events of November 23, 1988, and June 30, 1989, respectively); being a felon in possession of firearms, in violation of 18 U.S.C. § 922(g)(1) (count 4, relating to events of November 23, 1988); and possession with intent to distribute cocaine, in violation of 21 U.S.C. § 841(a)(1) (count 8, relating to events of February 20, 1990).

Lloyd was charged with five counts: the conspiracy; distribution of crack within 1000 feet of a school, in violation of 21 U.S.C. § 860 (counts 11 and 12, relating to events of February 26 and 27, 1991, respectively); use and carrying of a firearm during drug trafficking, in violation of 18 U.S.C. § 924 (count 13, relating to events of February 27, 1991); and possession of crack with intent to distribute, in violation of 21 U.S.C. § 841(a) (count 17, relating to events of March 27, 1991).

Huffman was also charged with five counts: the conspiracy; the possession with intent to distribute described in count 2; the two section 924(c)(1) violations described in counts 3 and 6; and possession of false identification documents, in violation of 18 U.S.C. § 1028 (count 16, relating to events of February 28, 1991).

Taylor was charged with four counts: distribution of crack, in violation of 21 U.S.C. § 841(a)(1) (count 9, relating to events of August 25, 1990); use and carrying of firearms during drug trafficking, in violation of 18 U.S.C. § 924(c)(1) (count 10, relating to events of August 25, 1990); being a felon in possession of a firearm, in violation of 18 U.S.C. § 922(g)(1) (count 14, relating to events of February 28, 1991); and assaulting or impeding a federal agent, in violation of 18 U.S.C. § 111 (count 15, relating to events of February 28, 1991).

B. Factual Background1

This saga’s inception was in a November 23, 1988, search by Detroit police of the two-family residence located at 12122/12124 Ap-poline owned by Darryl Little.2 After receiving a report on November 22 that a man was being held against his will at 12122 Appoline, the lower-level apartment, the police arrived and encountered Little, who answered the door and permitted them to enter. Little refused the police access, however, to the upper-level apartment, and after surveying the largely empty lower apartment, the police left. Shortly after midnight on November 23, the police received another report about a man being shot and held against his will, but this time the address given was on Kentucky Street. At the Kentucky Street residence, the woman who answered the door told the police that she had made the call, and that she believed her brother had been shot and was being held against his will at the Appoline residence.

Four officers then proceeded to the Appo-line residence, where, a few minutes after they identified themselves as Detroit police officers, the door was again opened by Little. The police told Little that they were there to check for a person who had been shot. During this explanation, all four officers had their guns drawn, but the weapons were not pointed at Little, and the officers made no threats. Little told them that “there’d been officers out there earlier that day, and they had been inside and they didn’t find anything, and if we’d like, we could come in and look ourselves.” Little appeared to have been drinking, but did not appear frightened. After he allowed the police to enter the house, they “followed him up to the second story.” Little then opened the door to the upstairs apartment, and the police entered.

*1204The officers found several people upstairs, some of whom were playing video games, and ordered everyone into the dining room in order to contain them while they continued to talk to Little. Inside the front door, the officers saw a rifle leaning against a doorway in the hall. While unloading the weapon, one officer observed a large stack of cash and a clear plastic bag of what appeared to be cocaine in an adjoining bedroom. That same officer then saw a woman exit a back bedroom; after securing her in the dining room, he entered the bedroom to secure it, and there observed more cocaine, as well as drug paraphernalia. In addition, cocaine was found in a bowl under a bathroom sink, and a coffee table had a white residue of cocaine across the top.

After obtaining a search warrant for the Appoline residence, police seized approximately 1000 grams of cocaine, 226.16 grams of crack, $11,154 in cash, and nine rifles and handguns. A piece of jewelry monogrammed with one of Huffman’s multiple aliases was also seized. Scattered about the house were drug paraphernalia, scales, and kilo wrappers for cocaine, as well as baking soda, quinine, lactose, and small Ziploc bags, all of which led police to conclude that the residents of Appoline were processing and selling cocaine. One of the firearms, a Colt AR-15 semiautomatic rifle, contained a latent fingerprint of Huffman’s right ring finger. Little and Huffman were arrested.3

Little signed a statement agreeing that he had consented to a search of the upstairs premises for the purpose of looking for the individual who had allegedly been shot. He then told the officer who was processing him, “Alls I know is they won’t find my prints on nothin’.” Little also told the supervisor who had ordered the search warrant that the money the police seized was “chump change,” and that he had “sufficient resources to beat this case in any court, and this was no big deal to him, just a nuisance.”

Officers4 conducted surveillance at the Ap-poline residence between early and mid-December 1988 because, based on the November 23 search, they believed Appoline served as a major narcotics distribution center. The surveillance confirmed their belief that the individuals at Appoline were involved in an ongoing narcotics enterprise. They observed, on multiple occasions, “cars pulling up to the location, people running in and out within just a matter of moments, carrying bags in and out, and then driving away.” They observed “[fjoot traffic going to the location, ... people entering, staying a very short period of time, and leaving.” The investigators would often “follow! ] cars away from the Appoline address where they met other cars ... a short distance away and exchanged bags.” Then, “after an exchange, people would go back to the Appoline address.” The investigators observed Little and Huffman at the Appoline residence many times, engaging in what appeared to be drug sales. On one occasion, they observed a parking lot exchange, and when the courier returned to Appoline, Little “came out on the porch of th[e] upper level armed with a long gun.”

The officers obtained a second search warrant for Appoline, again searching the house on December 20, 1988. On that occasion, Lloyd was there, and the officers observed him throwing cocaine in the fireplace as they entered. They managed to seize the cocaine before it was burnt, and seized large amounts of cash that had been on Lloyd’s person. They also found drug paraphernalia, including scales, throughout the house.5

*1205The investigators next conducted surveillance of a residence on Patton Street in Detroit during June 1989. Over the course of a single day, they obseived seven or eight people go to the house, stay for a brief period, and then leave. They could occasionally see people making exchanges at the door before leaving. Little’s BMW automobile was parked in front of the house during this period.

The investigators attempted to make an undercover buy at the Patton Street residence on June 21. An officer went to the house and asked for “Tweed,” which was one of Little’s aliases, and Little came to the door. The officer said to Little, “Let me get one,” to indicate that he wanted to buy one rock of crack. In response, Little ordered the officer off the porch. The officer was able to look through the screen door, however, and saw a person handling a clear plastic bag containing what appeared to be rocks of crack.

On June 29, another undercover officer attempted to make a buy at Patton, and this time was successful. He bought three rocks of crack, for which he paid $25 using prerecorded bills.

The following day, the investigators obtained a search warrant. Prior to executing the warrant, an officer conducting surveillance observed Little arrive at the house in his BMW, and open the door of the house with a key. That officer alerted his supervisor, who told him to immediately prepare to conduct a raid. He left Patton Street to put on his raid gear, and returned within a few minutes with the other officers — but by then, Little had left.

They nonetheless raided the house. Five men were there, including Huffman. Seized were a .22-caliber Calico rifle, a 9-millimeter automatic pistol, more than $15,000 in cash, and some drug paraphernalia, including scales, but no drugs. Among the cash that was discovered, bundled together in a shoebox hidden in a closet, was the money that had been used to make the undercover purchase the previous day. The pistol was found in the same room as the cash, about eight feet away, hidden between the mattress and box springs of a bed. The rifle was found in another bedroom that faced the street corner. There was also a box of ammunition sitting on the windowsill of that room.

After the house had been secured during the raid, one officer left in order to secure the cars in the driveway. While outside, he “observed Mr. Little drive back up to the location. [They] made eye contact, and [Little] sped off at a high rate of speed.”

About six months later, on December 12, 1989, Michigan state police officers engaging in a routine traffic patrol in Detroit observed a black BMW belonging to Darryl Little travelling at a high rate of speed at 3:00 a.m. The police pursued the car, and stopped it near the interstate highway. All four individuals in the car put their hands up as the officers approached. One officer approached from each side of the car, and the officer at the driver’s side asked the driver, who was later identified as Little, to roll down the window. Using his flashlight, the officer saw a semi-automatic handgun on the armrest between Little and the front seat passenger, later identified as Huffman, and a rifle in the back seat. The officer instructed Little not to move, and as he approached “the driver’s door to open it, ... the driver, with his hands up, looked at [the officer], and he just stepped on the accelerator and took off.” The police then returned to their car and, using their sirens and lights, pursued the BMW. As they drove, the police saw “objects coming out of the vehicle and hitting the ground, and they were making sparks.” They lost the BMW after following it for about six miles, and then returned to retrieve the objects that had been thrown out of the car. They recovered a broken Calico .22 long semi-automatic rifle in the area where they had seen the objects thrown, but found nothing else.

