This case involves an elaborate drug distribution network in Tulsa, Oklahoma. Five defendants were convicted of conspiracy to distribute and to possess with intent to distribute “crack” cocaine in violation of 21 U.S.C. §§ 841 and 846. They were sentenced to long-term imprisonment pursuant to the Sentencing Guidelines.
On appeal, the defendants attack their convictions and sentences on numerous grounds.1 Most importantly, they contend that (1) the government did not present sufficient evidence to establish a single conspiracy and to connect them to it, and that (2) the sentencing court miscalculated the quantity of drugs attributable to each individual defendant for purposes of the Sentencing Guidelines. After careful consideration of the record, we reverse the conviction of Diana Brice because there was insufficient evidence to establish that she joined the extensive conspiracy that was charged. We affirm the convictions and sentences of the remaining defendants.
I. BACKGROUND
On March 7, 1990, Donald B.W. Evans, Jr., his brother Dominic Evans, Diana J. Brice, James E. Joubert, Perry Roberts III, Robert Norfleet, Jr., Brian K. Woods, James J. Backward, Christopher Wyman, and Eric D. Rentie were indicted for conspiracy to distribute and to possess with intent to distribute 50 grams or more of cocaine base (“crack”) in violation of 21 *666U.S.C. §§ 841(a)(1), 841(b)(l)(A)(iii) & 846.2 The government contends that these individuals were involved in an elaborate drug distribution network.
The indictment generally alleged a conspiratorial agreement with the following parameters: (1) The conspiracy began in early 1987 and continued through March 7, 1990. (2) The conspiracy involved at least ten individuals. (3) The objective of the conspiracy was to distribute crack cocaine. (4) This objective was accomplished by transporting powder cocaine from California to the Northern District of Oklahoma, converting it into crack cocaine, and distributing the crack cocaine.3
Only Donald Evans, Dominic Evans, Jou-bert, Roberts, and Brice were prosecuted in the instant case. The remaining defendants pled guilty pursuant to a cooperation agreement with the government. In addition, Carl Walker, a key figure in the drug distribution network, was granted immunity from federal prosecution in return for his agreement to forfeit any drug proceeds and to cooperate with the government.
On May 30, 1990, a jury found the defendants 4 guilty of conspiracy to distribute and to possess with intent to distribute crack cocaine. The district court then reluctantly sentenced the defendants to long-term imprisonment in accordance with the Sentencing Guidelines. Donald Evans was sentenced to a life term of imprisonment without parole; Dominic Evans was sentenced to a 295-month term of imprisonment; Joubert was sentenced to a 210-month term of imprisonment; Roberts was sentenced to a 292-month term of imprisonment; and Brice was sentenced to a 210-*667month term of imprisonment.- The defendants appealed.
Our jurisdiction to hear this case arises under 28 U.S.C. § 1291. We are called upon to assess the validity of the defendants’ convictions and the propriety of their sentences. This inquiry is highly fact-specific. Thus, familiarity with the cast of characters, together with an understanding of the often confusing web of events connecting these individuals, is important.
We start with the testimony of Carl Walker. Walker began his short-lived career in the drug business in 1987, buying kilogram quantities (also referred to as “kilos” or “keys”) of powder and crack cocaine from an individual named Jesse Griffith — later to become his principal source of cocaine5 — and selling that cocaine throughout Tulsa, Oklahoma. Walker’s career ended when he was arrested in Oklahoma City in 1988 and sentenced to 15 years in the state system for his involvement with cocaine.
The government considers Walker to be one of the central figures in the crack distribution network at issue. In fact, the government characterized the network as a wagon wheel conspiracy with Walker at the hub. Thus, the government focused upon his relationship with the defendants when presenting its case. Several of the defendants had direct dealings with Walker. Donald Evans served as Walker’s secondary source of crack cocaine, and Joubert and Brice were among his many customers. The remaining defendants had a tenuous relationship with Walker. Roberts and Dominic Evans can be connected to Walker only by their presence at several drug-related meetings between Walker and Donald Evans.
Although the defendants’ relationship with Walker is certainly relevant, their relationship to the conspiracy as a whole is the critical inquiry. The defendants’ respective roles may be summarized as follows:
Donald Evans was a central figure in the crack distribution network, acting as both importer and dealer. By means of a joint venture with James Backward, he imported powder cocaine from California and converted it into crack cocaine through a process known as “cooking.”6 He then sold this crack to numerous individuals, including Roberts, Walker, Norfleet, and possibly his brother Dominic. Dominic Evans sold and “fronted”7 powder cocaine to Backward, accompanied Donald Evans to a drug-related meeting with Walker, and told acquaintances that he was waiting for Donald to send him crack cocaine. Roberts purchased crack cocaine from Donald Evans, fronted crack to Rentie, and accompanied Donald Evans to a drug-related meeting with Walker. Joubert purchased crack cocaine from Walker and Rentie, fronted crack to Rentie, and, together with Rentie, borrowed Brice’s scales in order to weigh crack. Brice made a single purchase of crack cocaine from Walker through Walker’s girlfriend Jackie Smallwood and lent scales to Joubert and Rentie so that they could weigh crack.
The above summary adequately conveys the notion that the defendants and the coconspirators who cooperated with the government were not strangers to one another. However, it is difficult to visualize how interconnected they were and to understand their roles in the conspiracy charged without charting the relationships that underlie this crack distribution net*668work. The diagrams at the end of this opinion should prove useful in these respects.8
II. DISCUSSION
The defendants attack their convictions and sentences on numerous grounds. Two of the questions raised — whether the government presented sufficient evidence to connect the defendants to a single conspiracy and whether the sentencing court properly calculated the quantity of drugs attributable to the defendants for sentencing purposes — are complicated and close issues. They can be answered only by revisiting the age-old problem of what constitutes a conspiracy and confronting the more recent problem of how to control the potential abuse of excessively broad conspiracy charges. Accordingly, those questions will be the focus of this opinion.
The remaining contentions — that the district court erred in refusing to give the jury a multiple conspiracy instruction and in not granting a severance to several of the defendants, that the sentences given to the defendants violate due process and constitute cruel and unusual punishment under the Eighth Amendment, and that the court erroneously denied various motions — are without merit.
