A jury convicted Charles Howard and Darren Green of distributing eight-tenths of a gram of crack cocaine to Eddie Lee Brown, a government informant, in violation of 21 U.S.C. § 841(a)(1) and 18 U.S.C. § 2. The conversations surrounding the defendants' procurement of the cocaine for Brown were covertly recorded and transcribed. Howard and Green contend that the transcript was riddled with inaccuracies and should not have been introduced at trial. Howard also challenges the district court's refusal to comply with the jury's request during deliberations for the transcript of a key witness' testimony and the sufficiency of the evidence against him. Green challenges the quantities of cocaine attributed to other transactions treated as relevant conduct for sentencing purposes. We affirm the convictions of both defendants, but vacate Green's sentence and remand for reconsideration of the drug quantities attributed to him.

In July or August of 1993, Eddie Lee Brown informed Carbondale police officer Chuck Shiplett (on assignment to the Southern Illinois Enforcement Group, a narcotics task force comprised of federal, state, and local law enforcement officials) that he could purchase crack cocaine from Darren Green. Brown himself had used crack cocaine, and had purchased small amounts of the drug from Green on twenty to thirty occasions. Green had told Brown that he obtained the cocaine from Charles Howard. Law enforcement officials agreed to have Brown attempt to make a purchase from Green and Howard.

In the early evening of August 31, agents dropped Brown near a group of housing projects in Carbondale known as the Elm Street projects, where Brown's aunt Willabelle Brown lived. Previously the agents had frisked him to make sure he had no drugs on his person and supplied him with $120 to purchase the crack. Brown proceeded to his aunt's residence and there met Darren Green and his uncle Donald Green. Donald Green then drove them all to the Carbondale Mobile Home Park, where Howard had a trailer. En route to the trailer, Brown gave Darren Green the purchase money; Donald Green gave him another $40 for a smaller purchase of his own. When they arrived, Green got out of the car alone and met briefly with Howard outside of Howard's trailer. Brown later testified that he saw Green hand Howard the purchase money. Green then returned to his companions, telling them that he had given Howard the money and that Howard had said he would have "your all shit" in twenty minutes. Aug. 31 Tr. 13. A moment later Green spotted an acquaintance, Melvin Foster, who invited them all to wait in his own trailer, not far from Howard's. They accepted the invitation. Eventually, Green left Foster's trailer and again met with Howard alone. When he returned, he delivered what was purported to be a "sixteenth" of crack cocaine (one-sixteenth of an ounce) to Brown and two "twenties" (small, $20 "rocks" of crack cocaine) to Donald Green. The others proceeded to smoke some of the crack Green had procured for Donald, but Brown abstained. With encouragement from Foster, however, Darren Green repeatedly urged Brown to share with them a portion of the cocaine he had purchased; Brown refused. An unhappy Darren Green and his uncle drove Brown back to his aunt's home. Brown proceeded immediately to the authorities and turned over the drug; he was again searched to ensure that he had not retained any of the narcotic or the purchase money for himself. Tests confirmed that the substance Brown had produced was 0.8 grams of cocaine base.

Brown testified at the defendants' trial, so the jury had the benefit of his first-hand account of the transaction. Brown was wearing a microcassette recorder and two transmitters throughout the transaction, and the resulting tape recording documented Brown's conversations that evening with Darren and Donald Green. Thus, Brown is heard counting out the purchase money to Green during the drive to the trailer, and Green is heard, following his first meeting with Howard, telling Brown and Donald Green that Howard would have the cocaine in twenty minutes. He is also heard in the course of the ensuing wait in Foster's trailer discussing his history of trafficking in narcotics with Howard.

In addition to this evidence, the jury heard the testimony of Carbondale police officer Scott Miller, who was one of six or seven people who conducted surveillance of the transaction. Miller observed Brown and the Greens arrive at the mobile home park and then saw Darren Green meet with Howard. He watched as Brown and the Greens retired to Foster's trailer, and later noticed Darren Green leave and return to Howard's trailer. Howard met Green at the door of the trailer and then the two met alone inside of a vehicle in which two women had recently arrived to visit Howard.

Clinton Wooley, a user of crack cocaine, testified that he had purchased the drug from Charles Howard on a number of occasions. He had also purchased crack from Darren Green on approximately five occasions. Like Brown, Wooley recalled Green saying that he obtained the cocaine from Howard.