The police then went to Little’s house on Appoline, and a block away, discovered the BMW with four occupants leaving the car. One officer got out of the patrol car and identified himself, and all four occupants then began running. Little and Huffman were both apprehended and arrested within a few blocks; both gave false names to the police.

*1206The next phase of the investigation involved surveillance of a house on Promenade Street. In December 1989, two undercover officers, working with two unwitting informants,6 purchased $1,200 worth of crack from someone at the Promenade address. One of the officers then returned to the house in February 1990, without the unwit-tings, to attempt to buy more crack. An unidentified man told the officer that although they had cocaine at the house, they could not sell him any drugs because their cocaine had not yet been “rocked up.”

The investigators obtained a search warrant and raided Promenade on February 20. No one was there, but they found a card table covered with cocaine residue and crumbs, and also found scales. The house was sparsely furnished, with only a television, card table, and couch, which led the officers to conclude that the residence was a “cook-distribution-type house.” Also confiscated were phone bills addressed to the Promenade residence in the name of Little’s girlfriend,7 as well as a cellular phone bill made out to one of Little’s aliases.

Simultaneously with the investigation of the Promenade residence, the conspiracy extended its distribution of drugs to environs outside of Detroit. At trial, testimony regarding this period was mainly elicited from a man named Anthony Holt who was a longtime friend of Lloyd, and who had lived and sold cocaine with Lloyd beginning in 1989.

In fall 1989, Lloyd and Holt travelled to Wadesboro, North Carolina, a small town of about 1000, in order to attend Lloyd’s mother’s funeral. Little went with them, as Lloyd’s mother was his aunt. They stayed at Little’s father’s house in Wadesboro for about four days, where they first met a local resident known as Fat Cat. All three then returned to Detroit, but went back to Wades-boro a few weeks later in order to attend the funeral of Little’s and Lloyd’s grandmother. On this visit, the three had a conversation with Fat Cat, and learned that Wadesboro residents, though familiar with cocaine, were ignorant of crack.

Lloyd and Holt returned to Wadesboro yet again in October 1989, in order to put a headstone on Lloyd’s mother’s grave. On that trip, Lloyd told Holt “that there was a killing to be made” in drug trafficking in Wadesboro. They therefore gave free samples of crack to Fat Cat, and, in the words of Holt, “the next thing you know, boom, business starts.” But Lloyd and Holt again did not stay long in Wadesboro before returning to Detroit. In early 1990, however, Holt overheard Little talking about selling crack in Wadesboro, and volunteered to go. Holt thus went by himself to Wadesboro and, at Little’s suggestion, lived in Little’s father’s house and began selling crack. Holt returned on at least one occasion to Lloyd’s house in Detroit, where Little gave him packages of crack to take back down to Wades-boro. Little also contacted Holt periodically by phone in Wadesboro to inquire after business, and sometimes visited Wadesboro.8 At Little’s instruction, Holt regularly wired money from the Wadesboro Western Union to a third individual, in order to reimburse Little for the crack that Little supplied.

Two Western Union representatives testified at trial about the substantial increase in wire transfer business from the Wadesboro office beginning in December 1989. One witness identified Little, Lloyd, and Huffman as people who had been responsible for, on multiple occasions, sending cash from Wadesboro to various addressees in Detroit.9 In February 1990, investigators observed Little and his girlfriend arrive at a Western Union office in Detroit, where Little’s girlfriend entered and picked up a money wire from Holt *1207in North Carolina while Little waited in the car.

Also in February 1990, the Wadesboro sheriffs office received reports from unspecified sources that cocaine was being sold from Little’s father’s house. A search warrant was executed at the house on March 3, 1990. Little and Holt, as well as others, were found in the house. The officers confiscated 117 grams of cocaine, approximately $3,000 in cash, three firearms, and narcotics paraphernalia. Also found was an invoice for cable installation at the house, which showed Lloyd, billed at his Detroit address, as the subscriber.

Following the events in Wadesboro, two undercover officers arranged to make a cocaine purchase from Shawn Huffrnan’s brother Darren10 in the area of Detroit’s 30th Street in April 1990. During the transaction, in which the officers purchased an ounce of crack, they received a phone call on their mobile phone from Mario Taylor. Identifying himself as “Boo,” Taylor asked only if the transaction were satisfactory, and indicated that he had been the source.

A few days later, the same officers arranged another transaction with Darren Huffman. Darren joined them in their parked car, and moments later, another car pulled up alongside. Mario Taylor’s brother Keenan11 got out of the caí-, and the officers could see that he had a gun tucked in his waistband. Mario Taylor was standing across the street during the transaction, apparently serving as a lookout. The transaction was completed despite the presence of the Taylors, and the officers paid $2,000 for two ounces of crack.12

Throughout the summer, these two officers continued buying progressively larger amounts of cocaine in the general vicinity of 30th Street, attempting to move up the chain of the narcotics conspiracy. Then, on August 25, 1990, one officer called the number that he had been given as a source for the buys, and Mario Taylor answered, again identifying himself as Boo. Taylor directed him to a house on 24th Street, where the officer stood in line at the back door to make his purchase. When he eventually entered the house, he was greeted by Taylor. Two men flanked Taylor, one of whom pointed a gun at the officer; according to the officer, Taylor then “advised him that [the undercover officer] was OK, that ... [he] had been buying cocaine from them.-...” The officer then purchased three-sixteenths of an ounce of cocaine for $270.

The 24th Street residence was raided in October 1990. The police seized seven small packages of crack, individually wrapped in Ziploc baggies, and $155 in cash.

The final major phase of this investigation involved a house on Strathmoor Street in Detroit, owned by Lloyd. Lloyd sold cocaine from the house beginning in at least spring 1989. Little was responsible for “cooking” powdered cocaine into crack rocks at the Strathmoor address, and did so a couple of times per week. According to a witness who had lived at the house for several months, Lloyd said that he got the crack from his cousin, apparently meaning Little.

On February 26, 1991, an undercover officer went to Strathmoor and purchased one-quarter ounce of crack for $200 from Lloyd. The officer returned on February 27 in order to purchase an additional quarter ounce. On that occasion, after entering the house, the officer “realized that Mr. Lloyd was aimed with a chrome-plated three fifty-seven revolver” that he held in his hand throughout the entire transaction. “Mr. Lloyd ... indicated that the reason that he had the firearm was he had been told that there were two men in the area who were robbing certain narcotic traffickers.... [H]e felt that [the officer] fit th[e] description and had that firearm for his protection.”

*1208Agents returned to the house on February 28 in order to execute a federal search warrant. They found a Winchester .12 gauge pump-action shotgun in an upstairs closet, but no drugs, and neither Lloyd nor the .357 were in the house at the time.

Also on the morning of February 28, police were conducting surveillance at the Appoline residence. They observed Huffman enter the house using a key, and exit ten minutes later. As Huffman was pulling out of the driveway, the police stopped him and presented a warrant for his arrest. He told them that his name was Shane Tillman, and showed three pieces of false identification — a Michigan driver’s license, a U.S. identification card, and a social security card — all showing his picture and the name of Shane Tillman.

Also on February 28, three ATF agents were responsible for executing arrest warrants on Mario and Keenan Taylor. All three agents were dressed in their raid gear, which clearly indicated “ATF” in several places. The agents followed the Taylors, who were in a car driven by Mario, but as they approached the interstate, the agent who was driving turned on the “bubble light” on his dashboard. They continued following the Taylors for about half a block, and as Mario made a left-hand turn onto the service drive, the agent pulled parallel to them and turned his siren on for three or four seconds. The other two agents motioned for Mario to pull over, and Mario and his brother raised their hands in the air and stopped at a red light. When the light turned green, the agent accelerated quickly in order to pass and cut the Taylors off, but Mario accelerated and turned his wheel, intentionally ramming the side of the agents’ car. The agent immediately turned his siren on, but Mario drove off. Mario stopped, however, within a few blocks.