A. The Elements of Conspiracy
We must consider the issues presented for review in light of the expansive, yet somewhat elusive, body of law that governs conspiracy. In so doing, we are mindful that the conspiracy doctrine is inherently subject to abuse and that the government frequently uses conspiracy to cast a wide net that captures many players. Thus, we must be careful to guard against guilt by association, to “scrupulously safeguard each defendant individually, as far as possible, from loss of identity in the mass”:
When many conspire, they invite mass trial by their conduct. Even so, the proceedings are exceptional to our tradition and call for use of every safeguard to individualize each defendant in his relation to the mass....
Kotteakos v. United States, 328 U.S. 750, 773, 776, 66 S.Ct. 1239, 1252, 1253, 90 L.Ed. 1557 (1946).
To prove conspiracy, the government must show “[1] that two or more persons agreed to violate the law, [2] that the defendant knew at least the essential objectives of the conspiracy, ... [3] that the defendant knowingly and voluntarily became a part of it,” and [4] that the alleged coconspirators were interdependent. United States v. Fox, 902 F.2d 1508, 1514 (10th Cir.) (citation omitted), cert. denied, — U.S. —, 111 S.Ct. 199, 112 L.Ed.2d 161 (1990). By necessity, the government may establish these elements by direct or circumstantial evidence. See United States v. Andrews, 585 F.2d 961, 964 (10th Cir.1978) (“The nature of the offense of conspiracy with its attendant aspects of secrecy often requires that ele*669ments of the crime be established by circumstantial evidence.”).
1.Agreement
“In conspiracy cases brought under 21 U.S.C. § 846, the government is required to prove that two or more persons agreed to commit an offense under the Controlled Substances Act.” United States v. Espinosa, 771 F.2d 1382, 1391 (10th Cir.) (citation omitted), cert. denied, 474 U.S. 1023, 106 S.Ct. 579, 88 L.Ed.2d 561 (1985). Here, the essence of the alleged agreement was to distribute crack cocaine in the Northern District of Oklahoma from 1987 to 1990 on a large scale.
This agreement need not be explicit, but rather may be inferred from the facts and circumstances of the case. An agreement to distribute drugs can sometimes “rationally be inferred” from “frequent contacts” among the defendants and from “their joint appearances at transactions and negotiations.” United States v. Esparsen, 930 F.2d 1461, 1472 (10th Cir.1991), cert. denied, — U.S. —, 112 S.Ct. 882, 116 L.Ed.2d 786 (1992);9 see also United States v. Horn, 946 F.2d 738, 743 (10th Cir.1991) (when the defendant agreed to bring in customers and deliver drugs, the “defendant became part of the larger common plan to distribute well in excess of fifty grams of cocaine”). It is not enough, however, for the government to show only “ ‘mere association’ ” with conspirators known to be involved in crime, United States v. Dickey, 736 F.2d 571, 585 (10th Cir.1984) (citation omitted), cert. denied, 469 U.S. 1188, 105 S.Ct. 957, 83 L.Ed.2d 964 (1985)10; “[cjasual transactions” between the defendant and conspirators known to be involved in crime, Horn, 946 F.2d at 741 (citation omitted); or a buyer-seller relationship between the defendant and a member of the conspiracy, Fox, 902 F.2d at 1514 (citation omitted).
2. Knowledge of Objective
It is necessary to show that the “defendant shared a common purpose or design with his alleged coconspirators.” Horn, 946 F.2d at 740 (citation omitted). See, e.g., id. at 741 (objective of conspiracy was “to distribute large amounts of cocaine for profit”); Dickey, 736 F.2d at 582 (objective of conspiracy was “to possess and distribute drugs (marijuana and cocaine) for profit”) (emphasis omitted). In this case, the objective of the conspiracy was to distribute crack cocaine in Oklahoma.
The objective of the conspiracy becomes especially important when the government attempts to establish a conspiracy on the basis of purchases and sales. Evidence that an intermediate distributor bought from a supplier might be sufficient to link that buyer to a conspiracy to distribute drugs because both buyer and seller share the distribution objective. However, a consumer generally does not share the distribution objective and thus would not be part of a conspiracy to distribute crack cocaine. Of course, a consumer may conspire to possess crack cocaine.
3. Knowing and Voluntary Participation
A defendant may be convicted of conspiracy only if the government proves that the defendant had knowledge of the conspiracy and voluntarily participated therein. A conspirator “need not know of the existence or identity of the other members of the conspiracy or the full extent of the conspiracy,” United States v. Metro*670politan Enters., 728 F.2d 444, 451 (10th Cir.1984) (citing Blumenthal v. United States, 332 U.S. 539, 557, 68 S.Ct. 248, 256, 92 L.Ed. 154 (1947)), but he or she must have a general awareness of both the scope and the objective of the enterprise to be regarded as a coconspirator.
This is not to say, however, that a defendant may be convicted of a conspiracy that defies common sense simply because he or she possesses a general awareness of the breadth of its illegal activities. For example, at oral argument, the government suggested that a drug dealer who knows that his supply can be traced to the Medillin cartel has joined a vast conspiracy with the members of the cartel to distribute crack illegally for profit. Under such an approach, a small-time drug dealer could be held responsible for all of the drugs originated by the cartel for sentencing purposes, resulting in a guaranteed life sentence. Such an approach would pervert the concept of conspiracy. Mere knowledge of illegal activity, even in conjunction with participation in a small part of the conspiracy, does not by itself establish that a person has joined in the grand conspiracy.
4. Interdependence
Finally, “[t]he conduct of the alleged coconspirators, including the defendant, may be diverse and far-ranging, but it must be interdependent in some way.” Horn, 946 F.2d at 740 (citation omitted). Interdependence is present when “each alleged coconspirator ... depend[s] on the operation of each link in the chain to achieve the common goal.” Fox, 902 F.2d at 1514 (citation omitted).
In essence, the defendant’s actions must “facilitate[ ] the endeavors of other alleged coconspirators or facilitate[ ] the venture as a whole.” Horn, 946 F.2d at 740-41. See, e.g., Fox, 902 F.2d at 1515 (interdependence present and conspiracy conviction proper where a “scheme for distributing cocaine for profit in Denver depended for its success on the successful achievement of several integrated steps, including regular meetings between [the defendants], the pooling of their resources to purchase drugs, and ... several wholesale cocaine purchases”); United States v. McIntyre, 836 F.2d 467, 472 (10th Cir.1987) (interdependence not present and conspiracy conviction improper where the defendant was a buyer in several unrelated transactions and “[t]he Government [did] not show[] that if defendant had failed to possess and distribute drugs on any one of the named occasions, the failure would have had any effect on the success of the other transactions.”).