Finally, Melvin Foster testified that when Brown and the Greens had visited his trailer on the day of the transaction, all of them had immediately begun smoking crack cocaine that Brown had brought with him. Foster insisted that he had not seen anything change hands between Darren Green and Brown.1

The conversations recorded on August 31, 1993 by virtue of the microphone hidden on Brown's person are, like so many covertly recorded dialogues, difficult to make out at times. The original transcript produced by the government to the defendants is thus rife with "inaudibles" and unidentified speakers. However, two weeks in advance of trial, the government produced a revised transcript in which much of the dialogue is clarified and the speakers are in most instances identified. The government reported that it had taken the prosecution team four twelve-hour days to make the corrections. Motion Hrg. Tr. 18. Both defendants sought in limine to exclude the revised transcript from trial, arguing principally that the tape recording itself was so garbled that use of the transcript would unduly invade the jury's factfinding province and prejudice the defendants. The defendants themselves never submitted a transcript of their own.

At the start of trial, Judge Gilbert heard the defendants' objections to the transcript and subsequently reviewed the tape and transcript himself during a break in the proceedings. After listening to portions of the tape, Judge Gilbert agreed that the conversations were difficult to follow, but saw nothing in the revised transcript that he could discern to be "clearly inaccurate or a fabrication." Motion Hrg. Tr. 32. Finding that the transcript would aid the jury (id. at 33), he overruled the defendants' objections and permitted the government to provide copies of the transcript to the jurors when the tape was played. He did, however, admonish the jury that the tape recording itself was the evidence of the conversations, not the transcript. Tr. 95.

Green argues on appeal that the audio tape was so difficult to comprehend that the defense could neither be expected to stipulate to the accuracy of the government's transcript nor prepare an alternate version. Nor could the jury, he reasons, be expected to decipher the tape and make an independent assessment of the transcript's accuracy. Green also points out that the government never presented any evidence as to how the identity of the speakers was determined for purposes of the transcript. Under these circumstances, he argues, the district court erred in permitting the jury to see the transcript. Although, as we have noted, Judge Gilbert did deliver cautionary instructions about the limited purpose of the transcript, his failure to do so "consistently," in Green's view, "compounded the harm" to him. Green Br. 18.

Howard argues more broadly that in the absence of a stipulation to the accuracy of the transcript or the submission by the defense of an alternate version, the district court may not, when the defense has objected to the accuracy of the government's version, permit the jury to see that version. In this case, Howard objected to several passages of the transcript in which his name is mentioned. Where, as here, the tape recording is lengthy and in many instances difficult to hear, Howard reasons, it is unrealistic to expect that the jury will merely use the transcript as an "aid" in determining whether it really was his name that was mentioned and what else the speakers actually said. Pragmatically speaking, he argues, the jury will simply yield its fact-finding function to the government and accept the representations of the transcript.

The district court enjoys broad discretion in determining whether to permit the use of written transcripts as an aid to the jury in listening to recorded conversations. E.g., United States v. Durman, 30 F.3d 803, 811 (7th Cir.1994), cert. denied sub nom. Castellanos v. United States, --- U.S. ----, 115 S. Ct. 921, 130 L. Ed. 2d 801 (1995); United States v. Doerr, 886 F.2d 944, 966 (7th Cir.1989). Conversations recorded covertly are often challenging to follow. In part this is due to the technological limitations of surveillance equipment. But there are other reasons for the difficulty that are inherent in human discourse. People unaware that their words are being recorded for posterity do not take care with their diction, mumble at times, and often speak over one another. Listening to these conversations, it is sometimes difficult to keep up not only with what is being said but who is saying it. When more than two speakers are involved, as is the case here, the challenge to the listener is all the greater. Written transcripts thus play a useful role in helping listeners to keep pace with the conversation when the tape is played at trial (when jurors do not have the opportunity to pause and replay the tape at will), to get an overall sense of the conversation, and to identify the critical portions of the tape.

In this case, Judge Gilbert listened to "quite a bit" of the tape recording and found that "[i]t is one of the more difficult tapes in following it because of everybody speaking at the same time...." Motion Hrg. Tr. 32. The jurors, he predicted would "have to be on their toes listening to everything at the same time." Id. at 33. "I dare say that my snap, crackle and pop court reporter would never be able to take all that down with everybody talking at the same time." Id. He therefore found it appropriate to permit the government to provide jurors with the revised transcript to use as an aid. We see no abuse of discretion in this assessment. The conversations that took place in Donald Green's automobile and in Foster's trailer at times involved up to five speakers, and our own review of the tape recording leads us to agree with Judge Gilbert that the jury would have had a difficult time keeping up with these conversations without the transcript.