As the agents approached the car to make the arrest, they saw a .22 caliber Derringer revolver on the floor of the car between the driver’s seat and the pedals. The gun was loaded. After he was handcuffed, Mario— who had been uncooperative ánd resistant— “started yelling and looked up and said, I can hurt myself more than you can possibly hurt me, and started banging his head off of the trunk of his car” a total of seven or eight times. Mario also screamed at the agents, calling them “agents of Satan.”

Little was arrested in March 1991 at the Patton residence. Lloyd was arrested in March 1991 after being stopped for a traffic violation, and was in possession of eleven grams of crack, packaged for resale, at the time.

All of the defendants were convicted on all of the counts with which they were charged, and all filed timely appeals.

II.

A. Motions to Suppress

Prior to the first trial, Little made a motion to suppress the evidence seized on November 23 at the Appoline residence, essentially arguing that he had been coerced into allowing the officers to search his house. The district court denied the motion, and specifically noted that

> [t]he testimony of the defendant is totally contradictory and incredible, particularly in his attempts to overcome his previous written, initialed, and signed statement, and deny the fact that he had consented to the officers’ entry into the house.

> The argument that he was coerced in any way will not hold water. He was upstairs, apparently, with armaments of his own, as well as a number of other armaments, when he saw fit to come downstairs and let the officers in, confident in his ability to manipulate the legal system, apparently, as he says he had success in doing in the past.

Little then renewed his motion, in which Huffman joined, prior to the second trial. On that occasion, the defendants reiterated the arguments initially made, and also argued that an earlier state court proceeding granting the motion to suppress should be considered by the district court as “very compelling” — specifically noting, however, that they “realize[d] [the state court ruling] is in no way binding on [the federal] Court.” The court again denied the motion to suppress, although without specifically respond*1209ing to or rebutting the state judge’s conclusions.

On appeal, Little and Huffman again contend that the government failed to establish that the November 23 search was consensual.13 They argue that Little gave the police permission to search only the unused lower apartment, but that the consent to the search of the upper apartment was coerced.14

“It is ... well settled that one of the specifically established exceptions to the requirements of both a warrant and probable cause is a search that is conducted pursuant to consent.” *Schneckloth v. Bustamonte,*412 U.S. 218, 219, 93 S.Ct. 2041, 2044, 36 L.Ed.2d 854 (1973). The Court in *Schneckloth*held that “the Fourth and Fourteenth Amendments require that [the government] demonstrate that the consent was in fact voluntarily given, and not the result of duress or coercion, express or implied.” *Id.*at 248, 93 S.Ct. at 2059. “Voluntariness is a question of fact to be determined from all the circumstances .... ” *Id.*at 248-49, 93 S.Ct. at 2059. Accordingly, this court will not reverse the district court’s findings with regard to voluntariness absent clear error. *United States v. Rose,*889 F.2d 1490, 1494 (6th Cir.1989). This court has noted further that because “credibility is a key issue” in consent cases, *United States v. Cooke,*915 F.2d 250, 252 (6th Cir.1990), this court “accord[s] considerable deference to the credibility findings of the trial court.” *Id.*

The defendants’ challenge to the propriety of the police officers’ entry into the second floor of Appoline is without merit, as the district court committed no clear error in finding that Little consented to a search of the upper-level apartment. Little has made no persuasive showing of duress, and his own signed statement indicates his acquiescence to the officers’ entry — albeit for, allegedly, the limited purpose of looking for the man who had been shot. Little has pointed to nothing that could lead this court to reject the district court’s favoring, based on credibility considerations, the officers’ testimony over Little’s version of events.

The defendants make the further suggestion that the state court decision granting a motion to suppress the evidence should have been given preclusive effect in the federal proceedings.15 Although this court reviews *de novo*a district court’s decision with regard to issue or claim preclusion, *see Gargallo v. Merrill Lynch, Pierce, Fenner & Smith, Inc.,*918 F.2d 658, 660 (6th Cir.1990), we note that the defendants explicitly waived this argument before the district court when Little’s attorney conceded that the state court determination was in “no way binding” on the federal court, thus preventing this court from considering it on appeal. *See United States v. Cardinal,*782 F.2d 34, 36-37 (6th Cir.), *cert. denied,*476 U.S. 1161, 106 S.Ct. 2282, 90 L.Ed.2d 724 (1986); *see also*Fed.R.Crim.P. 51. We nonetheless underscore the total lack of merit to the defendants’ position. A prior adverse suppression decision in a state court simply does not preclude the federal government, which was not a party to the state action, from using the evidence in a federal proceeding. *See United States v. Mejias,*552 F.2d 435, 444 (2d Cir.), *cert. denied,*434 U.S. 847, 98 S.Ct. 154, 54 L.Ed.2d 115 (1977); *see also United States v. Safari,*849 F.2d 891, 893 (4th Cir.), *cert. denied,*488 U.S. 945, 109 S.Ct. 374, 102 L.Ed.2d 363 (1988).

B. Sufficiency of the Evidence of Conspiracy

Both Lloyd and Huffman argue that they should have been acquitted of conspira*1210cy because there was insufficient evidence on that count to convict them. Lloyd argues that his fingerprints were never found on any of the seized firearms; that he did not appear in any of the group photographs; that although he was present in Wadesboro, he was only there to attend funerals, and while there, he wired only small money orders; and finally, that although he was several times found to have cocaine on his person, that fact alone is insufficient to show his knowledge or participation in the conspiracy. Huffman contends that there is no evidence in the record that he sold, possessed, or bought cocaine, or that he directed anyone in those activities. The proof, he argues, showed only that he was present at locations where cocaine distribution was taking place, but presence and knowledge are not sufficient to prove guilt of conspiracy.16

In reviewing a district court’s denial of a motion for judgment of acquittal on a claim of insufficient evidence, “the relevant question is whether after viewing the evidence in the light most favorable to the prosecution, *any*rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” *Jackson v. Virginia,*443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979). If the evidence, however, is such that a rational fact finder must conclude that a reasonable doubt is raised, this court is obligated to reverse a denial of an acquittal motion. *United States v. Collon,*426 F.2d 939, 942 (6th Cir.1970).

In order to sustain a conspiracy conviction under 21 U.S.C. § 846, “the government is required to prove the existence of an agreement to violate the drug laws and that each conspirator knew of, intended to join, and participated in the conspiracy.” *United States v. Lee,*991 F.2d 343, 348 (6th Cir.1993). Circumstantial evidence is sufficient to prove the elements of conspiracy, and “[i]t is not necessary that circumstantial evidence remove every reasonable hypothesis except that of guilt.” *United States v. Stone,*748 F.2d 361, 363 (6th Cir.1984). It is also not necessary for the government to prove the existence of a formal agreement; evidence of a tacit agreement or mutual understanding is sufficient to demonstrate a conspiracy. *United States v. Sanchez,*928 F.2d 1450, 1457 (6th Cir.1991). Once the conspiracy itself has been proven to exist, it is not necessary to show that a defendant knew every member of the conspiracy or knew the full extent of the enterprise. *Id.*Such evidence can be inferred from the interdependence of the enterprise. *United States v. Bourjaily,*781 F.2d 539, 544 (6th Cir.1986), *aff'd,*483 U.S. 171, 107 S.Ct. 2775, 97 L.Ed.2d 144 (1987).

Turning to the evidence adduced at trial, we find it beyond peradventure that there was sufficient evidence of the existence of a conspiracy to distribute cocaine and crack, as well as of Lloyd’s and Huffman’s involvement in the conspiracy.

In particular, as to Lloyd, we note that he was present at Appoline, a drug distribution center, during the December 20, 1988, search, where he was observed throwing crack cocaine into the fireplace, and there found in possession of a large quantity of cash; that he, along with Little, travelled to Wadesboro and expressed an active interest in benefitting from the “killing” to be made there in drug trafficking; that he, along with Little and Huffman, had an ongoing presence in Wadesboro while crack was being sold from Little’s father’s house; that he, along with Little and Huffman, wired money from Wadesboro to Detroit;17 that he regularly *1211sold crack from his house on Strathmoor, for which he obtained cocaine in powder form from Little, who would then “cook” the powder into crack for Lloyd; that he kept guns at the Strathmoor house; that, on two separate occasions, he sold one-quarter ounce of crack to an undercover officer; that at one such sale, he wielded a .357 handgun throughout the transaction; and that he was carrying 11 grams of crack, packaged for resale, at the time of his arrest.

