
    UNITED STATES of America, Plaintiff-Appellee, v. Pedro A. GARCIA, Defendant-Appellant.
    No. 94-3141.
    United States Court of Appeals, Seventh Circuit.
    Argued April 6, 1995.
    Decided Sept. 19, 1995.
    
      Barry Rand Elden, Asst. U.S. Atty., Gil Soffer (argued), Office of the United States Attorney, Criminal Receiving, Appellate Division, Chicago, IL, for plaintiff-appellee.
    Richard R. Mottweiler, Catharine D. O’Daniel (argued), Chicago, IL, for defendant-appellant.
    
      Before BAUER, COFFEY and FLAUM, Circuit Judges.
   COFFEY, Circuit Judge.

The appellant, Pedro Abelardo Garcia, pled guilty to cocaine distribution (in violation of 21 U.S.C. § 841) and conspiracy to distribute cocaine (in violation of 21 U.S.C. § 846). These charges stemmed from the sale of cocaine to an associate in Chicago, Illinois during late October 1992. On August 24, 1994, Garcia was sentenced to concurrent sentences of 292 months imprisonment and five years of supervised release, plus a special assessment in the amount of $100. On appeal, Garcia challenges his sentence. Specifically, he takes issue with the district court’s finding that he was responsible for transactions involving a total of between 60 and 150 kilograms of cocaine. We affirm.

BACKGROUND

The cocaine deal that led to Pedro Garcia’s arrest and indictment in 1992 was not the first or only drug transaction involving Garcia and an associate named Joseph Dieppa. According to Dieppa’s testimony at Garcia’s sentencing hearing, the two men bought and sold cocaine from each other and distributed the drug in the Chicago, Illinois area throughout the years 1987-1992. Dieppa testified that the total amount of cocaine involved in these deals was at least 155 kilograms.

Garcia & Dieppa: 1987-1988

From late fall of 1987 through December 1988, Garcia “fronted” cocaine to Dieppa in a series of transactions that typically involved between 1 and 3 kilograms. After obtaining the drug from Garcia, Dieppa would sell it to his customers and then use the proceeds to pay Garcia (usually between $19,000 and $21,000 per kilogram). Dieppa and Garcia conducted their business at various locations in the Chicago area, including a shopping mall, a department store, the defendant’s apartment, and the defendant’s office.

The short-term consignment arrangement that existed between Garcia and Dieppa was not based solely on mutual trust. Rather, as is common in the drug trade, it was backed up by threats of violence. On one occasion, Garcia showed Dieppa a .38 caliber revolver he owned; on another, he showed Dieppa a .45 caliber weapon and told him that it had been a gift from a local gang leader. Garcia let Dieppa know that he carried a gun with him at times during drug transactions and that he “did not get burned” when it came to cocaine debts. He also related the story of how he had dispatched his son Pedro, Jr. to shoot up the shop of a drug customer who had been delinquent in paying off a cocaine debt.

Dieppa testified at the sentencing hearing that this early course of dealing between Garcia and himself, lasting from the Fall of 1987 through late 1988, involved a total of 60 kilograms of cocaine.

Garcia & Dieppa: 1988-Spring 1992

Towards the end of 1988, Garcia encountered supply problems. At about the same time, Dieppa and his wife moved to California, where a friend, Mike Massillo, introduced Dieppa to Carlos and Henry (“Juan”) Bejarano. The Bejaranos became a source of cocaine for Dieppa, who now switched roles and acted as Garcia’s supplier rather than his purchaser. Based on the testimony of Dieppa, the series of transactions involving the Bejaranos, Dieppa, and Garcia between late 1988 and the end of 1990 probably encompassed 85 or more kilograms of cocaine. Dieppa’s final purchase from the Bejaranos was a 95 kilogram transaction (only 20 of which ended up with Garcia). Dieppa never paid for 55 of the 95 kilograms he purchased in this final deal. After exhausting the supply of cocaine that he had thus stolen, Dieppa resumed purchasing cocaine from Garcia and probably bought 10-15 kilograms from him between late 1991 and March of 1992.