Of course, as the defendants have aptly pointed out, the danger in using a written transcript is that the jury ultimately will ignore the real evidence of who said what--the tape itself--and rely solely on the transcript. When the tape is particularly difficult to decipher, this danger is perhaps most acute. The district court thus bears an obligation to make sure in the first instance that the tape recording is, within reason, intelligible. See United States v. Vega, 72 F.3d 507, 513 (7th Cir.1995) ("the trustworthiness of a recording is left to the discretion of the district court") (citing Durman, 30 F.3d at 811), petition for cert. filed (March 11, 1996) (No. 95-8299). A tape that is partially unintelligible may still be admitted unless the incomprehensible portions are so significant as to render the tape as a whole unreliable. United States v. Robinson, 956 F.2d 1388, 1395 (7th Cir.), cert. denied, 506 U.S. 1020, 113 S. Ct. 654, 121 L. Ed. 2d 581 (1992). But "[t]he inaudibility of a portion of a tape, which is generally audible, is relevant only to its weight, a jury question, not its admissibility." Id.

Although in this case, Judge Gilbert did not review the entire tape, he listened to significant portions, focusing particularly on passages where the government's revised transcript indicated that Howard's name ("Chuck") was spoken and where Howard's counsel insisted she could not hear it. Having done so, Judge Gilbert was satisfied that the tape, although difficult to decipher, was not unintelligible. Given that the matter was not brought to him until the trial was already underway, he was obligated to do no more. Having listened to the tape ourselves, we too are satisfied that the tape was not so unintelligible that a jury could not reasonably be expected to rely on it, rather than a written transcript, as the evidence of the recorded conversations.

Which brings us to the government's transcript. When objections are raised to the accuracy of any transcript that is to be supplied to the jury, the preferred procedure is for the judge to conduct a hearing and assess the accuracy of the transcript. United States v. Allen, 798 F.2d 985, 1003 (7th Cir.1986).2 But beyond making sure that the transcript is reasonably accurate, it is not the district court's job to resolve every dispute as to who said what on the tape. Rather, as we explained in United States v. Zambrana, 841 F.2d 1320 (7th Cir.1988):

Initially, the district court and the parties should make an effort to produce an "official" or "stipulated" transcript, one which satisfies all sides. If such an "official" transcript cannot be produced, then each side should produce its own version of the disputed portions. In addition, each side may put on evidence supporting the accuracy of its version or challenging the accuracy of the other side's version.

Id. at 1336 (quoting United States v. Llinas, 603 F.2d 506, 509 (5th Cir.1979), cert. denied, 444 U.S. 1079, 100 S. Ct. 1030, 62 L. Ed. 2d 762 (1980)). The transcripts with which we were concerned in Zambrana were English translations of recorded conversations spoken in Spanish. But its mandate applies here as well. See Robinson, 956 F.2d at 1395.

In this case, the parties did not stipulate to the accuracy of the government's revised transcript and neither defendant offered an alternate version as to any portion he disputed. We should note that Howard did propose to submit as his own version the government's first draft of the transcript, which he viewed as more favorable to him, but in view of the fact that this was merely the government's own preliminary transcript, it was within the district court's discretion to exclude it. Motion Hrg. Tr. 27. Green, on the other hand, suggests that it is unreasonable to expect him to have either stipulated to the accuracy of the revised transcript or prepared an alternate, given that the government's revisions were tendered to the defense only two weeks before trial. But taking into consideration the fact that the tape recording itself was but one hour long and had long been available to the defense, we do not think it unreasonable to expect the defendants to prepare any alternate within that time. See Zambrana, 841 F.2d at 1335. Most tellingly, neither defendant sought more time in which to prepare such an alternate.