As to Huffman, we note that he, along with Little, was present at Appoline on November 23, when, given the enormous amount of drugs, money, guns, and drug paraphernalia, it was clear that processing of cocaine into crack and subsequent trafficking thereof was the predominant activity; that his fingerprint was found on a gun positioned to protect the entrance to the second floor of Appoline, and that a piece of his jewelry was found there; that he, along with Little, was later observed engaging in drug trafficking activity at Appo-line; that investigators found drug paraphernalia, although concededly not drugs, at the 33rd Street residence frequented by Huffman; that he was present at Patton, a house frequented by Little, the day after an undercover drug buy, and that investigators seized on that day two guns, some $15,000 in cash (including the prerecorded “buy” money), and drug paraphernalia; that he was present in the car when Little engaged in a high-speed chase; that police observed two guns in that car, at least one of which was thrown from the car; that after first trying to escape on foot from the car, he gave a false name when eventually apprehended; that he was seen at Little’s father’s house in Wadesboro, and is known to have wired large amounts of cash from there; that he was' sufficiently intimate with the activities at the Appoline residence to enter the house with a key; and that when arrested, he gave a false name and presented false identification to authorities. It is simply inconsequential that, as Huffman repeatedly asserts, he was not actually caught making a sale to an undercover officer. That precise overt act is not a necessary showing in order for there to be sufficient evidence of his involvement in the drug trafficking conspiracy.

In sum, the circumstantial and direct evidence of the ongoing involvement between Little, Lloyd, and Huffman, and of their illicit activities, was sufficient to allow a reasonable jury to conclude that a mutual understanding existed between them that they would together violate the drug laws with which they were charged.

C. Sufficiency of the Evidence of Section 924(c)(1) Violations

Little, Lloyd, and Huffman all argue that there was insufficient evidence to convict them of violating 18 U.S.C. § 924(c)(1).

Little takes issue with the sufficiency of the evidence of only one of his section 924(c)(1) convictions, arguing, with respect to count 6, that there was no evidence that he had ever used or possessed the two guns found in the Patton house on June 30, 1989, and further, no evidence that *anyone*ever used either of the firearms in relation to a drug offense. Lloyd argues that because the government never produced the .357 revolver that the agent testified Lloyd wielded at a drug transaction on February 27, 1991, there was insufficient evidence to convict him of having used it.18 Finally, Huffman contests both of his 924(c)(1) convictions, arguing (1) that there was no evidence of when or why he touched the gun seized in the November raid at Appoline, and (2) that there is no evidence of a nexus between drug trafficking at the Patton address and use of the guns.

*1212The statute under which the defendants were convicted reads, in relevant part, as follows:

> Whoever, during and in relation to any crime of violence or drug trafficking crime ... uses or carries a firearm, shall, in ' addition to the punishment provided for such crime of violence or drug trafficking crime, be sentenced to imprisonment for five years.

18 U.S.C. § 924(c)(1). The statute thus requires a dual showing: that the defendant “used or carried a firearm,” and that the carrying was “during and in relation to” a “drug trafficking crime.” *See Smith v. United States,*— U.S. -, -, -, 113 S.Ct. 2050, 2053, 2058, 124 L.Ed.2d 138 (1993). And this court has extended the *Pinkerton*doctrine19 to encompass cocon-spirator liability under 924(c)(1). *United States v. Christian,*942 F.2d 363, 367 (6th Cir.1991).

In *Smith,*the Court made clear that in order to constitute “use” within the meaning of section 924(c)(1), a defendant’s action must “facilitate[ ] or further[] the drug crime.” *Id.*- U.S. at -, 113 S.Ct. at 2056. Courts, including this one, have construed the “during and in relation to” language of 924(c)(1) quite expansively. *See id.*at -, 113 S.Ct. at 2058-59. Thus,

> [i]n cases involving firearms found on premises under the control of a drug offense offender, the courts have developed a “fortress analogy” theory, which holds that if it reasonably appears that the firearms found on the premises controlled or owned by a defendant and in his actual or constructive possession are to be used to protect the drugs or otherwise facilitate a drug transaction, then such firearms are used “during and in relation to” a drug trafficking crime.

*United States v. Henry,*878 F.2d 937, 944 (6th Cir.1989). Nonetheless, “[t]he phrase ‘in relation to’ ... clarifies that the firearm must have some purpose or effect with respect to the drug trafficking crime; its presence or involvement cannot be the result of accident or coincidence.” *Smith,*-, U.S. at -, 113 S.Ct. at 2059. Mere possession of a firearm, therefore, when the firearm’s presence is “entirely ‘unrelated’ to the crime,” *id.*(citation omitted), does not merit conviction under 924(c)(1). *See United States v. Brown,*915 F.2d 219, 224 (6th Cir.1990). But “[e]ven if a firearm remains hidden throughout a crime, its concealed presence may have been in relation to the crime if it facilitated the crime by emboldening the defendant, giving him the security and confidence to undertake the criminal act.” *Id.*

We will first dispose of the arguments which present the easiest cases. Lloyd’s argument is patently lacking in merit. It is plainly not necessary to actually produce the weapon in order for a reasonable jury to be convinced beyond a reasonable doubt that Lloyd in fact did use or carry the weapon during and in relation to a drug trafficking crime. The agent’s decisive testimony in this regard was sufficient to support the jury’s verdict.

Next, Huffman’s argument that there was insufficient evidence to warrant a 924(c)(1) conviction on count 3, relating to the gun found at the Appoline residence, is also patently lacking in merit. His liability could either be direct, because his fingerprint was found on the gun and he was in close proximity to it, or could be coconspiratorial. And the government adduced sufficient evidence to show that drug trafficking was occurring at Appoline, and therefore, a loaded weapon in the hallway of the residence is without question a weapon that a jury could reasonably conclude was used during and in relation to a drug trafficking crime.

Turning now to the convictions of Little and Huffman with respect to the guns seized at the Patton residence, we are not entirely unpersuaded by their arguments: the paucity of evidence showing that the guns were used *during and in relation to*drug trafficking — that is, the failure to find drugs at the Patton house during the June *121320, 1989, raid — -makes these convictions more controversial than those already discussed. Several factors convince us, however, of the propriety of the convictions. First of all, only the day before, the investigators purchased crack from the residence, and at the time of the raid, drug paraphernalia and large amounts of cash were found in the house. Thus, it is clear that the residence was habitually used as a drug distribution center. We next consider the location of the weapons. One gun — a riñe, no less — was found in the corner bedroom, and a box of ammunition was found, readily accessible, on the windowsill. The other gun was found under a mattress, only a few feet from the closet containing the drug proceeds. Viewing this evidence in the light most favorable to the prosecution, we think that a rational jury could have found that the purpose for which the firearms were present was to protect the drugs and drug proceeds, and could have thus found the elements of 924(c)(1) to have been proven beyond a reasonable doubt.20

D. Section 924(c)(1) Jury Instructions

Little and Huffman next raise arguments with respect to the jury instructions on the firearm counts.21 Little argues that the jury instructions allowed the conspiracy count to act as the predicate offense for both of the charges, but that the government was required to prove that the different firearms relate to different drug offenses. Little is correct that in obtaining multiple convictions under section 924(c)(1), it is *not*“the number of guns involved that controls” the number of counts for which a defendant may be liable, and that it is necessary that a separate predicate offense be charged to correspond to each 924(c)(1) charge. *Henry,*878 F.2d at 942. Our review of the jury instructions, however, reveals no error on this score. Each of Little’s 924(c)(1) counts was supported by a separate predicate drug offense — the conspiracy and the possession with intent on November 23 — and when the jury charge is read as a whole, *see United States v. Williams,*952 F.2d 1504, 1512 (6th Cir.1991), this fact is quite clear. And given that Little was in fact convicted on each of these separate predicate charges, we find his argument quite unconvincing.

We turn now to Huffman’s argument that the jury instructions did not adequately explain the “during and in relation to” clause of 924(c)(1), because they failed to charge that the gun must be an integral part of the drug trafficking operation. Sitting *en banc,*this court held in *United States v. Morrow,*977 F.2d 222 (6th Cir.1992) *{en banc),*that the phrase “in relation to” does not require explanation in order for the jury to understand and correctly apply it. *Id.*at 227. Thus, while a court *may*instruct a jury by further explaining “in relation to,” such an explanation is superfluous, because the phrase “is neither uncommon nor ambiguous; its content is not so arcane as to require exhaustive exposition.” *Id. Morrow,*therefore, manifestly forecloses Huffman’s claim of error. *See Williams,*952 F.2d at 1512. But we note that, in any event, the district court provided a clear explanation of the phrase “during and in relation to.” The court told the jury that “if you find beyond a reasonable doubt that a defendant had the weapons ... readily accessible for possible use to secure, enforce, or protect the drugs, the money to purchase the drugs, the drug transaction, or the participants in the drug transaction, you can find him guilty of those counts.” The court’s instruction more than adequately addressed Huffman’s concern.