Garcia & Dieppa: Denouement (Spring-Fall 1992)

When Carlos Bejarano expressed interest in arranging another deal with Dieppa in March or April of 1992, Dieppa stopped buying cocaine from Garcia. Dieppa planned to purchase 25 kilograms of cocaine from the Bejaranos, which he would then sell to Garcia and Mike Massillo. Unbeknownst to Dieppa, the Bejaranos were now cooperating with the government. On April 27, 1992 Dieppa met with Carlos Bejarano and Massillo at a shopping mall in a Chicago suburb to discuss the deal. Garcia stood on a balcony above them in order to protect Dieppa, who understandably feared for his own safety because of his earlier theft from the Bejaranos. The deal contemplated by Dieppa was never consummated. Instead, DEA agents arrested Diep-pa on June 8, 1992. On August 26, 1992, he pled guilty to a drug conspiracy charge and agreed to cooperate with the government. Dieppa was released from custody in late September 1992 and for most of the month of October, as part of his cooperation with the government, recorded his telephone conversations with Garcia. The two discussed potential sources of cocaine, including the Be-jaranos. After lengthy negotiations, Garcia agreed to have his son Jose deliver one kilogram of cocaine to Dieppa in Chicago on October 27,1992. Jose made the delivery as planned, and Garcia was arrested the next day when he met Dieppa at a parking lot to collect his $20,000 payment.

Garcia and Martinez: 1989-1990

Although it was Garcia’s relationship with Joseph Dieppa that eventually led to his arrest and indictment, the defendant’s buying and selling of cocaine was not limited to Dieppa. In late 1989, Garcia began supplying cocaine to Rudy Martinez, a leader of the Chicago street gang known as the “Latin Rings.” Up until this time, Martinez had been Garcia’s neighbor and social companion, as well as being one of his cocaine suppliers. One of Martinez’s distributors, Cynthia Pluff, testified that she distributed between 2-3 kilograms of Martinez’s cocaine every week, on average, during the spring, summer, and fall of 1990. Martinez would purchase the cocaine and give it to Pluff in Chicago; she would then travel to St. Paul, Minnesota, where she distributed her drug supply to her regular customers. Pluff recalled that the cocaine came from Garcia approximately half of the time, and that she was able to tell when Garcia “fronted” the cocaine to Martinez because there was typically not much urgency about re-paying the source. By contrast, when Martinez received cocaine from his other major supplier, Jose Paz or “Pep,” payment was expected as soon as possible. According to Pluff, “When it was coming from Pep, I had to be back right away and when it was coming from Pedro [Martinez would] say, “You can take your time; you got two days,’ because it was coming from Pedro.”

Garcia’s Indictment and Guilty Plea

Following his arrest in October of 1992, Garcia was indicted by a federal grand jury, with his son Jose, on charges stemming from the sale of cocaine to Dieppa. As noted above, Dieppa was cooperating with law enforcement officials at the time of this transaction. The indictment charged father and son with conspiracy to distribute cocaine, in violation of 21 U.S.C. § 846 (Count I), and distribution of cocaine, in violation of 21 U.S.C. § 841(a)(1) (Count II). At their arraignment late in 1992, both defendants entered pleas of not guilty to these charges.

On March 31, 1993, the grand jury returned a superseding six-count indictment against Pedro and Jose Garcia. Count I of the superseding indictment, like its counterpart in the original indictment, charged that the Garcias had conspired with each other and with others to distribute cocaine, in violation of 21 U.S.C. § 846. However, the conspiracy charged in the superseding indictment was much broader in scope, extending from the fall of 1987 through October 28, 1992. Count VI of the superseding indictment was identical to Count II of the original indictment; it charged the Garcias with distribution of one kilogram of cocaine in late October of 1992 (the sale to Dieppa). On July 19, 1993, both defendants pled guilty to Counts I and VI of the superseding indictment. As part of the plea agreement, the government dismissed Counts II-V, which charged Pedro Garcia with additional drug-related offenses.

The Sentencing Reaving

Garcia senior was sentenced by the United States District Court for the Northern District of Illinois after a hearing conducted July 8 and August 5, 1994. Two witnesses, Joseph Dieppa and Cynthia Pluff, testified for the government. Prosecutors also introduced exhibits seized from the defendant’s apartment and office, stipulations regarding those exhibits, and transcripts of telephone conversations between Garcia and Dieppa recorded in the month preceding the defendant’s arrest.