Under these circumstances, we find no abuse of discretion in the district court's decision to permit the government to use its transcript at trial. Having heard the defendants' objections to the accuracy and reliability of the transcript, the district court had itself reviewed portions of the tape and compared it with the written transcript. The court found that "the government's second version is as accurate as a [transcript] can be knowing that there may be some interpretation between the tape and what's on the transcription, but that's what the cautionary instruction is for. And I do not see anything that the government has included in their second version of the transcription that is clearly inaccurate or a fabrication...." Motion Hrg. Tr. 32. Again, having reviewed the tape ourselves, we are satisfied that the revised transcript was sufficiently faithful to the tape that it could be tendered to the jury as an aid. The defendants were free to challenge the accuracy of that transcript before the jury as we indicated in Zambrana and as the district court itself apprised the defense here. Motion Hrg. Tr. 33. Indeed, it is worth noting that despite their complaints about the accuracy of the transcript, the defendants have not singled out any portion of that transcript on appeal that they believe to be inaccurate.

As should now be clear, we reject the defendants' contention that the tape was so difficult to hear that, in the face of defense objections, the transcript should have been excluded lest the jury rely on the transcript as the real evidence. The jury was given ample guidance as to the nature of the transcript. Before the tape was played for the jury, Judge Gilbert carefully explained to the jurors that the transcript was merely the government's representation of what was said on the tape, that it was being provided to them merely as an aid to assist them in listening to the tape, that they should listen carefully to the tape, that the tape rather than the transcript was the evidence, and that if their understanding of the tape diverged from the transcript, their own interpretation of the tape was controlling. Tr. 95. The judge repeated this admonishment in his final charge to the jury. R. 39 (Court's Jury Instr. No. 11). The tape was by no means so difficult to hear that the jury could not comply with this instruction, and we presume that it did. See generally, e.g., United States v. Butler, 71 F.3d 243, 252 (7th Cir.1995); United States v. Mohammad, 53 F.3d 1426, 1433 (7th Cir.1995). Green's suggestion that the court did not admonish the jury "consistently" enough on this subject is frivolous. At the outset of the trial, the court recited to counsel the instruction it would give (Motion Hrg. Tr. 28-29), and the record reflects no request by any party that he instruct the jury differently or more often that he did.3 Any error in this context would have to be plain for us to recognize it (see generally United States v. Kellum, 42 F.3d 1087, 1092 (7th Cir.1994)), and there was no plain error here.

We are troubled by one aspect of the transcript. Because among the various participants in the conversations recorded on the tape, only Brown and Foster testified, the jury did not have an evidentiary basis from which it could independently determine the identity of any speaker other than these two individuals. Only the transcript, which was not admitted into evidence, provided that information. Brown was not asked to identify particular speakers on the tape, nor was he even asked whether the transcript's representations as to the identity of the speakers was correct. This is a significant omission, and had either defendant objected below to the use of the transcript on this ground, we would consider the issue to be serious. In fact, however, our review of the record reveals that this point was never brought to the district court's attention.4 Short of plain error, therefore, the issue has been waived. Moreover, Green, who has raised this issue on appeal (Howard did not participate in any of the recorded conversations) does not identify any prejudice to him flowing from the lack of evidence on this subject. He does not, for example, claim that a particular remark attributed to him on the transcript was in fact made by someone else. Under these circumstances, we view any error in the use of the transcript, even if plain, to be harmless.*B. Sufficiency of the Evidence Against Howard

Howard was convicted of aiding and abetting Green in the distribution of the cocaine. He contends that the evidence was not sufficient to sustain this charge. He points out that Brown did not see where Green went when he left Foster's trailer to obtain the cocaine. Moreover, none of the surveillance officers who witnessed both of Green's meetings with Howard saw anything change hands on either occasion. Finally, when Green surrendered himself to the police, he identified not Howard but Robert Lewis, who lived in a trailer nearby Howard's, as his sole source of crack cocaine.