Thus, a single conspiracy does not exist solely because many individuals deal with a common central player; they must be interconnected in some way. See United States v. Sophie, 900 F.2d 1064, 1080 (7th Cir.), cert. denied, — U.S. —, 111 S.Ct. 124, 112 L.Ed.2d 92 (1990). The Supreme Court elaborated upon this notion in Kotteakos, 328 U.S. 750, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946). In Kotteakos, one defendant secured fraudulent loans under the National Housing Act for a number of different persons and groups. The Court held that many separate conspiracies did not become one merely because they all included a common defendant. Id. at 773, 66 S.Ct. at 1252. The Court reasoned by analogy that “ ‘[t]hieves who dispose of their loot to a single receiver — a single “fence” — do not by that fact alone become confederates: they may, but it takes more than knowledge that he is a “fence” to make them such.’ ” Id. at 755, 66 S.Ct. at 1243 (citation omitted).
Separate spokes meeting at a common center constitute a wheel conspiracy only if those spokes are enclosed by a rim. Id. What is required is a shared, single criminal objective, not just similar or parallel objectives between similarly situated people. See id. at 769, 66 S.Ct. at 1250 (Court cautioned that considering all of the illegal loan participants as part of a single illegal conspiracy “obviously confuses the common purpose of a single enterprise with the several, though similar, purposes of numerous separate adventures of like character”) (emphasis added). It is not enough that a group of people separately intend to distribute drugs in a single area, nor even *671that their activities occasionally or sporadically place them in contact with each other. People in the same industry in the same locale (even competitors) can occasionally be expected to interact with each other without thereby becoming coconspirators. What is needed is proof that they intended to act together for their shared mutual benefit within the scope of the conspiracy charged.
B. Sufficiency of the Evidence
Dominic Evans, Joubert, Roberts, and Brice contend that the government did not present sufficient evidence to connect them to a single large conspiracy to possess and distribute crack cocaine.11 The defendants raised this exact contention below by means of a motion for acquittal. The district court denied the motion and left this question to the jury, who concluded that the government did indeed present sufficient evidence.
Although this is a close issue as to some of the defendants, the restrictive standard of review for a sufficiency of the evidence question provides us with very little leeway:
It is essential to emphasize initially that the question whether there existed evidence sufficient to establish a single conspiracy is one of fact for the jury to decide. When reviewing the jury's decision, we must view all of the evidence, both direct and circumstantial, in the light most favorable to the government, and all reasonable inferences and credibility choices must be made in support of the jury’s verdict.
Dickey, 736 F.2d at 581 (citations omitted). Of course, “we cannot sustain a conspiracy conviction if the evidence does no more than create a suspicion of guilt or amounts to a conviction resulting from piling inference on top of inference.” Horn, 946 F.2d at 741 (citation omitted).
After a careful examination of the lengthy record in this case, we conclude that the government presented sufficient evidence to establish a single large conspiracy to distribute and to possess with intent to distribute crack cocaine, as well as to link Dominic Evans, Joubert, and Roberts to such a conspiracy. The government did not, however, present sufficient evidence to link Brice to that conspiracy. Accordingly, we reverse Brice’s conviction, but affirm the convictions of the remaining defendants.
1. Sufficient Evidence as to Dominic Evans, Joubert, and Roberts
Applying the legal principles set forth above, we conclude that the following evidence was sufficient to connect Dominic Evans, James Joubert, and Perry Roberts to the conspiracy charged:
a. Dominic Evans
(1) James Backward testified that he engaged in two separate drug transactions with Dominic Evans in 1988. Dominic sold Backward nine ounces of powder cocaine in California and later fronted him two ounces of the same in Tulsa.
(2) Carl Walker testified that he had a drug-related conversation with Dominic in 1988, during which time Dominic reported *672that he could get Walker kilos of crack cocaine from California at a good price.
(3) Walker also testified that Dominic was present when Walker went to Donald Evans’ house to purchase seven ounces of crack cocaine in early 1988. Walker observed crack cocaine and several guns at the house. However, Walker did not speak with Dominic about drugs, nor did he see him handling drugs.
(4) Richard Reynolds testified that Dominic told him in the summer of 1988 that he was waiting for his brother Donald to send cocaine to him.
(5) Reynolds also testified that he saw drugs in Dominic’s possession in June 1988.
(6) A hotel clerk testified that Dominic and Donald Evans paid for a room in Tulsa with large amounts of cash.
(7) George Anderson testified that he solicited drugs from Dominic and Donald Evans as part of a “controlled buy” and was told to come back later.
(8) Police Officer Nick Hondros testified that Dominic Evans was riding in a vehicle in which the police discovered approximately six and a half grams of crack in November 1988. Although some of the cocaine was recovered from the floorboard of the vehicle, some of the crack was found in a pair of sweatpants that also contained Dominic Evans’ driver’s license.
b. James Joubert
(1) Carl Walker testified that he sold crack cocaine to Joubert approximately eighteen times between 1987 and 1988, in quantities ranging from four to nine ounces. Griffith and Rentie corroborated this testimony by discussing specific transactions, including fronted transactions.
(2) Walker further testified that Joubert accompanied him to a meeting with Donald Evans in early 1988, during which time Evans discussed how much cocaine he was willing to sell to Walker and for what price. Joubert did not participate in the drug-related conversation. Nor did Perry Roberts, who was also present at that meeting.
(3) James Backward testified that Jou-bert was one of Evans’ “workers” “who paid [Evans] money and picked up cocaine from him.” R., Vol. V, at 157, 166.
(4) Eric Rentie testified that he sold approximately five ounces of crack to Joubert in 1987 and fronted crack to Joubert on five or six other .occasions.
(5) Rentie further testified that Joubert fronted him from one to five ounces of crack on approximately three occasions in 1988.
(6) Finally, Rentie testified that he accompanied Joubert to Jackie Smallwood’s house, where Joubert picked up approximately two and a half kilos of cocaine from Carl Walker. After they dropped this cocaine off “at someone’s house,” they went to Perry Roberts’ house to make a phone call, where they encountered Donald Evans. They then picked up Diana Brice, who led them to pick up some scales. After they dropped Brice off at her house, Jou-bert and Rentie used the scales to weigh the cocaine into ounce and half-ounce packages. The drugs were then distributed.
c. Perry Roberts
(1) Carl Walker testified that Roberts accompanied Donald Evans to a meeting, during which time Donald Evans discussed how much cocaine he was willing to sell to Walker and for what price. Roberts did not participate in the conversation. As mentioned supra, Joubert also attended this meeting.