The district court made the following finding:

I [have] had time to evaluate the testimony of Mr. Dieppa and Miss Pluff, and, while I recognize that they are hardly models of virtue or pillars of the community in their backgrounds and indeed in the dealings that they’ve discussed, the Court did find them credible on the issue of the continuance of the conspiracy and to some extent the amount of kilograms that were involved.
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As I said earlier, I’m reluctant to go to the full number of kilograms — these people are estimating — over a long, long period of time, now some almost seven years ago. For starters, and the Court is satisfied it’s clearly more than SO, but, taking all of this thing and adding it all up and coming out with 203, I’m just not disposed to say that’s the proper range.
So I don’t know the exact amount, but I’m going to find that it’s less than 150 kilograms of cocaine. But it was very substantial. The Court accepts the testimony of these two people on this issue.

As determined by the court (and disputed by the appellant), the total quantity of cocaine involved in Garcia’s course of drug-dealing was between 50-150 kilograms. This gave Garcia a base offense level of 36. Because of his role in the offense of conviction (as an organizer or leader) and his use of a gun, he was assigned an adjusted offense level of 40. He fell within criminal history category I. Therefore, the court could have sentenced him to between 292-365 months in prison. The sentence actually imposed by the district court (292 months or slightly more than 24 years) was at the lower end of this range.

ISSUES

Garcia appeals his sentence. Specifically, he challenges the district court’s finding, set forth above, that the total amount of cocaine attributable to him was between 50-150 kilograms. Garcia first argues that he should not be sentenced on the basis of testimony by Dieppa and Pluff because these witnesses are inherently unreliable. Additionally, Garcia argues that the court defined the scope of his “relevant conduct,” for sentencing purposes, too broadly. In other words, even if the testimony of Pluff and Dieppa were credible, the transactions to which they testified were not part of the “same course of conduct” as the offense of conviction and it was therefore improper for the court to consider them in calculating a base offense level.

DISCUSSION

I. Reliability of Testimony at Sentencing Hearing

The first prong of Garcia’s attack is on the reliability of Pluff and Dieppa, whose testimony provided the basis for the court’s findings. Garcia contends that these witnesses are inherently unreliable because (1) they each have criminal records, (2) they each testified in exchange for lighter sentences (stemming from other charges), and (8) there are discrepancies between the testimony of Pluff and Dieppa and between Dieppa’s testimony and the government’s pre-sentence investigation report (“PSI”). The appellant also argues that Pluff is not reliable because much of her testimony was hearsay and because she was a heavy marijuana user at the time of her association with Martinez and Garcia.

A Standard of Review

In establishing factors that determine the base offense level, the government is only required to prove such factors by a preponderance of the evidence. United States v. Hatchett, 31 F.3d 1411, 1418 (7th Cir.1994) (citations omitted). The standard of review in such cases is a deferential one. This court has consistently held that factual determinations in the sentencing context will be reversed only for “clear error.” United States v. Montgomery, 14 F.3d 1189, 1196 (7th Cir.1994); United States v. Cedano-Rojas, 999 F.2d 1175, 1179 (7th Cir.1993). A finding of fact is clearly erroneous and will be disturbed by this court “only if, after reviewing the entire evidence, we are left “with the definite and firm conviction that a mistake has been committed.’ ” United States v. Herrera, 878 F.2d 997, 1000 (7th Cir.1989) (quoting Anderson v. City of Bessemer City, 470 U.S. 564, 574, 105 S.Ct. 1504, 1511-12, 84 L.Ed.2d 518 (1985)).

The reasons for this deferential standard of review are well-established. Congress has mandated this standard of review in sentencing and stated that “the court of appeals shall give due regard to the opportunity of the district court to judge the credibility of the witnesses, and shall accept the findings of fact of the district court unless they are clearly erroneous and shall give due deference to the district court’s application of the guidelines to the facts.” 18 U.S.C. § 3742(e) (emphasis added). As a matter of sound jurisprudence, we do not second-guess the sentencing judge because he or she has had

the best ‘opportunity to observe the verbal and non-verbal behavior of the witnesses focusing on the subject’s reactions and responses to the interrogatories, their facial expressions, attitudes, tone of voice, eye contact, posture and body movements,’ as well as confused or nervous speech patterns in contrast with merely looking at the cold pages of an appellate record.