We must view the evidence in the light most favorable to the government, of course (e.g., United States v. Brown, 71 F.3d 1352, 1354 (7th Cir.1995)), and so viewed it is more than enough to sustain Howard's conviction. Whatever Green may have said to the authorities upon his arrest, to his friends he identified Howard as the source of the cocaine. For example, when Brown first met with Green that evening, he explained that he would have to go to Howard to obtain the crack. "Cause Chuck ain't comin back out. He's on house arrest so I got to go out there." Aug. 31 Tr. 3. As Brown drove with the Greens to the mobile home park, Green asked him: "Will you give me the money, so I can give it to Chuck man?" Id. at 5. When they arrived at the park, Green met with Howard in view of Brown as well as the surveillance officers. None of them could hear what the two men said to one another, and Officer Miller conceded it was possible that Howard told Green to obtain the cocaine elsewhere. Tr. 157. And yet Brown saw Green hand the money to Howard (Tr. 88, 112), and when Green returned to the car, he assured Brown that "I gave him ya' all money. He said come back twenty minutes, he have your all shit in twenty, you know Chuck ain't gonna fuck you all, man." Aug. 31 Tr. 13. During their wait for the cocaine, when Brown asked Green how long he had been selling for Howard, Green explained that he had "just started sellin' for Chuck," although together the two "owned" Elm Street, Green working one end and Howard the other. Id. at 30. Finally, when Green left Foster's trailer to pick up the cocaine, it was Howard that he was seen to meet with, not Lewis. Tr. 149-52. Thus, although none of the prosecution's witnesses actually saw Howard hand the cocaine to Green, Green's own words and the balance of the circumstances support the inference that Howard was indeed Green's source. Under these circumstances, the jury could reasonably conclude that Howard aided and abetted Green in the distribution of the cocaine.

C. Jury's Request for a Transcript of Testimony

Shortly after the jury began deliberating, it sent a note to the court requesting a transcript of Officer Miller's testimony. Miller's testimony had not yet been transcribed, and Judge Gilbert did not want to delay the jury's deliberations while a transcript was prepared; he also expressed some concern that providing the jury with a transcript might give undue emphasis to Miller's testimony. "Note from the Jury" Tr. 3-4.5 Over Howard's objection, Judge Gilbert therefore denied the request, explaining to the jury that a transcript was not available and that the jury should rely on its recollection of Miller's testimony. R. 37. Howard contends that the refusal amounted to an abuse of discretion. He emphasizes that Miller was a key witness because only he saw Green visit Howard's trailer to pick up the cocaine. Howard also argues that Miller's testimony "was confusing in nature and in need of review by the jury" because, at the time Miller was cross-examined, the defense was unaware that Miller had prepared a report of his surveillance on August 31st. Thus, although Miller was subjected to lengthy defense cross-examination about what he saw that evening, he was not tested as to the consistency between his report and his testimony at trial.6

It is well settled that the decision whether to comply with the jury's request for the transcript of a witness' testimony is one " 'purely within the trial court's discretion.' " United States v. Guy, 924 F.2d 702, 708 (7th Cir.1991) (quoting United States v. Keskey, 863 F.2d 474, 476 (7th Cir.1988)). The trial in this case lasted only two days, and although Howard argues that there may have been some "confusion" as to Miller's testimony, our own review of the record reveals the testimony to be fairly straightforward. Any questions raised by the late disclosure of Miller's report could, as Howard himself suggests, have been answered by asking that he be recalled to the stand. Howard Br. 12; see n. 6. Howard elected not to pursue that course, and we do not see how provision of the transcript would have helped the jury resolve any matters left lingering as a result. Under these circumstances, it was reasonable to expect the jury to rely on its own collective recollection of Miller's testimony. See Guy, 924 F.2d at 708.

When choosing the base offense level in a narcotics case, the district court must take into consideration not only the drug amounts involved in the offense of conviction, but any "that were part of the same course of conduct or common scheme or plan as the offense of conviction." U.S.S.G. § 1B1.3(a)(2) & comment. (n. 2); see United States v. Beler, 20 F.3d 1428, 1431 (7th Cir.1994). The government must establish the drug quantity for which the defendant is to be held accountable by a preponderance of the evidence. Id. Given its factual nature, the district court's calculation of the drug amount is a determination we review only for clear error. Id. We must be satisfied, however, that the calculation is based on reliable evidence; speculation and unfounded allegations will not do. Id. at 1432-33.

At trial, Brown testified that he had begun purchasing cocaine from Green "last year," i.e. the same year as the charged offense. Tr. 70. Brown explained that he became a customer of Green's because, during the summer of 1993, Green spent most of his time at the home of Willabelle Brown, whom Brown visited often. Tr. 70-71. Brown estimated that he had purchased $20 rocks from Green on approximately twenty to thirty occasions, "kind of." Tr. 67, 71. Brown did not indicate just how big a $20 piece of cocaine was, other than to say it was small. Tr. 67. Brown did make clear, however, that these previous purchases were for his own personal use and that he never sold crack cocaine. Id.