(2) James Backward testified that Roberts was one of Evans’ “workers” “who paid him money and picked up cocaine from him.” R., Yol. V, at 157, 166.
(3) Eric Rentie testified that Roberts fronted him a half-ounce of crack in 1987.
(4) Richard Reynolds testified that he overheard Donald Evans arguing with Roberts over money that Roberts owed him for previously fronted crack cocaine. This argument occurred during the summer of 1988.
Viewing the evidence in the light most favorable to the government as we must, we conclude that the government presented sufficient evidence to establish a large con*673spiracy among a number of individuals to distribute crack cocaine in Tulsa, Oklahoma, and that it adequately established that Dominic Evans, Joubert, and Roberts joined that conspiracy. The government presented sufficient evidence from which to infer that these defendants agreed to violate 21 U.S.C. §§ 841 and 846. Specifically, the jurors heard testimony regarding frequent drug transactions among the defendants and their coconspirators, as well as testimony regarding the defendants’ attendance at and sometimes participation in drug-related discussions. This evidence is sufficient to show that these defendants had knowledge of the general nature and scope of the illegal enterprise and that they all shared the distribution objective. See Esparsen, 930 F.2d at 1472.
Accordingly, we affirm the convictions of Dominic Evans, James Joubert, and Perry Roberts.
d. Insufficient Evidence as to Brice
We reverse the conviction of Diana Brice, however, because the following evidence was insufficient to connect her to the conspiracy charged:
(1) Carl Walker testified that Brice purchased four ounces of crack from him in early 1988.
(2) Eric Rentie testified that Brice lent scales to Rentie and Joubert to aid them in weighing some crack cocaine in 1988. There is no doubt that Brice knew the purpose behind the request because she warned them not to leave any crack “crumbs” on the scales. Brice did not own the scales, but she did have ready access to them.12
This evidence falls short for several reasons. First, it does not establish that Brice shared in the common distribution objective of the conspiracy. There is no evidence that Brice resold the four ounces of crack that she purchased from Walker for profit. Nor is there evidence that she was in the distribution business merely because on one isolated occasion she loaned scales to Rentie and Joubert so that they could weigh cocaine. That act could have been merely a gratuitous favor or isolated act among friends. Cf. McIntyre, 836 F.2d at 471 (defendant did not share common purpose of possessing and distributing cocaine where “[tjhere [was] no indication that defendant was making a profit or distributing cocaine when he merely shared his purchases with his friends present at the time of sale”).
Second, and more importantly, the evidence does not establish that Brice agreed to participate in a conspiracy of such extensive scope as the one charged. “ ‘[P]roof of the existence of a buyer-seller relationship [here, the transaction between Brice and Walker], without more, is inadequate to tie the buyer to a larger conspir-acy_’ ” Fox, 902 F.2d at 1514 (citation omitted); see also Dickey, 736 F.2d at 583 (same); United States v. Watson, 594 F.2d 1330, 1337 (10th Cir.) (same), cert. denied, 444 U.S. 840, 100 S.Ct. 78, 62 L.Ed.2d 51 (1979). Nor can we presume that Brice was aware of the scope of this conspiracy because there was no evidence that she attended meetings wherein other transactions were discussed. Furthermore, a onetime purchaser of four ounces of crack cocaine can in no way be characterized as a “major buyer.” Compare id. at 1340 (“Where large quantities of narcotics are being distributed, each major buyer may be presumed to know that he is part of a wide-ranging venture, the success of which depends on performance by others whose identity he may not even know.”) (emphasis added).
“ ‘[I]t is ... essential to determine what kind of agreement or understanding existed as to each defendant.’ ” United States v. Record, 873 F.2d 1363, 1368 (10th Cir.1989) (quoting United States v. Borelli, 336 F.2d 376, 384 (2d Cir.1964), cert. denied, 379 U.S. 960, 85 S.Ct. 647, 13 L.Ed.2d *674555 (1965)). The best way to assess a defendant’s intended involvement in a conspiracy is to examine the conspiracy from that defendant’s point of view. What exactly did Brice think she was joining? To answer this question, we need look only to common sense and to the facts of this case. We conclude that, at the most, Brice joined Joubert and Rentie in a much smaller conspiracy to distribute crack cocaine on one instance.
However, the government made a tactical decision to charge all of the defendants, including Brice, with involvement only in a single large conspiracy, rather than a series of separate smaller conspiracies. The tactic of charging many defendants with a single massive conspiracy is fraught with the potential for abuse. Here, however, the government is hoisted with its own petard.13 Having chosen to allege that Brice joined a single large conspiracy, that is what the government obligated itself to prove. It failed in that regard. We find a total absence of evidence that Brice intended to join such a conspiracy as alleged.14
Brice’s erroneous conviction serves as a reminder that we must be particularly vigilant when the government seeks to bring many individuals under the umbrella of a single conspiracy. The risk is that a jury will be so overwhelmed with evidence of wrongdoing by other alleged coconspira-tors that it will fail to differentiate among particular defendants. The government must not be allowed to use conspiracy as a tool to circumvent the fundamental principle that “ ‘[gjuilt with us remains individual and personal.... It is not a matter of mass application.’ ” Kotteakos, 328 U.S. at 772, 66 S.Ct. at 1252.
It may be time for the government to heed the admonition given by the Second Circuit in United States v. Sperling, 506 F.2d 1323, 1340-41 (2d Cir.1974), cert. denied, 420 U.S. 962, 95 S.Ct. 1351, 43 L.Ed.2d 439, and cert. denied, 421 U.S. 949, 95 S.Ct. 1682, 44 L.Ed.2d 103 (1975):15
[W]e take this occasion to caution the government with respect to future prosecutions that it may be unnecessarily exposing itself to reversal by continuing the indictment format reflected in this case. While it is obviously impractical and inefficient for the government to try conspiracy cases one defendant at a time, it has become all too common for the government to bring indictments against a dozen or more defendants and endeav- or to force as many of them as possible to trial in the same proceeding on the claim of a single conspiracy when the criminal acts could be more reasonably regarded as two or more conspiracies, perhaps with a link at the top.
C. Refusal To Give A Multiple Conspiracy Instruction
Donald Evans, Joubert, and Roberts contend that a prejudicial variance occurred in this case because the indictment charged a single conspiracy but the evidence presented during the trial below was of multiple conspiracies.16 Thus, they argue, the district court erred in failing to instruct the jury on multiple conspiracies. We disagree.