United States v. Tolson, 988 F.2d 1494, 1497 (7th Cir.1993) (quotation omitted).

On numerous occasions, we have held that the clearly erroneous standard applies to estimates of drug quantities made for sentencing purposes because “the district court, as the trier of fact, not only has the authority but is in the best position to determine the amount of narcotics attributable to the [defendant].” Id. at 1502; see also United States v. Ferguson, 35 F.3d 327, 333 (7th Cir.1994), cert. denied — U.S. -, 115 S.Ct. 1832, 131 L.Ed.2d 752 (1995); United States v. Robinson, 30 F.3d 774, 785 (7th Cir.1994); United States v. Mumford, 25 F.3d 461, 476 (7th Cir.1994).

B. Credibility of Government Witnesses

This court has noted that a convicted defendant “has the right to be sentenced on the basis of accurate and reliable information” and that looser evidentiary standards at sentencing “are in some tension with that right.” United States v. Beal, 960 F.2d 629, 634 (7th Cir.1992), cert. denied — U.S. -, 113 S.Ct. 230, 121 L.Ed.2d 166 (1992) (citation omitted); see also United States v. Westbrook, 986 F.2d 180, 182 (7th Cir.1993). Nevertheless, we are not empowered to disturb factual determinations in the sentencing context unless clear error has been committed. Beal, 960 F.2d at 632.

To buttress his claim that the government’s witnesses are unreliable, Garcia cites the criminal background of both Pluff and Dieppa. Garcia makes much of the fact that Pluff is a convicted felon who has admitted to being a prostitute and a large-scale drug dealer, and also argues that Dieppa’s criminal activity makes him untrustworthy. The criminality of Pluff and Dieppa, while a consideration for the fact-finder, does not by itself establish unreliability. The sentencing judge acknowledged that Pluff and Dieppa were “hardly models of virtue or pillars of the community,” but found them credible nonetheless. Garcia

might prefer a rule requiring all government witnesses to be pillars of their communities, ... [but] in this imperfect world, a litigant must often take the witness as he or she is, imperfections and' all. We cannot expect that witnesses will possess the credibility of people of the cloth, such as rabbis, [ministers], priests, and nuns.

United States v. Rose, 12 F.3d 1414, 1425 (7th Cir.1994).

Similarly, the witnesses’ motives for testifying do not render their testimony inherently unreliable. As this court has explicitly stated, such arguments are “wasted on an appellate court” because questions of credibility are solely for the trier of fact. United States v. Molinaro, 877 F.2d 1341, 1347 (7th Cir.1989); see also United States v. Ferguson, 35 F.3d 327, 333 (7th Cir.1994), cert. denied — U.S. -, 115 S.Ct. 1832, 131 L.Ed.2d 752 (1995) (“district court’s evaluation of witness credibility will not be disturbed unless it is completely without foundation”). In fact, a district court is entitled to credit even testimony that “is totally uncorroborated and comes from an admitted liar, convicted felon, large scale drug-dealing, paid government informant.” Molinaro, 877 F.2d at 1347 (quotation omitted).

To impugn the reliability of the government witnesses further, Garcia emphasizes alleged “discrepancies” between the testimony of Pluff and Dieppa, citing, for example, differing statements on what type of packaging Garcia used for cocaine and what sort of payment deadlines he insisted on when “fronting” cocaine. These “discrepancies” are, in the first place, not necessarily discrepancies at all. It is possible that Garcia used different packaging on different occasions as well as for different customers and that he required immediate re-payment from certain customers while allowing others more time for payment. Furthermore, although the statements of the two witnesses did not match perfectly, their testimony was, as the district court observed, consistent “to the extent it brushed across common lines.” At the close of the hearing, the sentencing judge concluded: “I thought the government’s witnesses were largely credible and were corroborated on important matters that gave me confidence in the fact that they were telling the truth.” One example of such corroboration comes from the witnesses’ testimony concerning Garcia’s methods of packaging cocaine. While each witness described packaging methods that the other did not (hence the alleged “discrepancy”), both witnesses recalled that the defendant dealt cocaine packaged by the half-kilogram in perfume boxes. As noted by the government in its brief, this method of packaging “is nothing if not distinctive.” This common aspect of the witnesses’ testimony was further corroborated by the introduction into evidence of a perfume box discovered in Rudy Martinez’s apartment.