Clinton Wooley testified, as we noted earlier, that he had purchased cocaine from Green on at least five occasions during the previous fall and winter (in other words, after the August 31st transaction for which Green and Howard were indicted). Tr. 220, 225. Like Brown, Wooley bought "twenties" from Green, single rocks of cocaine that Wooley described as small. Tr. 220-21.

Based on this testimony, the probation officer made the following finding in her presentence report:

The total amount of cocaine base that is readily attributable to the defendant under the relevant conduct provision of the sentencing guidelines is 0.8 grams (distribution in the indictment), plus 0.5 gram[s] (purchased by Clinton Wooley), plus at least 2 grams (Darren Green's sales to Eddie Lee Brown). The minimum total amount attributable to Darren Green is at least [3.3] grams.

Green PSR at 4 para. 9.7 Use of this drug quantity resulted in a base offense level of 22 and a corresponding sentencing range of 41 to 51 months. Green objected to the calculation, contending primarily that any amounts he allegedly sold to Brown and Wooley on occasions other than the one charged in the indictment were too distant in time and location to be considered relevant conduct for purposes of section 1B1.3(a)(2).8 The district court overruled the objection and adopted the probation officer's calculation. Green was sentenced to the maximum term of 51 months.

Green contends on appeal that the evidence does not support the district court's finding that the other sales to Brown and Wooley were part of the same course of conduct or common scheme or plan as the 0.8 gram sale underlying the conviction.9 As he did below, Green argues that these other sales were not sufficiently close to the August 31st sale to be treated as relevant conduct. He adds that the August 31st sale, unlike the other purchases from Green that Brown and Wooley had recounted, was of a resale rather than a personal use quantity. He also attacks the testimony of Brown and Wooley as incredible, noting that both were admitted users of crack and that both were somewhat vague about when, how often, and how much cocaine they had purchased from Green. Finally, he points out that nowhere did either Brown, Wooley, or any other witness estimate, as the probation officer and the district court did, that the $20 rocks these two had purchased from Green weighed at least 0.1 gram apiece.

We find no clear error in the district court's decision to treat the additional sales to Brown and Wooley as relevant conduct for purposes of the guideline. The fact that these other sales took place at the Elm Street projects rather than the Carbondale Mobile Home Park and at times in 1993 other than August does not undermine the court's determination that these sales were part of the same course of dealing. All of the sales took place in the Carbondale area and in the months preceding and following the transaction for which Green was indicted. Green consistently identified Howard as the source of the crack he sold to Brown and Wooley. Green himself is heard to boast on the August 31 tape that he and Howard "owned" Elm Street. The sale that Green helped arrange on that date would thus appear to be part of an ongoing pattern of distributing crack cocaine that he obtained from Howard to residents and visitors of the Elm Street projects. The fact that the August 31st sale took place at the mobile home park is explained, as Green himself pointed out on tape, by the fact of Howard's house arrest as opposed to any break in the defendants' trafficking or their relationships with Brown, Wooley, and their other customers. Finally, the fact that on August 31 Brown purchased a relatively large amount of crack--a quantity large enough for resale--certainly made this transaction unique from Brown's point of view. Brown testified that he previously had bought only smaller quantities consistent with personal use. Tr. 71, 82-83. But there is nothing in the record suggesting that the quantity rendered the transaction unique from Green's point of view; whether Brown was purchasing the crack for his own use or to sell to others was immaterial to Green, who in either instance was paid up front in cash for the purchase. Compare United States v. Kipp, 10 F.3d 1463, 1465-66 (9th Cir.1993), with United States v. Snook, 60 F.3d 394, 395-96 (7th Cir.1995).