E. Severance

Prior to trial, Taylor moved for severance pursuant to both Fed.R.Crim.P. 8(b) and 14. He argued that the counts with which he was *1214charged had nothing to do with the activity for which his codefendants were charged, and that the guns and drugs that would be admissible to prove his codefendants’ participation in the conspiracy would be highly prejudicial to him. In addition, Little, Lloyd, and Huffman moved to sever following the testimony regarding Taylor’s arrest, arguing that the testimony of Taylor’s “bizarre” behavior was prejudicial.

Taylor then also requested, immediately prior to trial, that all evidence relating to his involvement in the conspiracy, but not relating to his guilt on the underlying substantive counts, not be admitted. Although denying this motion, the court agreed to attempt to limit any prejudicial impact of the evidence. To that end, the court gave the following preliminary instruction to the jury:

> [Although the defendants are being tried jointly, you must give separate consideration to each defendant.

> In doing so, you must analyze what the evidence in the case will show with respect to each defendant, leaving out of consideration any evidence admitted solely against another defendant.

Throughout the first four days of trial, Taylor’s attorney objected to any evidence of the conspiracy activities coming in against his client, which objections the district judge consistently overruled. After hearing argument on the matter on the fourth day of trial — the first day on which Taylor’s counsel was prepared with the case law — the district judge reversed her earlier position, and accordingly instructed the jury as follows:

> [Ejvidence that I am permitting to be introduced among the three people charged with the conspiracy you may not consider against Mr. Taylor. He is not charged with the conspiracy. He is not charged until later, his own individual acts. He may only be held to evidence that’s been introduced against him alone.

> An alternative would have been to sever Mr. Taylor from trial with the people he was indicted with. I did not do that, and I instead am trying him with them, and that runs a greater risk of him being prejudiced by what’s received against all the others.

> I’m counting on you to be able to separate him out, consider him only for his own acts and activities, because he is not even charged, there is no way you can ultimately find him to be a coconspirator with the others.

A similar instruction was repeated to the jury following trial.

On appeal, Taylor contends both that the initial joinder of the defendants was improper under Fed.R.Crim.P. 8(b), and that he suffered prejudice by the district court’s denial of his motion to sever under Fed. R.Crim.P. 14; in support, he essentially repeats the arguments made to the district court. Little and Huffman also rely on the arguments we have already described, in contending that they suffered prejudice under Rule 14.

 Although the remedy for misjoinder under Rule 8(b) and prejudicial joinder under Rule 14 is the same — severance and separate trials — the two rules are analytically and procedurally distinct. A motion for severance based on misjoinder under Rule 8 alleges an error in the indictment, and severance must be granted if the defendants were improperly joined. This court reviews a district court’s decision to join cases under Fed. R.Crim.P. 8(b) for harmless error, and joinder should be upheld unless it results in “actual prejudice” because it had a “substantial and injurious effect or influence” on the jury’s verdict. *United States v. Lane,*474 U.S. 438, 449, 106 S.Ct. 725, 732, 88 L.Ed.2d 814 (1986) (citations omitted). Rule 8(b) reads as follows:

> Two or more defendants may be charged in the same indictment or information if they are alleged to have participated in the same act or transaction or in the same series of acts or transactions constituting an offense or offenses. Such defendants may be charged in one or more counts together or separately and all of the defendants need not be charged in each count.

In *United States v. Hatcher,*680 F.2d 438 (6th Cir.1982), this court articulated the standard for joinder under Rule 8(b) as follows:

> *1215The joinder of multiple defendants is proper under Rule 8(b) only if each of the counts of the indictment arises out of the same act or transaction or series of acts or transactions, even if all counts of the indictment include a common defendant.

*Id.*at 441 (citations omitted). “[A] group of acts or transactions constitutes a ‘series’ if they are logically interrelated.” *United States v. Johnson,*763 F.2d 773, 777 (6th Cir.1985).

Rule 14 comes into play only if join-der was initially proper under Rule 8 but a joint trial would prejudice one or more defendants. It is addressed to the discretion of the trial judge, and a denial of severance is reviewable to determine if there was an abuse of that discretion. *United States v. Williams,*711 F.2d 748, 750 (6th Cir.), *cert. denied,*464 U.S. 986, 104 S.Ct. 433, 78 L.Ed.2d 365 (1983). Rule 14 reads:

> If it appears that a defendant or the government is prejudiced by a joinder of offenses or of defendants in an indictment or information or by such joinder for trial together, the court may order an election or separate trials of counts, grant a severance of defendants or provide whatever other relief justice requires.

In *United States v. Warner,*971 F.2d 1189 (6th Cir.1992), this court considered a defendant’s argument that “the trial court’s failure to grant her motion to sever was error because ‘her individual guilt was seriously undermined due to the enormous amount of evidence introduced at trial against Warner dealing with her wealth and expenditures on [luxury items] this Defendant did not enjoy.’ ” *Id.*at 1196. The court summarized the applicable law as follows:

> A showing that a defendant would have a better chance of acquittal in a separate trial does not establish prejudice requiring severance....

> Generally, persons indicted together should be tried together.... Where the same evidence is admissible against all defendants, a severance should not be grant-ed_ However, severance is not required if some evidence is admissible against some defendants and not others.... A defendant is not entitled to severance because the proof is greater against a co-defendant. Nor is a defendant entitled to a severance because a co-defendant has a criminal record....

> Severance is not required merely because evidence on one joined count is “separable and distinct” from evidence on another. ... However, the evidence of one crime or series of crimes must be related to the others.

*Id.*(citations omitted). Moreover, the mere fact that there “is a substantial difference in the amount of evidence produced against each defendant ... is not grounds to overturn a denial of severance unless there is a substantial risk that the jury could not compartmentalize or distinguish between the evidence against each defendant.” *Williams,*711 F.2d at 751. Even if a defendant establishes some potential jury confusion, this must be balanced against society’s need for speedy and efficient trials. *Johnson,*763 F.2d at 777.

In light of these extremely deferential standards, we conclude that there was neither misjoinder of the defendants under Rule 8(b), nor was there an abuse of discretion in the district court’s denial of severance under Rule 14. As to Rule 8(b), we note that all of the counts in this indictment are logically related. Even though Taylor had already been acquitted of being a eoeonspirator, the evidence was clear that his involvement with drug trafficking was not independent of the conspiracy of Little, Lloyd, and Huffman.- Furthermore, as the government points out, the joinder permitted the introduction of evidence identifying Taylor, and mistaken identity had been Taylor’s primary defense at trial.

With regard to Rule 14, we conclude that there has been an insufficient showing by the defense to support the argument that prejudice results from the joinder of the defendants in this case; the defendants have simply1 failed to make the necessary strong showing of factually specific and compelling *1216prejudice resulting from the joint trial.22 The trial judge was very careful to instruct the jury on its duty to consider separately the evidence against each defendant, and the defendants do not challenge the clarity of these instructions.23 Moreover, this case, while lengthy, was not a case of such complexity that the jury could not compartmentalize the evidence. We do not think there was any significant danger of jury confusion, let alone such a danger as would warrant a severance. We therefore conclude that the defendants’ claims of error on this score are without merit.24

F. Evidentiary Rulings

Following Holt’s testimony, Little attempted to impeach Holt with signed statements Holt had given to law enforcement officials prior to trial, in which he had named Lloyd, not Little, as the conspiracy’s ringleader. The court, following objection from Lloyd’s attorney and the government, would not permit Little to show that Holt had specifically named Lloyd, but did permit extensive questioning that showed that Holt had changed his story and earlier had named someone other than Little.

After the close of testimony, Little moved to introduce the statements themselves as substantive evidence, redacted so as to remove Lloyd’s name. The government argued that the statements were inadmissible hearsay, and that they should therefore be excluded. Lloyd’s attorney argued also that the statements would be cumulative because Little had adequately impeached Holt with these statements on cross-examination. The court sustained the objections and refused to receive the documents.