The appellant also points to discrepancies between Dieppa’s testimony and statements in the PSI. Dieppa testified that he kept no records of his drug-dealing activity and that the defendant, Garcia, kept no drugs in his office. Dieppa’s testimony contradicts the PSI on both of these points. However, these discrepancies are irrelevant because (a) the record does not reflect that the court relied on the PSI in determining the drug amounts attributable to Garcia, and (b) the court did not incorporate, refer to, or adopt the challenged portions of the PSI. The sentencing judge made an indirect reference to the PSI by saying that he thought the probation officer “got it exactly right” when he calculated a base offense level of 36. However, it is clear from the judge’s statements that he arrived at this figure independently, extrapolating drug amounts from the testimony of Dieppa and Pluff. The judge described this testimony as largely “credible on the issue of ... the amount of kilograms that were involved,” noting the substantial consistency of the witnesses’ testimony and the fact that their statements were independently corroborated by physical evidence introduced at the sentencing hearing.

Finally, the appellant raises special concerns regarding the testimony of Pluff. As a preliminary matter, it is probably worth noting that the testimony of Dieppa — if credited, as it was by the sentencing judge — provides more than enough evidence to support a finding that Garcia’s drug-dealing encompassed between 50-150 kilograms of cocaine. See United States v. Cedano-Rojas, 999 F.2d 1175, 1180 (7th Cir.1993) (citation omitted) (testimony of a single witness, even one arguably biased against the defendant, is sufficient to support a finding of fact). Pluffs testimony, which concerns a comparatively small amount of cocaine, would be superfluous except that it tends to corroborate Diep-pa’s statements and therefore undermines the appellant’s claim of “inherent unreliability.” Notwithstanding the greater importance of Dieppa’s testimony, Garcia devotes considerable energy to an attack on Pluffs credibility.

First, the appellant complains that much of Pluffs testimony was hearsay, a point emphasized by counsel for Garcia at oral argument. In making a sentencing determination, however, the trial court “may consider relevant information without regard to its admissibility under the rules of evidence ... provided that the information has sufficient indicia of reliability to support its probable accuracy.” U.S.S.G. § 6A1.3. Consistent with the Sentencing Guidelines, we have held that a defendant must “have a reasonable opportunity to rebut contested hearsay” and that the contested hearsay must be “rehable.” United States v. Beal, 960 F.2d 629, 634 (7th Cir.1992) (citation omitted). Here, Garcia had ample opportunity to cross-examine Dieppa and Pluff at the sentencing hearing, bringing to light their ' criminal backgrounds, their cooperation with the government, and other factors that may have affected their credibility. As mentioned by the district court judge, the reliability of that testimony was indicated by points of similarity between Pluffs testimony and Dieppa’s (discussed supra). We emphasize that the reliability of hearsay testimony in this context is a determination best left to the sentencing judge, who will only be reversed if he abused his discretion in making that determination. United States v. Francis, 39 F.3d 803, 810 (7th Cir.1994).

A second concern of the defendant Garcia with Pluffs testimony was that she admitted to being a “heavy marijuana user” at the time she was running drugs for Rudy Martinez. Garcia cites United States v. Beler, 20 F.3d 1428 (7th Cir.1994) for the proposition that testimony of drug addicts should be subjected to a higher level of scrutiny than would ordinarily apply in sentencing. However, the factual scenario in Beler is quite dissimilar to the instant case. In Beler, a government informant named Covington (a cocaine addict, not a marijuana user) presented two affidavits and oral testimony, each of which contained different versions of the amount of cocaine Covington had purchased from the defendant, the length of time he had known the defendant, and other details. Covington’s drug use only compounded these problems with his testimony; accordingly, we held that his second affidavit was insufficient to support the district court’s calculation of drug quantity. In this case, by contrast, Pluffs testimony consists of a single, intemally-consistent statement, which is corroborated to some extent by Dieppa’s testimony.