We recognize that a few circuits do indeed hold that a defendant is entitled to a multiple conspiracy instruction as a theory *675of the defense to counteract an indictment charging only a single, overarching conspiracy when the facts warrant such a defense. See, e.g., United States v. Dennis, 917 F.2d 1031, 1033 (7th Cir.1990) (where there was substantial evidence to show multiple conspiracies rather than a single conspiracy, district court’s failure to give a multiple conspiracies instruction was error and denied the defendant a fair trial); United States v. Cambindo Valencia, 609 F.2d 603, 625 (2d Cir.1979) (“a multiple conspiracy charge is required whenever several conspiracies might be inferred from the evidence offered”), cert. denied, 446 U.S. 940, 100 S.Ct. 2163, 64 L.Ed.2d 795 (1980).
In this circuit, however, a failure to instruct the jury on uncharged multiple conspiracies is not reversible error as long as the jury instructions adequately conveyed that “the government had the burden of proving beyond a reasonable doubt the [single] conspiracy as alleged, and that the evidence should be considered separately as to each individual defendant.” Watson, 594 F.2d at 1340; see also Fox, 902 F.2d at 1516-17. In this case, the court instructed the jury as follows:
Although the defendants are being tried together, you must consider the case against each separately. In doing so you must decide what the evidence shows about each defendant, without considering any evidence that may have been received about the other defendants. Each defendant is entitled to have the case against him or her decided solely on the evidence and the law that applies to him or her.
R., Vol. I, Doc. 113, at 14. In addition, the court instructed:
[A] conspiracy agreement is not necessarily proved when the government shows merely that individuals acted similarly, that they may have associated with one another, and that they may have together discussed common aims and interests.
Id. at 16. These instructions satisfy the standard set forth in Watson.
Furthermore, the court’s failure to submit this defense theory to the jury did not impair the defendants’ ability to argue to the jury that they were in fact involved in a number of separate conspiracies rather than a single unified conspiracy.
For these reasons, we conclude that, although an instruction on multiple conspiracies might have been preferable, the district court’s refusal to give such an instruction was not reversible error.
D. Requests for a Severance
Dominic Evans and Roberts attack their convictions on the ground that the district court erroneously denied their motions for severance, thereby causing substantial prejudice. “The decision whether to grant a severance is within the sound discretion of the trial court.” United States v. Esch, 832 F.2d 531, 537 (10th Cir.1987) (citation omitted), cert. denied, 485 U.S. 908, 108 S.Ct. 1084, 99 L.Ed.2d 242, and cert. denied, 485 U.S. 991, 108 S.Ct. 1299, 99 L.Ed.2d 509 (1988). We will not disturb the trial court’s decision absent an affirmative showing of abuse of discretion and a strong showing of prejudice. United States v. Williams, 897 F.2d 1034, 1037 (10th Cir.1990) (citation omitted), cert. denied, — U.S. —, 111 S.Ct. 2064, 114 L.Ed.2d 469 (1991); Esch, 832 F.2d at 537-38. “ ‘To establish abuse of discretion more is required than that separate trials might have offered a better chance for acquittal of one or more of the accused.’ ” Williams, 897 F.2d at 1037 (citation omitted).
These defendants failed to show either abuse of discretion or sufficient prejudice to warrant reversal of the trial court’s decision to adhere to “[t]he general rule in our circuit ... that persons jointly indicted should be tried together.” United States v. Rinke, 778 F.2d 581, 590 (10th Cir.1985) (citation omitted). “ ‘This [rule] is especially true in conspiracy charges, from the very nature of the case.’ ” Davenport v. United States, 260 F.2d 591, 594 (9th Cir.1958) (citation omitted), cert. denied, 359 U.S. 909, 79 S.Ct. 585, 3 L.Ed.2d 573 (1959). Accordingly, we reject this contention.
*676 E. Search and Seizure
Finally, Donald Evans alleges that the district court committed reversible error in overruling his motion to suppress the fruit of a warrantless search committed on June 2, 1988 at the Tulsa International Airport. The district court found that he had voluntarily consented to the search. During this search, police officers seized $4900 in cash from Donald Evans and obtained statements from him.
In considering the district court’s denial of a motion to suppress evidence, “the reviewing court must accept the trial court’s findings of fact unless clearly erroneous and must consider the evidence in the light most favorable to the government.” United States v. Soto-Ornelas, 863 F.2d 1487, 1490 (10th Cir.1988) (citations omitted). Applying this standard, we cannot say that the district court’s ruling constituted reversible error. See United States v. Mendenhall, 446 U.S. 544, 100 S.Ct. 1870, 64 L.Ed.2d 497 (1980).
F. Sentencing
For the reasons stated above, we affirm the convictions of Donald Evans, Dominic Evans, Joubert, and Roberts. We must now consider the propriety of the sentences imposed upon them.
The defendants challenge their sentences on the ground that the district court improperly calculated the quantity of drugs attributable to them for sentencing purposes. However, a defendant is accountable ■ for the quantity of drugs that was within the scope of the agreement and was reasonably foreseeable to him or her. U.S.S.G. § 1B1.3, comment, (n. 1) (1989). Because there is evidence that the district court carefully considered the extent of each defendant’s participation in the conspiracy and the quantity of drugs that was foreseeable to each, we affirm the defendants’ sentences.17
The lengthy sentences imposed upon the defendants in this case in accordance with the Sentencing Guidelines underscore the maxim “crime doesn’t pay.” Donald Evans was sentenced to a life term of imprisonment without parole; Dominic Evans was sentenced to a 295-month term of imprisonment; Joubert was sentenced to a 210-month term of imprisonment; Roberts was sentenced to a 292-month term of imprisonment; and Brice was sentenced to a 210-month term of imprisonment.
The sentences imposed upon the defendants who chose to cooperate with the government are shockingly low in comparison. Norfleet was sentenced to 5 years of probation; Wyman was sentenced to 1 year of supervised release; Rentie was sentenced to 5 years of supervised release; and Backward was sentenced to 5 years of probation.18 Furthermore, Walker and Griffith were not even indicted.
We recognize that a discrepancy is justified between the sentence of a defendant who cooperates with the government and a defendant who does not cooperate because “a rational connection exists between obtaining information concerning narcotics and providing an opportunity for a sentence reduction in exchange for such information.” Horn, 946 F.2d at 746 (cita*677tion omitted). We also recognize that this circuit has rejected the argument that “the government’s discretionary power to recommend departures below the statutory minimum should be matched by a mechanism which would allow the court to avoid sentencing disparities between those who substantially assist the government and those who assert their constitutional right to a trial.” See Horn, 946 F.2d at 745-46.