This court reviews a district court’s evidentiary rulings under either a *de novo*or abuse of discretion standard, depending upon the evidentiary issue involved. Because, here, the evidentiary issues relate to a claimed violation of the Sixth Amendment and Fed.R.Evid. 801, we review the district court’s rulings *de novo.*In doing so, we are obligated to consider the trial record as a whole and to ignore errors that are harmless. *Lane,*474 U.S. at 445, 106 S.Ct. at 729.

On appeal, Little argues that his inability to elicit Lloyd’s name from Holt severely detracted from the effectiveness of the cross-examination, and violated his rights under the confrontation clause of the Sixth Amendment.25 He also suggests that the statements were admissible as substantive evidence.26

*1217The Sixth Amendment guarantees the criminal defendant the right “to be confronted with the witnesses against him.” U.S. Const, amend. VI. A primary interest secured by the confrontation clause is the right of cross-examination. *See Douglas v. Alabama,*380 U.S. 415, 85 S.Ct. 1074, 13 L.Ed.2d 934 (1965). However, in *United States v. Blakeney,*942 F.2d 1001 (6th Cir.), *cert. denied,*— U.S. -, 112 S.Ct. 646, 116 L.Ed.2d 663 (1991), this court considered a claim similar to that made here by Little. Although first noting the fundamental merit to the defendant’s contention regarding the importance of cross-examination, *id.*at 1022, the court went on to note the limits to this principle:

> The confrontation clause guarantees an opportunity for effective cross-examination; it does not, however, guarantee cross-examination “that is effective in whatever way, and to whatever extent, that defense might wish.” ... Trial judges retain wide latitude “to impose reasonable limits on such cross-examination based on concerns about, among other things, harassment, prejudice, confusion of the issues, the witness’ safety, or interrogation that is repetitive or only marginally relevant.” ... ‘TT]he Confrontation Clause is generally satisfied when the defense is given a full and fair opportunity to probe and expose ... through cross-examination, thereby calling to the attention of the factfinder the reasons for giving scant weight to the witness’ testimony.”

*Id.*(quoting *Delaware v. Fensterer,*474 U.S. 15, 20, 21-22, 106 S.Ct. 292, 295-96, 88 L.Ed.2d 15 (1985), and *Delaware v. Van Arsdall,*475 U.S. 673, 679, 106 S.Ct. 1431, 1435, 89 L.Ed.2d 674 (1986)).

Little’s arguments are without merit. First, as *Blakeney*makes clear, a court may take account of competing considerations in limiting the scope of a cross-examination, and the district court properly did so in this case. Making clear that Holt had previously named Lloyd would simply have been cumulative impeachment of Holt’s testimony, given that Little had already made clear that Holt’s testimony changed and that he had not originally named Little as the supplier. Thus, Little’s cross-examination of Holt was hampered only mildly, if at all, by not being able to bring out Lloyd’s name, and he is not entitled to a new trial on these grounds. Secondly, the statements were properly excluded as substantive evidence. The statements were hearsay, and no exception exists that would permit their admission.27

Huffman makes a different argument than Little, and contends that when considered together, the mass of prejudicial evidence requires reversal. He specifically points to testimony of threatening comments another defendant *(not*Huffman) made to a police officer witness during trial, which testimony the court struck; testimony regarding Little’s statements of disdain for the criminal justice system following the November 23 raid, for which the court gave a limiting instruction; testimony regarding the chase in the BMW, which he argues is irrelevant as to Huffman since he was not driving; and a photograph of an unidentified child smothered in dollar bills.

Huffman’s arguments likewise fail.28 We again conclude that the evidence with regard to Taylor was simply not prejudicial to the other defendants and is there*1218fore not grounds for a new trial. Likewise, the evidence that Huffman contends was “inflammatory” was either entirely unrelated to Huffman, and so not prejudicial to him, or was evidence of his own actions (such as throwing the guns from the window of the BMW) and so properly probative of his guilt. And although we agree that the picture of the unidentified child smothered in dollar bills should have been excluded as unduly prejudicial, *see United States v. Parker,*997 F.2d 219 (6th Cir.1993), we conclude that admission of that small piece of evidence in the context of this long trial was harmless error.29

G. Distribution Within 1000 Feet of a School

At trial, Little requested that the following jury instruction be given in relation to the counts charging distribution within 1000 feet of a school:

> To establish a defendant’s guilt to Counts Two or Five you must find more than that the defendant possessed the narcotics within 1,000 feet of a school intending to distribute them. You also must find that the defendant’s distribution was *intended*to occur within 1,000 feet of a school.

(Emphasis added.) The court instead instructed the jury that the “[t]he government need not prove that the defendant intended to distribute the cocaine or base within a thousand feet of the school.” On appeal, Little argues that this instruction was erroneous.

Under 21 U.S.C. § 860 (formerly § 845a), a district court may double the penalty for anyone found to have distributed cocaine in violation of section 841(a), where that person sold the cocaine within 1,000 feet of a school. This court has interpreted this statute as not incorporating any *mens rea*requirement, *United States v. Cross,*900 F.2d 66, 68-69 (6th Cir.1990); thus, the jury did not need to find an intent on Little’s part to deliver drugs within 1000 feet of the school. Therefore, the instruction that Little requested was an incorrect statement of the law of this circuit, while the instruction actually given by the district court did accurately state the law. *See Williams,*952 F.2d at 1512. There was therefore no error in the district court’s refusal to instruct the jury as Little requested.

III.

We turn now to the defendants’ various sentencing challenges.

A. Little’s Sentence

Little’s total offense level of 40, based on his distribution of between 50 and 150 kilograms of cocaine, and on a four-level increase for his role in the offense. Specifically, Little was held responsible — as were Lloyd and Huffman — only for distribution of the cocaine and crack seized during raids on the houses linked to the conspirators or purchased in undercover controlled buys from members of the conspiracy, and not for amounts under negotiation. These amounts totalled 511 grams of crack, which the applicable statute and sentencing guideline mandate be treated as 5110 grams of cocaine, and 1,093 grams of powder cocaine; the total is thus equivalent to 62 kilograms of cocaine. Little’s applicable criminal history category was II. The resulting imprisonment range was 324 to 405 months, but mandatory minima for the 924(c)(1) counts (3 and 6) of five and twenty years resulted in a total range of 624 to 705 months. The district court sentenced him to an imprisonment term of 660 months.

Little first argues30 that the base offense level used in the PSR was incorrect, because the calculation included a large quantity of crack never shown to have any connection with him. A district court’s determination of the quantity of drugs used to compute a defendant’s sentence is a finding *1219of fact that should not be rejected unless clearly erroneous. *United States v. Wilson,*954 F.2d 374, 376 (6th Cir.1992). The finding must be supported by a preponderance of the evidence. *United States v. Hodges,*935 F.2d 766, 774 (6th Cir.), *cert. denied,*— U.S. -, 112 S.Ct. 251, 116 L.Ed.2d 206, *and cert. denied,*— U.S. -, 112 S.Ct. 317, 116 L.Ed.2d 259 (1991). A member of a conspiracy is responsible for the total amount of cocaine involved in the conspiracy, including other conspirators’ conduct, only if that conduct was reasonably foreseeable to him and in furtherance of the execution of the jointly undertaken criminal activity. *United States v. Jenkins,*4 F.3d 1338, 1345 (6th Cir.1993); *see United States v. Williams,*962 F.2d 1218 (6th Cir.), *cert. denied,*— U.S. -, 113 S.Ct. 264, 121 L.Ed.2d 194 (1992). Under this standard, we find it plainly proper to have held Little accountable for the amounts distributed by him and his coconspirators over the course of the conspiracy. Here, it is apparent that the scope of the criminal activity jointly undertaken by Little, Lloyd, and Huffman was the same as the scope of the entire conspiracy. *Cf. United States v. Okayfor,*996 F.2d 116, 120-21 (6th Cir.1993). All three conspirators were shown to have been involved in the conspiracy from its inception. All three were, moreover, shown to have been active participants throughout the conspiracy. In short, Little can make no persuasive argument that these amounts were not reasonably foreseeable to him, nor that the amounts were not distributed in furtherance of the jointly undertaken criminal activity.31

Little’s next argument, however, presents a serious challenge to the validity of his sentence. Under 21 U.S.C. § 860(b), a defendant’s second conviction for distribution near a school merits an increased maximum sentence. The statute does not purport to increase the minimum sentence, however, and the mandatory minimum sentence applicable to Little, pursuant to 21 U.S.C. § 841(a), was twenty years. Little argues that the district court, apparently misled by an erroneous PSR, believed that the mandatory minimum sentence was thirty years.