C. Amounts of Cocaine Attributable to Garcia

In estimating the quantity of cocaine attributable to Garcia, the sentencing judge was entitled to rely on the government’s witnesses, weigh their testimony, and make any allowances he felt appropriate for their criminal background, lack of first-hand knowledge, or ulterior motives for testifying. We are of the opinion that the court did not commit clear error in finding these witnesses credible, nor did it err in extrapolating cocaine quantities attributable to Garcia from their testimony.

The sentencing judge was not pulling numbers out of the air when he determined that Garcia was responsible for transactions total-ling between 50-150 kilograms of cocaine. Dieppa’s testimony alone clearly provides a basis 'for determining that Garcia was responsible for at least 155 kilograms of cocaine dealing between 1987 and his arrest in 1992. The government asked Dieppa to estimate how much cocaine passed hands between himself and Garcia in connection with particular deals or during certain time periods. In response, Dieppa provided either a single number (e.g., 60 kilograms between late 1987 and December 1988) or a range of amounts (e.g., between 10 and 15 kilograms between late 1991 and March 1992). By taking the most conservative numbers from Dieppa’s testimony and combining them, one reaches a total of 155 kilograms. This figure does not include cocaine from the contemplated 25-kilogram deal between Dieppa and the Bejaranos in April of 1992 (half of which would ultimately have ended up with Garcia).

Similarly, PlufPs testimony established that Garcia was responsible for deals involving substantial amounts of cocaine. If Garcia did supply half of the cocaine distributed by Pluff during the nine month period she describes in her testimony, that amount would be roughly 45 kilograms (an average of 2.5 kilograms per week, multiplied by 36 weeks and then divided by 2). When added to the amounts testified to by Dieppa (155 kilograms, using the most conservative estimates provided by that witness), one arrives at a figure in excess of 200 kilograms of cocaine.

When asked about the amounts of cocaine attributable to Garcia, both Dieppa and Pluff provided estimates and not mathematically precise figures. We have held that relying on such estimates is an appropriate way for the district court to determine the quantity of drugs involved in an offense. United States v. Duarte, 950 F.2d 1255, 1265 (7th Cir.1991) (as long as “nebulous eyeballing” is avoided, “factual determinations under the Guidelines need not emulate the precision of Newtonian physics.”).

We also note that the district court approached and relied upon these estimates in a conservative fashion. The sentencing judge observed that Dieppa and Pluff were:

doing their best to reconstruct numbers, which extended over a long period of time, and while I don’t have much trouble with the credibility of these people, I do have some trouble with their ability to recall accurately all the different transactions that went on for [a lengthy period].

Accordingly, the judge announced that he would “err on the side of being conservative with the amounts” and arrive^ at the 50-150 kilogram range, well below the amounts actually suggested by the testimony.

II. Scope of “Relevant Conduct” for Sentencing Purposes

In addition to attacking the testimony which formed the basis for the district court’s sentencing determinations, Garcia challenges the breadth with which the court defined his “relevant conduct” for sentencing purposes. Under § 1B1.3 of the Sentencing Guidelines, the court is required to consider “relevant conduct” in calculating a base offense level. “Relevant conduct,” in a narcotics ease, includes “all ... acts and omissions that were part of the same course of conduct or common scheme or plan as the offense of conviction.” U.S.S.G. § lB1.3(a)(2). Thus, “Mon-duct that is not formally charged or is not an element of the offense of conviction may enter into the determination of the applicable Guidelines sentencing range.” U.S.S.G. § 1B1.3 cmt. 10 (background). According to the commentary that accompanies the Guidelines, this means that “in a drug distribution ease, quantities and types of drugs not specified in the count of conviction are to be included in determining the offense level if they were part of the same course of conduct or common scheme or plan as the count of conviction.” U.S.S.G. § 1B1.3 cmt. 10. As the appellant reminds us, “[a] question involving the interpretation of a Guidelines term ... is a matter of law subject to de novo review.” United States v. Cojab, 978 F.2d 341, 348 (7th Cir.1992). Whether the drug quantities testified to by Dieppa and Pluff should be considered relevant conduct, however, is primarily a factual inquiry. We have held that “[a] district court’s calculation of the quantity of drugs attributable to a defendant for purposes of sentencing is a finding of fact, which we review under a clearly erroneous standard.” United States v. Robinson, 30 F.3d 774, 785 (7th Cir.1994) (citations omitted).