Nevertheless, the radical disparity in this ease causes us concern.19 This concern is not obviated by the government’s representation at the sentencing hearing and at oral argument that it gave all of the defendants an opportunity to cooperate in exchange for leniency. Rather, it is heightened by the prospect that the use of this tactic in a large-scale conspiracy prosecution might effectively chill a defendant’s right to trial. In the face of a looming threat that the government might seek to attribute all of the drugs handled by the members of a single massive conspiracy to each defendant, regardless of the significance of his or her role in the scheme, even an innocent individual against whom there is little evidence might justifiably feel that he or she has no option but to plead guilty in the hope of leniency.
Thus, we share the discomfort that the district court expressed at the time of sentencing:
The Court’s concern with the application of guidelines is apparent. I am bound by the guidelines unless I can find that there is an area within a specific case not addressed by the Federal Sentencing Commission, or if I cannot find a basis for departure. What concerns this Court in this specific case is the level of punishment prescribed by the guidelines. Under the evidence in this case, if it were not covered by the guidelines, then this Court would not impose the sentences dictated by the guidelines. Sentences are harsh but they are also the law at this point which binds this Court.
I do have one concern that I will express for the record and this in no way faults the district attorney’s office. I do understand the difficulty of pursuing, investigating and prosecuting drug offenses. And I think this message somehow should be taken to the community in some way, that any young men who would involve themselves in profit making in the drug business make a gross error in light of the applicable guidelines, particularly with crack cocaine which is accorded a much higher punishment than even powder cocaine. But my concern, and I’m going to express it for this record for the appellate court to review, that I am concerned and not content with what I’m required to do under the guidelines. The whole concept was to avoid disparity of sentences in drug cases. And the Court sees in this case those individuals who opted to cooperate, those who opted to cooperate and were given that opportunity by the government now stand, except the one that is not sentenced, on probation with a probationary sentence. The remaining defendants who opted to compel the government to prosecute them now stand facing horrendous sentences. Now, the disparity of sentencing here is not by reason of the subjective attitude of a trial judge but it’s by reason of the tactical decision of the prosecutor. That’s just the way it works and that’s the way it works here. I do not think that allowing that option to the executive branch and denying it to the judicial is a healthy result but it’s the result that has occurred and the result that we all must live with until such time as the sentencing guidelines are eventually dealt with. And I will state that for the record as the Court’s concern for whatever, if any, value it may have.
*678R., Vol. IX, at 20-21. We share these concerns.
The jury did not make any findings as to how much crack cocaine the conspiracy handled or the amount of crack that was foreseeable to each defendant. Rather, the sentencing court undertook this task. Calculating the quantity of drugs attributable to a defendant in a large-scale conspiracy for sentencing purposes is not an easy task. Section 2D1.4 of the Sentencing Guidelines, which governs' attempts and conspiracies, provides that “the offense level [for a defendant convicted of conspiracy] shall be the same as if the object of the conspiracy ... had been completed.” U.S.S.G. § 2D1.4(a). The Application Notes then reference Application Note 1 to section 1B1.3 of the Guidelines, which provides:
In the case of criminal activity undertaken in concert with others, whether or not charged as a conspiracy, the conduct for which the defendant “would be otherwise accountable” ... includes conduct of others in furtherance of the execution of the jointly-undertaken criminal activity that was reasonably foreseeable by the defendant. Because a count may be broadly worded and include the conduct of many participants over a substantial period of time, the scope of the jointly-undertaken criminal activity, and hence relevant conduct, is not necessarily the same for every participant. Where it is established that the conduct was neither within the scope of the defendant’s agreement, nor was reasonably foreseeable in connection with the criminal activity the defendant agreed to jointly undertake, such conduct is not included in establishing the defendant’s offense level....
U.S.S.G. § 1B1.3, comment, (n. 1) (emphasis added).20
A defendant is not necessarily liable for the entire quantity of drugs involved in a drug conspiracy. In applying the Guidelines, courts have focused on the reasonable foreseeability to the defendant that a particular quantity of drugs would be involved in the conspiratorial activity. See United States v. Matthews, 942 F.2d 779, 784-85 (10th Cir.1991) (person who undertakes one-time drug deal in concert with others does not thereby assume responsibility for past misdeeds of coconspirators for sentencing purposes); United States v. Edwards, 945 F.2d 1387, 1396 (7th Cir.1991), cert. denied, — U.S. —, 112 S.Ct. 1590, 118 L.Ed.2d 308 (1992) (defendants were convicted of a large heroin distribution conspiracy but held accountable only for reasonably foreseeable conduct for sentencing purposes; “the Government must do more than allege that- a particular defendant has entered some aspect of the conspiracy in order for a defendant to be held liable for the entire amount of heroin distributed during the course of the conspiracy”) (citation omitted); United States v. Willard, 909 F.2d 780, 781 (4th Cir,1990) (“A defendant is not necessarily held responsible at sentencing for the entire criminal conduct of the conspiracy. Rather, he is held accountable only for the criminal conduct in furtherance of the conspiracy which was either known to him or ‘reasonably foreseeable’ by him.”) (citations omitted); cf. United States v. North, 900 F.2d 131, 134 (8th Cir.1990) (under previous version of Sentencing Guidelines, “[sjimple knowledge that the supplier supplies other persons is not enough ... to assess all quantities distributed by the supplier to each person who purchased drugs from that supplier” for sentencing purposes for conspiracy to distribute and possess methamphetamine and cocaine). Thus, all defendants in this case are not necessarily responsible for the distribution of nine and a half kilos of crack cocaine, the amount that the presentence reports attribute to the conspiracy.21
*679Illustration e to section 1B1.3 demonstrates the practical application of this rule in a drug conspiracy context and is thus a useful guide for the instant ease:
Defendants H and I engaged in an ongoing marihuana importation conspiracy in which Defendant J was hired only to help off-load a single shipment. Defendants H, I, and J are included in a single count charging conspiracy to import marihuana. For the purposes of determining the offense level under this guideline, Defendant J is accountable for the entire single shipment of marihuana he conspired to help import and any acts or omissions in furtherance of the importation that were reasonably foreseeable. He is not accountable for prior or subsequent shipments of marihuana imported by Defendants H or I if those acts were beyond the scope of, and not reasonably foreseeable in connection with, the criminal activity he agreed to jointly undertake with Defendants H and I (i.e., the importation of the single shipment of marihuana).