Our review of the record confirms Little s assertion. At the sentencing hearing, Little’s attorney objected to the PSR’s finding that Little was subject to a thirty-year mandatory minimum:

> One matter that I don’t think is discussed by any of the other sentences is the presentence report indicated there was minimum term of 30 years on count [2], which was.a schoolyard count as to my client.

The AUSA then conceded that “[ijt’s my understanding that the schoolyard count enhances the maximum, and it really doesn’t affect anything for today’s purposes.” The court nonetheless exhibited confusion:

> THE COURT: Well, it does — it does result in a net increase.

> [AUSA]: The schoolyard—

> THE COURT: From 324 to 360 months. But go ahead.

Instead of then continuing to argue this point, Little’s attorney simply moved on to his next argument. On the judgment imposing Little’s sentence, the court noted that “[t]he guidelines require the sentence imposed, at a minimum,” thus indicating that the court continued to believe that thirty years was the statutory minimum.

The government argues that Little waived any argument about the thirty-year sentence by failing to clarify his argument to the district court, and that because this sentence falls within the permissible range, therefore, it should be affirmed. We disagree. It is apparent from the transcript and from the notations on the judgment that the district judge did not understand that she had discretion to sentence Little to less than thirty years on count 2. This court has the authority to review a district court’s mistaken belief that it lacks discretion. *See United States v. Dellinger,*986 F.2d 1042, 1044 (6th Cir.1993); *United States v. Spedalieri,*910 F.2d 707, 710 (10th Cir.1990). We will vacate Little’s sentence and remand for resentenc-ing, to allow the district court to sentence Little in consideration of the fact that he is not statutorily required to serve a thirty-year minimum term on count 2.

*1220B.Lloyd’s Sentence

The district court sentenced Lloyd to 188 months of imprisonment on counts 1, 11, 12, and 17, to be served concurrently, and 60 months on count 13, to be served consecutively to the other terms, for a total of 248 months. On appeal, Lloyd argues that the different statutory sentencing treatment of crack and cocaine is unconstitutional. He contends it offends the principle of equal protection and substantive due process.

A defendant’s challenge to his sentence on constitutional grounds presents a question of law over which this court should exercise *de novo*review. *Cf. United States v. Knipp,*963 F.2d 839, 843 (6th Cir.1992).

This court has upheld on many occasions the constitutional validity of the statutory scheme requiring that 1 gram of crack is treated for sentencing purposes as if it were 100 grams of cocaine. Most recently, in *United States v. Tinker,*985 F.2d 241 (6th Cir.1992), *cert. denied,*— U.S. -, 113 S.Ct. 1872, 123 L.Ed.2d 491 (1993), this court wrote as follows:

> Defendant argues that treating cocaine base as equal to 100 times the same cocaine amount for sentencing purposes violates due process and equal protection. ' These constitutional challenges are merit-less. *United States v. Williams,*962 F.2d 1218, 1227-28 (6th Cir.1992); *United States v. Pickett,*941 F.2d 411, 418 (6th Cir.1991). “Congress’s act was sufficiently rational to meet the demands of substantive due process.” .... Moreover, 21 U.S.C. § 841(b) and the United States Sentencing Guidelines, which treat one gram of crack as the equivalent of 100 grams of cocaine, do not violate equal protection. *Williams,*962 F.2d at 1227-28 (joining “every circuit which has addressed this issue”).

*Id.*at 242 (footnote omitted). We conclude that *Tinker*and the cases it cites leave no room for debate on this issue. The sentencing scheme of which Lloyd complains simply does not violate constitutional dictates.32 We will therefore affirm Lloyd’s sentence.

C. Huffman’s Sentence

At Huffman’s sentencing hearing, he contended that he was entitled to a reduction in his offense level because of his minor role in the offense. The district court rejected the argument, and sentenced him to a total of 540 months.

On appeal, Huffman argues that the district court erred in not reducing his offense level by two points because of his minor role in the offense. The “minor participant” reduction is available only to a party who is “less culpable than most other participants” and “substantially less culpable than the average participant.” U.S.S.G. § 3B1.2, comment. (n. 3) & (backg’d.). The culpability determination is “heavily dependent upon the facts,” *id.,*and the defendant has the burden of proving mitigating factors by a preponderance of the evidence. Perry, 908 F.2d 56 at 58. We therefore review a district court’s determination of a defendant’s role in the offense only for clear error. *Williams,*962 F.2d at 1226. The evidence showed that Huffman was not substantially less culpable than the other conspirators. He was therefore not entitled to a two-point reduction, and the district court’s sentencing determination should stand.

D. Taylor’s Sentence

Taylor was assigned a base offense level of 32 for count 9, based on distribution of 60.86 grams of cocaine, and received a two-level increase for his role in the offense. His total offense level was thus 34, and his criminal history category was II. Including the mandatory minimum sentence for his 924(c)(1) conviction, his imprisonment range was 228 to 270 months. He received a total imprisonment term of 228 months.

At sentencing, Taylor objected to the amount of drugs charged to him as relevant conduct, and took the position that he was accountable only for the 1.69 grams that he was convicted of distributing under count 9. The government took the position that although he had earlier been acquitted of two of the underlying substantive charges, the court could nonetheless include the approxi*1221mately 59 grams of crack related to those counts. The court found as follows:

> The Court does accept the government’s position on this issue and finds that the 60 grams are attributable to the defendant.

> The evidence was offered at trial. It’s true, the jury found there was no conviction beyond reasonable doubt, but the Court finds by a preponderance that 60 grams should be attributed there.

On appeal, Taylor renews this argument, and contends that principles of double jeopardy preclude his being held accountable for amounts of which he was acquitted. Because he presents a legal challenge to the district court’s determination of the amount of drugs attributable to him, we exercise *de novo*review. *See*18 U.S.C. § 3742(e); *see also United States v. Garner,*940 F.2d 172, 174 (6th Cir.1991).

This court has accepted the principle that the “relevant conduct system now makes acquittal by the jury on some counts irrelevant to the sentence imposed for the convicted offense.” *United States v. Silverman,*976 F.2d 1502, 1527 (6th Cir.1992) *(en banc)*(Merritt, C.J., dissenting), *cert. denied,*— U.S. -, 113 S.Ct. 1595, 123 L.Ed.2d 159 (1993). Most recently, this court wrote that “[tjhere is *no*merit to [the defendant’s] contention that because he was acquitted on the substantive count involving the mason jar of crack cocaine, that cocaine should not have been included in the total amount of cocaine attributable to him.” *United States v. Jenkins,*4 F.3d at 1344 (6th Cir.1993) (citing *United States v. Moreno,*933 F.2d 362, 374 (6th Cir.), *cert. denied,*— U.S. -, 112 S.Ct. 265, 116 L.Ed.2d 218 (1991)). “The rationale supporting these decisions is that in order to convict at trial, the government bears the burden of proving the elements of the offense beyond a reasonable doubt. However, the burden of proof at sentencing is the lesser preponderance of evidence standard.” *Moreno,*933 F.2d at 374. Thus, acquittal does not require the district court to ignore otherwise relevant conduct,33 and Taylor’s argument is unavailing. We therefore affirm his sentence.

IV.

We AFFIRM the judgments of conviction and sentences of Lloyd, Huffman, and Taylor. We AFFIRM the judgment of conviction of Little, but VACATE his sentence and REMAND for resentencing in accord with this opinion.

1

. Because the resolution of many of the defendants’ challenges is so fact-dependent, we feel compelled to set out the underlying facts of this rather wide-ranging conspiracy in what we recognize is exhaustive detail.

2

. The Appoline residence is 430.26 feet from the Dr. Charles Oakman School for Crippled Children.

3

. The other two defendants were not present at Appoline that night.

4

. Although this opinion refers to "officers” and "investigators,” the record indicates that the investigation of this conspiracy was conducted, beginning at some unspecified point, by a task force consisting of various federal agencies as well as of Detroit police. Because the record often does not make clear with what law enforcement agency the various officers are associated, we have opted for general terminology.

5

.While engaging in surveillance at Appoline, the police observed that Huffman, on multiple occasions, would "arrive! ] at the Appoline address, ... [go] in, c[o]me out with a bag, and dr[i]ve to an address on 33rd Street where he took the bag into, and at — a short time after that, foot traffic started arriving at that home on 33rd.” The police, accordingly, obtained and executed a search warrant at the 33rd Street residence in December 1988. They did not find any controlled substances in that search, although they did find narcotics paraphernalia.