The appellant claims that his relationship with Dieppa between 1987 and 1992 was “sporadic at best” and that the defendant’s acts during this time period were more in the nature of isolated transactions than a regular course of conduct or common scheme. The district court found otherwise, and we are obligated to review that finding deferentially. The federal sentencing statute declares that the court of appeals “shall give due deference to the district court’s application of the guidelines to the facts.” 18 U.S.C. § 3742(e) (emphasis added). Accordingly, “we will uphold a sentence so long as the district court correctly applied the Guidelines to findings of fact that were not clearly erroneous.” United States v. Duarte, 950 F.2d 1255, 1262 (7th Cir.1991).

We have previously held that the district court’s findings of fact were not clearly erroneous. Moreover, in light of our decisions interpreting § 1B1.3, we do not believe that the district court erred in its application of the Guidelines to the facts in this case. Whether Garcia’s early transactions were part of the “same course of conduct” as the offense of conviction (selling one kilogram of cocaine) “depends upon the similarity, regularity and temporal proximity of the incidents in question.” United States v. Cedano-Rojas, 999 F.2d 1175, 1180 (7th Cir.1993) (citations omitted). While it is at least arguable that the deals between Garcia and Dieppa lacked regularity and temporal proximity, most of the interruptions in the relationship were due to factors such as Garcia’s supply problems or Dieppa’s arrest. We have held that these kinds of involuntary breaks in a drug-dealing relationship do not prevent a court from finding a course of conduct. Id. at 1181 (interruption occasioned by supply problems); United States v. Nunez, 958 F.2d 196, 198 (7th Cir.1992), cert. denied — U.S. -, 113 S.Ct. 168, 121 L.Ed.2d 115 (1992) (interruption caused by arrest and imprisonment of buyer). Furthermore, we have held that a court may find a course of conduct even without regularity and temporal proximity, “when there is a ‘stronger showing’ of similarity between the offense of conviction and the uncharged conduct.” Cedano-Rojas, 999 F.2d at 1180 (citations omitted); see also U.S.S.G. § 1B1.3 cmt 9(B). To determine whether acts are sufficiently similar for purposes of § 1B1.3, “a court must look to the identity of the participants and their roles.in the events at issue, as well as the nature, structure and location of the allegedly related transactions.” Id. at 1181 (drug deals were “substantially similar” because they all took place in Chicago, involved large quantities of cocaine, and were structured such that the defendant “fronted” cocaine to buyers). Here, the cocaine deals described by the government’s witnesses may be considered part of the same course of conduct because of the strong similarities among them: most of the transactions involved the same parties (Garcia and Dieppa), whenever the defendant acted as supplier he would “front” the cocaine to his buyer, all of the deals took place in the Chicago area, and all of them involved large quantities of cocaine.

Two additional considerations buttress a finding that Garcia engaged in an ongoing course of criminal conduct, such that the aggregation of drug amounts for sentencing purposes is both fair and appropriate. First, there is the inescapable fact that Garcia freely and knowingly pled guilty to a conspiracy charge that covered the entire period 1987-1992, and thus included all of the transactions to which Dieppa and Pluff testified. Count I of the superseding indictment specifically charged that Garcia, as part of the conspiracy, “sold Dieppa in excess of 125 kilograms of cocaine, and purchased over 80 kilograms of cocaine from Dieppa” between 1987 and 1992. We have held that “those convicted of conspiring to violate the drug laws are criminally responsible for the total quantity of drugs in which the conspiracy they joined can reasonably be estimated to have dealt.” United States v. Campbell, 985 F.2d 841, 344 (7th Cir.1993) (quotation omitted). Thus, it can fairly be said that Garcia’s acts during this period were more than relevant conduct; they were, in fact, the offense of conviction.

Secondly, evidence other than Dieppa’s testimony confirms that the October 1992 sale was merely the latest in a long series of deals between Garcia and Dieppa. In recorded telephone conversations with Dieppa, Garcia alluded to the longstanding nature of their relationship several times, saying, for example: “Between you and me, we’ve never screwed up.” Garcia also told Dieppa that the price for this one-kilogram sale would be the same as for the last one. Dieppa’s testimony, the evidence introduced at the sentencing hearing, and Garcia’s plea of guilty (entered after full consideration and consultation with legal counsel) all point to an ongoing series of strongly similar transactions. We thus reject the appellant’s suggestion that only the one-kilogram transaction that led to his arrest may be considered “relevant” for sentencing purposes.