Illustration e to U.S.S.G. § 1B1.3. This example reinforces an obvious, yet important point: “a critical factor in determining the proper sentence is the degree of any given defendant’s involvement in the conspiracy.” Edwards, 945 F.2d at 1389.
The record reveals that the defendants’ sentences were imposed in accordance with existing case law and the Sentencing Guidelines. The sentencing judge in this case attempted “to make a distinction ... among the defendants as to the extent of their participation.” See R., Vol. IX, at 40. First, the sentencing judge made various adjustments when calculating the defendants’ total offense levels in an effort to reflect their respective roles in the conspiracy charged. Second, the sentencing judge adopted the factual findings and guideline application in the presentence reports, which attributed to each defendant a quantity of crack cocaine that was reasonably foreseeable to that particular defendant: Donald Evans, 9V2 kilos; Dominic Evans, 720g; Joubert, more than 500g but less than 1.5 kilos; and Roberts, 9V2 kilos.22 As a result, the total offense levels were calculated as follows: Donald Evans, 46; Dominic Evans, 38; Joubert, 36; and Roberts, 38.
Accordingly, we affirm the sentences imposed on Donald Evans, Dominic Evans, James Joubert, and Perry Roberts.
III. CONCLUSION
For the foregoing reasons, we REVERSE the conviction of Diana Brice and REMAND to the district court with instructions to order her release forthwith. We AFFIRM the convictions of the remaining defendants and the sentences imposed upon them.
*680EXHIBIT A
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*681EXHIBIT B
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. Although the defendants argued their cases separately, the issues presented on appeal are closely related and the evidence presented below overlapped with respect to all five cases. Accordingly, this Court will decide all five cases in this single opinion.
. Section 841(a)(1) provides that "[e]xcept as authorized by this subchapter, it shall be unlawful for any person knowingly or intentionally to manufacture, distribute, or dispense, or possess with intent to manufacture, distribute, or dispense, a controlled substance_”
Section 841 (b)( 1) (A) (iii) states that the penalty for a violation of § 841(a) involving 50 grams or more of cocaine base is "a term of imprisonment which may not be less than 10 years or more than life.”
Section 846 provides that ”[a]ny person who attempts or conspires to commit any offense defined in this subchapter shall be subject to the same penalties as those prescribed for the offense, the commission of which was the object of the attempt or conspiracy."
. The indictment stated as follows:
Beginning in or about early, 1987, and continuing until on or about the date of this Indictment [March 7, 1990], in the Northern District of Oklahoma, and elsewhere, defendants DONALD B.W. EVANS, JR., DOMINIC EVANS, a/k/a MITCHELL, DIANA J. BRICE, JAMES E. JOUBERT, ROBERT NORFLEET, JR., BRIAN K. WOODS, PERRY ROBERTS, III, JAMES J. BACKWARD, CHRISTOPHER WYMAN, and ERIC D. RENTIE, did willfully and knowingly combine, conspire, confederate and agree together, and with others both known and unknown to this Grand Jury, to commit offenses against the United States of America, in violation of Title 21, United States Code, Section 846, as follows:
(1) To knowingly and intentionally possess with intent to distribute 50 grams or more cocaine-base (crack), a Schedule II narcotic controlled substance, contrary to Title 21, United States Code, Sections 841(a)(1), 84 l(b)( l)(A)(iii).
(2) To knowingly and intentionally distribute 50 grams or more cocaine-base (crack), a Schedule II narcotic controlled substance, contrary to Title 21, United States Code, Sections 841(a)(1), 841(b)(l)(A)(iii)....
The objects of said conspiracy were to be accomplished and were accomplished as follows:
(1) Defendants DONALD B.W. EVANS, JR., DOMINIC EVANS, a/k/a MITCHELL, JAMES J. BACKWARD, BRIAN K. WOODS and other unindicted co-conspirators both known and unknown to the Grand Jury, would and did possess, transport and distribute large amounts of cocaine-base (crack) from California into the Northern District of Oklahoma.
(2) Defendants DONALD B.W. EVANS, JR., DOMINIC EVANS, a/k/a MITCHELL, DIANE [sic] J. BRICE, JAMES E. JOUBERT, ROBERT NORFLEET, JR., BRIAN K. WOODS, PERRY ROBERTS, III, JAMES J. BACKWARD, CHRISTOPHER WYMAN, and ERIC D. RENTIE, and other unindicted co-conspirators, both known and unknown to the Grand Jury, would and did receive, distribute, possess with intent to distribute, obtain with intent to distribute, and store with intent to distribute, cocaine-base (crack) and distribute and facilitate the distribution of cocaine-base (crack) in the Northern District of Oklahoma, for profit.
R., Vol. I, Doc. 1, at 1-2.
.For the sake of simplicity, Donald Evans, Dominic Evans, Joubert, Roberts, and Brice will often be referred to collectively as “the defendants."
.Although Griffith was not named in the indictment, he played a significant role in the crack distribution network as both importer and drug dealer. In fact, Griffith handled much larger amounts of crack than did the defendants in this case, including Donald Evans. It is estimated that Griffith was responsible for introducing thirty kilos of crack to the streets of Tulsa, whereas the district court held Donald Evans responsible for nine and a half kilos.
. This process usually takes approximately 15 minutes and can be done in a kitchen. The resulting substance takes on the form of a rock, which is broken down into smaller portions and distributed.
. "‘[F]ronting’ denotes a credit arrangement whereby a drug buyer is given drugs in exchange for a promise to pay for them at some later date.” United States v. Mosley, 965 F.2d 906, 915 (10th Cir.1992).
. We are unable to fit this crack distribution network neatly within one of the two different models of conspiracy that have evolved over the years — (1) the "wagon wheel" model and (2) the "chain” model — because of the multitude of characters and events involved. With some modifications, however, Chart A illustrates the wagon wheel model and Chart B the chain model.
In a wagon wheel conspiracy, "a single person or group (the ‘hub’) deal[s] individually with two or more other persons or groups (the ‘spokes’)." Wayne R. LaFave & Austin W. Scott, Jr., Criminal Law § 6.5, at 551 (2d ed. 1986). Separate spokes meeting at a common center constitute a wheel conspiracy only if those spokes are enclosed by a “rim." Kotteakos v. United States, 328 U.S. 750, 755, 66 S.Ct. 1239, 1243, 90 L.Ed. 1557 (1946). In a chain conspiracy, "there is succéssive communication and cooperation in much the same way as with legitimate business operations between manufacturer and wholesaler, then wholesaler and retailer, and then retailer and consumer." La-Fave & Scott, supra, at 551. This circuit has noted that “ '[m]ost narcotics networks involve loosely knit vertically-integrated combinations.’ ” United States v. Brewer, 630 F.2d 795, 799 (10th Cir.1980) (citation omitted).