6

. "Unwittings” are regular drug purchasers who are unaware that the apparent drug users with whom they are associating arc, in reality, undercover investigators.

7

. The phone bill showed several calls to Wades-boro, North Carolina, which, as is discussed below, was the site of some of the conspiracy’s activities.

8

. Holt testified that he also saw Huffman at Little's father’s house in Wadesboro on one occasion, but he could not remember the date or any details of the meeting.

9

. On almost every occasion, the senders would use aliases, and it is therefore difficult to identify precisely which defendant is responsible for which wire transfer.

10

. Darren Huffman was a codefendant who pled guilty.

11

. Keenan Taylor was a codefendant who pled guilty.

12

.At the first trial, Taylor was acquitted, *inter alia,*of the counts charging him with his involvement in these two cocaine transactions. At sentencing following the second trial, however, the district court held him responsible for the amounts distributed under the relevant conduct provisions of the sentencing guidelines.

13

. Although Huffman also argues at length that he has standing to object to the search, the government does not suggest otherwise. We assume, without deciding, that he does have standing.

14

. The defendants assert that the fact that the drugs and guns were in plain view demonstrates that Little would not have consented to the search. We find this argument unpersuasive. As the government points out, the annals of case law are replete with criminals who consent, for reasons that can only be guessed at, to searches despite almost necessarily knowing that contraband would be discovered.

15

.In support of this position, the defendants cite, without analysis, various federal cases holding that Fourth Amendment issues already determined in state court should not be relitigated in *habeas corpus*cases. These cases, for obvious reasons, are completely inapposite here, outside the context of and considerations peculiar to *habeas*proceedings.

16

. Huffman also asserts, cursorily, that the evidence was insufficient to convict him of possession of cocaine with intent to distribute, or alternatively, with aiding and abetting thereof, with regard to his presence in the Appoline residence on November 23, 1988. The abundance of cocaine spread throughout the house along with the presence of Huffman's latent fingerprint on the semi-automatic rifle found in the hallway constitutes evidence sufficient to allow a rational jury to find that the elements of this offense were shown beyond a reasonable doubt. *See, e.g., United States v. Pena,*983 F.2d 71, 72 (6th Cir.1993).

17

. We find it unimportant that, as he asserts, he was positively identified only to have wired amounts of $200 or less. Although that may have been an amount not inconsistent with that customarily wired by the residents of Wadesboro, that fact certainly does not constitute proof that the funds did not represent drug proceeds, and does not overcome the abundant circumstantial *1211evidence that he was involved in the ongoing drug trafficking at Sherman Little’s house.

18

. Lloyd also makes an argument that there was no evidence that the rifle that was found in the February 28 search of Strathmoor was actually used in connection with drug-trafficking. We find it unnecessary to address this argument, because the indictment clearly charged Lloyd with using and carrying a firearm on February 27, not February 28. It is thus clear that the government never argued that Lloyd was liable under 924(c)(1) for the rifle, and that its case was based solely on his possession of the .357. For this reason, we likewise find it unnecessary to address his argument that the court erred in'not giving a unanimity instruction; since he was charged only with using a single gun, the .357, the jury was necessarily unanimous that he used that gun when it voted to convict him.

19

. *See Pinkerton v. United States,*328 U.S. 640, 646-47, 66 S.Ct. 1180, 1183-84, 90 L.Ed. 1489 (1946). The *Pinkerton*doctrine "exists to punish conspirators for crimes committed by a cocon-spirator that are not the object of the conspiracy itself but are foreseeable and in furtherance of the conspiracy." *United States v. Christian,*942 F.2d 363, 367 (6th Cir.1991).

20

. We note, moreover, that we fail to find in the record any indication that Little preserved this issue by moving for acquittal under Fed. R.Crim.P. 29, or for a new trial under Fed. R.Crim.P. 33. If we are correct, then Little would have no remedy absent a showing of plain error. *See United States*v. *Williams,*940 F.2d 176, 180 (6th Cir.), *cert. denied,*- U.S. -, 112 S.Ct. 666, 116 L.Ed.2d 757 (1991); *cf. Cardinal,*782 F.2d at 36-37. Given that the government did not suggest waiver, however, we are loathe to rest our judgment on this basis.

21

. As already mentioned, *see*note 18, *supra,*we find Lloyd’s jury instruction argument to be without basis.

22

. In reaching this conclusion, wc view as significant the fact that the evidence against these defendants was simply overwhelming.

23

. Indeed, such argument would be unavailing, since defense counsel explicitly approved the district judge's choice of language prior to her instructing the jury.

24

. For largely the same reasons, wc also reject Taylor's argument that the district court erred in failing to declare a mistrial after four days of allowing evidence that was properly admissible only against the alleged coconspirators to be introduced against Taylor. Again, the evidence which he complains was "admitted against him” had, on the whole, nothing to do with him, and it is unclear why he thinks its admission prejudiced him. Taylor has presented the court with no reason to think that the jury did not follow the very clear curative instructions given by the district court on two occasions. *See United States v. Moreno,*933 F.2d 362, 368 (6th Cir.), *cert. denied, -*U.S. -, 112 S.Ct. 265, 116 L.Ed.2d 218 (1991). In short, we conclude that the district court did not abuse its discretion in denying Taylor's motion for mistrial, and Taylor has demonstrated no prejudice that would entitle him to a reversal. *Id.*

25

. Wc note that Little drastically mischaracter-izes Holt's testimony. Holt never testified that Little "recruited” him to go to North Carolina; he in fact testified that he had volunteered to go when he heard Little mention North Carolina. Furthermore, Holt was unambiguous about Lloyd's ongoing involvement in the North Carolina crack sales, although it is true that his testimony implied that Little was the leader of the operation. Finally, Little exaggerates the importance of Holt's testimony when he characterizes it as "the glue that held the government's conspiracy theory together.”

26

. Wc reject Little's and Huffman's argument that the introduction of evidence relevant only to Mario Taylor was severely prejudicial, and note that the court gave the following limiting instruction subsequent to the complained-of testimony: "Members of the jury, I must instruct you that the testimony that you had heard concerning Mario Taylor may be considered against him only and not against anyone else here.” We further note that the evidence related to an incident in which the other defendants were not involved, and so did not in any way implicate the other defendants.

27

. Some of the statements were made under oath. Because, however, they were made only to an investigating officer, they nonetheless do not fall within the purview of Fed.R.Evid. 801(d)(1)(A), which deems as not hearsay any statement that is "inconsistent with the declar-ant’s testimony [at trial], and [that] was given under oath subject to the penalty of perjury *at a trial, hearing, or other proceeding, or in a deposition*[.]" (Emphasis added.)

28

. We note, moreover, the lack of merit to Huffman’s suggestion that prosecutorial misconduct warrants reversal. First, as we discuss, there was nothing improper in the admission of the vast majority of evidence to which Huffman points, and it was therefore not misconduct for the prosecutor to introduce it. Second, the closing argument of which Huffman complains, in which the prosecutor stated that he could talk for "weeks and weeks” regarding the activities of other indicted coconspirators, was not improper, and so did not constitute misconduct; we agree with the government that the district court’s admonition to the juty was made out of an abundance of caution. *See United States v. Clark,*982 F.2d 965, 968 (6th Cir.1993).

29

. We note that the *Parker*court itself specifically cautioned that the errors that cumulatively required reversal, would, taken in isolation, have been considered harmless.

30

. Although in his original brief, Little makes an argument regarding his sentences for the two section 924(c) counts, he concedes error on this argument in his reply brief, based on the Supreme Court's recent decision in *Deal v. United States,*- U.S. -, 113 S.Ct. 1993, 124 L.Ed.2d 44 (1993). Huffman's argument on this score is likewise foreclosed.

31

. Lloyd's and Huffman's arguments in this regard likewise fail.

32

. Huffman also makes this argument, and we rcject it for the same reasons.

33

. We underscore, however, our discomfort with the district court's failure to articulate why it considered the distribution counts of which Taylor was acquitted, which charged him with conduct occurring some six months before the conduct of which he was convicted, to have been relevant conduct, that is, "conduct that was part of the same course of conduct or common scheme or plan as the offense of conviction.” U.S.S.G. § IB 1.3(a)(2). Because Taylor did not raise this argument either at sentencing or on appeal, however, we do not consider it a basis for reversal.