Finally, we address the appellant’s concern that the district court failed' to articulate sufficiently its reasons for finding the defendant responsible for a total amount of cocaine between 50-150 kilograms. The federal sen-téncing statute requires a sentencing judge to “state in open court the reasons for its imposition of [a] particular sentence.” 18 U.S.C. § 3553(c). We have held that “ ‘reasons’ means something more than conclusions.” United States v. White, 888 F.2d 490, 495 (7th Cir.1989). When a court aggregates drug quantities under the “same course of conduct” or aggregation rule, moreover, we have held that it “should explicitly state and support” its finding that the drug amounts considered as part of the same course of conduct “bore the necessary relation to the convicted offense.” United States v. Duarte, 950 F.2d 1255, 1263 (7th Cir.1991).

In this case, the court was only required to state that it found the witnesses’ testimony sufficiently credible to establish a course of conduct that encompassed at least 50 kilograms of cocaine. The sentencing judge need not have embarked on a lengthy discourse about the meaning of “same course of conduct” in order for his reasons to be clear. In short, we are satisfied with the court’s finding, set forth in his statement that the witnesses were “credible on the issue of the continuance of the conspiracy and to some extent the amount of kilograms that were involved.”

CONCLUSION

We are not left with a “definite and firm conviction” that the trial court was mistaken when it determined the amounts of cocaine attributable to the defendant for sentencing purposes. The district court did not commit error in relying on the testimony of Pluff and Dieppa, nor did it misinterpret the Sentencing Guidelines when it defined the scope of Garcia’s relevant conduct as it did. If anything, the court was conservative in reaching the 50-150 kilogram range. The court appears to have discounted the government’s estimates generously, evidently believing that the passage of time may have adversely affected the accuracy of the testimony. Considering the gravity of the crimes involved, the court was similarly generous in sentencing the defendant at the low end of the range established by the Sentencing Guidelines (292 months).

The sentence of Pedro Garcia is AFFIRMED. 
      
      . "Fronting” describes a transaction in which drugs are provided to a seller on credit, with the agreement that the seller will pay for the drugs with the proceeds from his sales.
     
      
      . Garcia owned a small business that provided insurance and tax-preparation services. According to the government's pre-sentencing report, he was the "financial wizard" of the Cuban community in Chicago.
     
      
      . The Bejaranos were arrested in Louisiana in late 1991 or early 1992 for an offense or offenses not disclosed by the record. The government granted immunity to Carlos Bejarano and promised a lighter sentence for Henry ("Juan") in exchange for Carlos' cooperation.
     
      
      . Counts II-IV of the superseding indictment charged that Pedro Garcia violated 21 U.S.C. § 841(a)(1) by possessing with intent to distribute more than one kilogram of cocaine in September 1989, October 1989, and November 1990, respectively. Count V charged that in December 1990, Pedro Garcia possessed with intent to distribute approximately 20 kilograms of cocaine, also in violation of 21 U.S.C. § 841(a)(1).
     
      
      . Jose Garcia was sentenced in October 1993 to sixty months in prison and five years of supervised release and ordered to pay a fine of $1,500.
     
      
      . Both Dieppa and Pluff were cooperating with the government in exchange for reduced sentences. Pluff testified that she had pled guilty to a drug conspiracy charge and would likely be sentenced to between 15-20 years if she did not cooperate with the government. By testifying at Garcia’s sentencing hearing and participating in an undercover investigation of prison officials, her sentence was reduced to l'k years. Dieppa, who had been facing a sentence of 14-18 years, was sentenced to 7 years in exchange for his cooperation with the government.
     
      
      . “Commentary in the Guidelines Manual that interprets or explains a guideline is authoritative unless it violates the Constitution or a federal . statute, or is inconsistent with, or a plainly erroneous reading of, that guideline.” Stinson v. United States, - U.S. -, 113 S.Ct. 1913, 123 L.Ed.2d 598 (1993).
     
      
      . As noted by the government at oral argument, discounting Dieppa’s estimates by % still yields a figure within the 50-150 kilogram range.
     