Apparently, the government had similar problems characterizing this conspiracy. At one point, the government described the crack distribution network in this case as "a wagon wheel conspiracy” with Walker at the hub. R., Vol. IV, at 38. At another point, the government described the network as a chain conspiracy with Donald Evans as the top link. Consolidated Brief of Appellee at 12.
. The defendants in Esparsen were convicted of conspiracy to distribute over 500 grams of cocaine in violation of 21 U.S.C. §§ 841(a)(1), 841(b)(1)(B) and 846. On appeal, they argued that the government did not present sufficient evidence that a conspiracy existed and that they were members of it. The court held, however, that ”[t]aken together, the incidents [about which the government presented proof] provide sufficient evidence of an agreement to distribute cocaine. The defendants’ 'common design’ to profit from drug dealing can be inferred from the completed sales [to undercover government agents], the defendants’ joint activities, and the detailed negotiations [for a particular deal].” Id. at 1473-74 (citation omitted).
. In Dickey, this Court concluded that acting as a partner in several drug transactions, loaning money for the purchase of drugs, and being connected to numerous telephone calls with co-conspirators constituted more than "mere association.” 736 F.2d at 585-86.
. Counsel for Donald Evans made a similar argument below. See R., Vol. Ill, at 7-8 ("There is no conspiracy nexus. There are simply a series of individuals who know each other to some extent. Some of them don’t know one another, and ... the framework of a conspiracy is sadly lacking herein.”). However, he does not adequately contest his conviction on this ground on appeal. His only reference to sufficiency of the evidence is an isolated sentence in the section of his brief that addresses the district court's refusal to instruct the jury regarding multiple conspiracies. See Appellant’s Brief-in-Chief at 22. This lone sentence does not meet the standard set forth in Federal Rule of Appellate Procedure 28(a)(4): "The brief of the appellant shall contain ... [a]n argument_ The argument shall contain the contentions of the appellant with respect to the issues presented, and the reasons therefor, with citations to the authorities, statutes and parts of the record relied on.” See American Airlines v. Christensen, 967 F.2d 410, 415 n. 8 (10th Cir.1992) (“It is insufficient merely to state in one’s brief that one is appealing an adverse ruling below without advancing reasoned argument as to the grounds for appeal.”) (citing Fed.R.App.P. 28(a)(4)). Even if Donald Evans had raised this issue properly, the record clearly contains sufficient evidence to support his conviction.
. The government also presented evidence, through the testimony of George Anderson, that Brice purchased 2.5 grams of crack (one-sixteenth of an ounce) from two unindicted individuals on three occasions in the fall of 1987. Evidence of this transaction is irrelevant for purposes of this appeal because the government did not present any evidence relating these individuals to the conspiracy charged.
. The government has the power to define the scope of the conspiracy as broadly as it thinks the facts will justify, but if it fails to prove the conspiracy as charged, it will fail to obtain a conviction. And, if the government is nevertheless able to persuade a jury to convict a defendant on evidence that does not prove the large conspiracy and connect the defendant to it, the district judge and the appellate courts are obligated to reverse that conviction.
. Accordingly, we need not address Brice's remaining arguments on appeal.
. The indictment in Sperling charged 28 defendants with various drug-related offenses, including conspiracy to violate the federal narcotics laws in violation of 21 U.S.C. § 846. As a result of the “serious problems” created by the government’s tactic, 506 F.2d at 1341, the court reversed several of the defendants' convictions. Id. at 1343.
. In Kotteakos, the Supreme Court held that it is prejudicial error for the government to charge a single large conspiracy but to prove only a number of smaller conspiracies. 328 U.S. at 775, 66 S.Ct. at 1253.
. Donald Evans, Dominic Evans, and Roberts also attack their sentences on Eighth Amendment and due process grounds. They emphasize the great disparity between the sentences of those defendants who exercised their right to go to trial and those who pleaded guilty and cooperated with the government. Although we share the concerns that the district court expressed during the sentencing phase of the trial below, see infra, this claim is precluded by Harmelin v. Michigan, — U.S. —, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991); United States v. Abreu, 962 F.2d 1425 (10th Cir.1992); and United States v. Horn, 946 F.2d 738 (10th Cir.1991).
In Harmelin, the Supreme Court upheld a mandatory term of life in prison without parole for a man who was convicted of possessing 672 grams of cocaine. 111 S.Ct. at 2684, 2702. In Abreu, this Court stated that “it is clear from the various opinions generated in [Harmelin ] that mandatory sentences are permissible for non-capital punishment” and that “considerable latitude is to be given to the legislature or Congress in setting sentences.” 962 F.2d at 1428. In Horn, this Court recognized that cooperation with the government justified a reduction in the cooperators’ sentences. 946 F.2d at 746.
. The record does not specify what sentence Woods received because he was a fugitive at the time of the proceedings below.
. This was not a case where the government gave favorable treatment to minor participants in the conspiracy for their testimony against major participants. To the contrary, several of the central figures in this conspiracy plea bargained and received little or no punishment in exchange for their testimony against the defendants, some of whom were relatively minor participants. Because of the large scope of the conspiracy alleged, the minor participants received very substantial sentences.
. The standard set forth in the Guidelines approximates the standard set forth in Pinkerton v. United States, 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946). Under Pinkerton, a defendant is liable for any crimes committed by a coconspirator if those crimes (1) were within the scope of the conspiracy or (2) were reasonably foreseen as a necessary or natural consequence of the unlawful agreement. 328 U.S. at 646-48, 66 S.Ct. at 1183-84.
. The probation office arrived at this figure by multiplying the amount of crack cocaine involved at each "cook” (approximately one kilo) *679by the number of "cooks" (more than one a week for three to four months). The defendants challenged this calculation during the sentencing hearing, but their objections were overruled.
. In support of these figures, the judge stated:
The Court has reviewed the quantities as contained in the evidence and as determined by the probation office. I have conferred with the probation officers involved in the presen-tence report because of the concern with estimating quantities, because this is where the long sentences come from in this case without any question, for most of these defendants, is the amount. But I am satisfied after a conference with the probation officers involved and the Court’s recall of the evidence that the amounts that they have allotted are in truth somewhat conservative because they also were concerned....
R., Vol. IX, at 38.