Despite our decision that the district court was correct in considering these other sales, the lack of an evidentiary basis from which one can reasonably infer the minimum quantity of cocaine Green distributed to Brown and Wooley on occasions other than that alleged in the indictment persuades us that Green's sentence must be vacated. Estimates of the drug quantities attributable to the defendant are permissible, of course, so long as they are based on evidence possessing sufficient indicia of reliability and not " 'nebulous eyeballing.' " United States v. Henderson, 58 F.3d 1145, 1151 (7th Cir.1995) (quoting United States v. Mumford, 25 F.3d 461, 467 (7th Cir.1994)); Beler, 20 F.3d at 1432-33; U.S.S.G. § 6A1.3(a). In this case, the probation officer arrived at an estimate of the total quantity of crack Green had distributed to Brown and Wooley by taking their own estimates of the minimum number of times they had purchased crack from Green and multiplying that figure by what she believed to have been the minimum quantity sold on each occasion. Her approach is one that we previously have deemed acceptable. E.g., United States v. Clay, 37 F.3d 338, 344 (7th Cir.1994); Beler, 20 F.3d at 1434. The problem here lies in the fact that although Brown and Wooley each testified that they typically purchased $20 rocks from Green, neither revealed just how much such a rock typically weighed. Drug quantities can, of course, be extrapolated from the amount of money used to purchase the drugs (e.g., Henderson, 58 F.3d at 1153; United States v. Rivera, 6 F.3d 431, 446 (7th Cir.1993), cert. denied, --- U.S. ----, 114 S. Ct. 1098, 127 L. Ed. 2d 411 (1994); see also U.S.S.G. § 2D1.1 comment. (n. 12)), but the record here contains little evidence from which we might surmise how much crack $20 would have gotten Brown and Wooley on the streets of Carbondale in 1993. None of the testifying police officers, for example, provided that information. We do know that on August 31st, the $120 authorities had given Brown netted 0.8 grams of crack. Using that purchase as a benchmark, we might surmise that $20 would have translated into 0.133 grams of the drug. The probation officer's assumption that each purchase involved only 0.1 grams appears fairly conservative against that backdrop. We do not know, however, whether the smaller quantities of cocaine Brown and Wooley purchased on other occasions would have been sold at the same price per gram or tenth of a gram as the larger quantity Brown obtained at the behest of the government.10 Indeed, the presentence report does not itself make clear whether the probation officer based her 0.1 gram estimate on the August 31st transaction or on something else altogether.

Where either the probation officer or the prosecution offers an estimate of the drug quantities for which the defendant should be held responsible, the defendant ought to be on notice of all assumptions, rationale, and methodology underlying the calculation. Here it is not apparent why the probation officer assigned a weight of 0.1 gram to each of the purchases Brown and Wooley had made from Green. Without this information, the defendant, in assessing the accuracy of the proffered estimate, can only speculate as to the basis for it. Because it is the government's burden to establish the drug quantity, we do not think the defendant should be placed in this position. For that reason, we decline the government's invitation to simply take judicial notice on appeal that no quantity smaller than 0.1 gram could have been purchased by either Brown or Wooley. Regardless of whether we are well versed enough in the facts of narcotics trafficking to make that determination (and we are not), the time for taking such notice is at sentencing, when the defendant has the opportunity to challenge it.11

It may well be true, as the government has argued, that the probation officer's calculation was conservative to the point of generosity to Green. But absent a reliable evidentiary basis supporting the probation officer's assumption as to the amounts Brown and Wooley were able to purchase from Green for $20, we are unwilling to rest on speculation. Cf. Henderson, 58 F.3d at 1152 ("The court could not appropriately choose a random number simply because it believed more drugs were involved than the sales indicated."); United States v. Sepulveda, 15 F.3d 1161, 1198-99 (1st Cir.1993) (district court erred in calculating total drug quantity using "average" drug purchase derived from witness' sweeping generalities as to minimum and maximum amounts involved), cert. denied, --- U.S. ----, 114 S. Ct. 2714, 129 L. Ed. 2d 840 (1994). The Sentencing Guidelines impose stiff penalties on distributors of crack cocaine, with the offense level rising in many instances with each gram of this particular narcotic. See U.S.S.G. § 2D1.1(c)(8)-(14). In this context, tenths of a gram do make a difference. See Sepulveda, 15 F.3d at 1198. Recall that Green was deemed responsible for 3.3 grams; had the total come to 2.9 grams, his offense level would have dropped to 20 (sec. 2D1.1(c)(10)) and the high end of the resulting sentencing range (41 months) would have been ten months less than the term he received.

On remand, it will be the government's responsibility to proffer some evidentiary basis from which a reasonable and reliable estimate may be made of the amounts Brown and Wooley purchased from Green on the other occasions. Green, of course, will have the opportunity to challenge that evidence and to present any of his own on this subject. Whether Brown and Wooley were credible in their estimates as to the number of times they purchased cocaine from Green is a matter for the district judge, who heard their testimony first-hand. See Clay, 37 F.3d at 344; United States v. Robinson, 30 F.3d 774, 787 (7th Cir.1994).

The convictions of Green and Howard are AFFIRMED. Green's sentence is VACATED and his case REMANDED to the district court for further proceedings consistent with this opinion.