#### UNITED STATES of America, Plaintiff-Appellee, v. Anthony A. SMITH, a/k/a Tony Montana, Kenneth D. Collins, a/k/a Kent, Gregory A. Collins, a/k/a Tony, a/k/a T.C., a/k/a T, Sylvia A. Lipson, a/k/a Sylvia Lipscomb, Defendants-Appellants.

Nos. 92-1877, 92-1924, 92-1983, and 92-2397.

United States Court of Appeals, Seventh Circuit.

Argued* Sept. 14, 1993.

Decided June 14, 1994.

Rehearing and Suggestion for Rehearing En Banc Denied Aug. 16, 1994.

*742James Porter, Asst. U.S. Atty., Crim. Div., Fairview Heights, IL, for U.S.

William C. Evers, III (argued), Collinsville, IL, for Anthony A. Smith.

Paul M. Storment, III (argued), Belleville, IL, for Kenneth D. Collins.

Robert H. Rice, Belleville, IL, for Gregory A. Collins.

Richard Black (argued), East St. Louis, IL, for Sylvia A. Lipson.

Before CUMMINGS and COFFEY, Circuit Judges, and ZAGEL, District Judge.**

*

 The appeal of Gregory A. Collins was submitted on the brief due to the death of his attorney.

**

 The Honorable James B. Zagel, District Judge for the Northern District of Illinois, is sitting by designation.

ZAGEL, District Judge.

On 17 July 1991, in a fifteen-count superseding indictment, a federal grand jury charged ten defendants with crimes arising from their concerted efforts to sell cocaine and crack cocaine from November 1987 through 31 March 1991 in St. Clair County, Illinois. Five of the ten went to trial: Gregory Anthony Collins, Kenneth Dale Collins, Sylvia Ann Lipson, Anthony Angelo Smith, ■and LaDatril Chevelle Spraggins. The others — Clifford Douglas, Marlon B. Mason, Mark Steven Nicholson, Andrea Ward, and Montuella F. Wright — pleaded guilty, and all testified against their alleged co-conspirators.

*743The jury acquitted LaDatril Spraggins. Anthony Smith was convicted of the only count against him, Gregory Collins was convicted on four out of six, and Kenneth Collins was convicted on one out of two. The trial judge imposed at least one sentence of life imprisonment on each of these defendants. The jury convicted Sylvia Lipson on both counts against her, and she received a custodial sentence of thirty years plus five more of supervised release.

Each convicted defendant now claims, as a matter of law, that the Government failed to prove guilt beyond a reasonable doubt. In addition, each asserts that one or more errors in the court below warrant re-sentencing or a new trial. One issue, concerning jury prejudice, cuts across all of the appeals. We will leave this issue for last.

Appeal of Gregory Anthony Collins, a/k/a “Tony,” a/k/a “T.C.,” a/k/a “T”

The jury convicted Gregory Collins of conspiring to distribute and to possess with intent to distribute cocaine and more than fifty grams of cocaine base (“crack”), 21 U.S.C. §§ 841(a)(1), 846; engaging in a continuing criminal enterprise by distributing and possessing with intent to distribute cocaine and cocaine base in concert with at least five others, 21 U.S.C. §§ 841(a)(1), 846, 848; employing a person under age eighteen to traffic in cocaine and cocaine base, 21 U.S.C. § 861; and money laundering, 18 U.S.C. § 1956(a)(l)(B)(i). For each of the first three counts, Collins drew a sentence of life imprisonment; he drew a concurrent custodial sentence of twenty years for money laundering. The jury acquitted him of one count of possession of cocaine base with intent to distribute, 21 U.S.C. § 841(a)(1), and one count of money laundering, 18 U.S.C. § 1956(a)(l)(A)(i).

Collins says the Government failed to prove his guilt beyond a reasonable doubt and that the district court erred in denying his motion for judgment of acquittal at the conclusion of the Government’s case. But that is all he says. He offers a conclusory assertion in a single paragraph without even identifying required elements that the Government failed to prove. In other words, he invites us to do precisely what we have repeatedly declined to do: “It is not the obligation of this court to research and construct the legal arguments open to the parties, especially when they are represented by counsel.” *United States v. Williams,*877 F.2d 516, 518-19 (7th Cir.1989) (citing cases). Collins has waived the issue.

He provides only a bit more argument for his claim that the trial judge erroneously disallowed sur-rebuttal testimony from his father, Sydney Collins. Gregory’s conviction for money laundering rested on proof that he had purchased a 1984 Chevrolet Corvette with proceeds from the sale of cocaine and crack cocaine. The Government presented evidence that Gregory and his sister, who actually purchased the car, lacked sufficient legitimate incomes to finance the purchase. During its case-in-chief, the defense responded by calling Sydney Collins, who testified that he had financed the transaction to the tune of $15,000 in cash.

Defense counsel asked Sydney where he got the money, and Sydney answered that he got it from his trash collection business:

> [Pjeople’s don’t like my cheeks and I have to have cash to be able to deal. I got a way of cashing cheeks when the money comes in and have cash on hand to make the payrolls and pay for fuel, gas, parts.

When asked how much cash he might have had on hand at any one time in the year 1989, Sidney Collins answered, “$100,000 in cash.” From there, the direct examination continued to explore the source of Sidney Collins’s cash reserves. He testified that his business received large payments from the City of East St. Louis and that he converted these sums to cash. He testified also that he received $34,000.00 in insurance benefits upon the death of his six-year old son in 1981, that he kept the money at home, and that he used $15,000.00 of that money to pay a fine owed by Gregory Collins in 1989 or 1990.

The Government called Internal Revenue Service Agent Sharon Buehrer in rebuttal. She testified that Sydney Collins’s tax returns showed negative adjusted gross incomes for the years 1985 through 1990, ex*744cept 1988 in which his adjusted gross income was $10,030. She also testified that Sidney Collins’s trash collecting business, MEG Corporation, had declared net losses with no indication of wages paid to employees in 1989 and 1990, despite receipts of $160,404.50 and $87,009.00 in each year respectively.

Gregory Collins wanted to recall his father in sur-rebuttal. The trial judge disallowed this because Sydney Collins had already testified about the source of the $15,000.00 he claimed to have advanced for the Corvette purchase. According to the offer of proof, if Sidney Collins had testified in rebuttal he would have established five points: (1) that he informed his tax-preparer of the $15,-000.00 Corvette purchase, although his tax returns do not reflect that transaction; (2) that in 1989, Gregory worked on the garbage truck and was paid from Sidney’s proceeds from the City of East St. Louis; (3) that receipts from the MEG Corporation totaled $160,404.50 in 1989; (4) that his tax returns did not reflect his cash-on-hand, which “carried forward from many sources;” (5) and that he had access to borrowed funds that would not have shown up on his tax returns and would have helped finance the Corvette transaction.

The first two points are irrelevant to explain how Sidney Collins had access to $15,-000.00 in cash in 1989. The third point merely repeats the testimony of the IRS Agent who testified for the Government in rebuttal. The fourth point, without more detail, adds nothing to Sydney’s testimony during the defendants’ case-in-ehief. The fifth point adds little; the offer of proof does not indicate that Sidney would have identified borrowed funds as his source of the $15,000.00, merely that Sidney had access to borrowed funds.

In any case, only abuse of discretion limits a district court’s authority to bar sur-rebuttal testimony, *United States v. Mitan,*966 F.2d 1165 (7th Cir.1992), and the judge ruled well within this parameter. Sidney Collins’s testimony on direct addressed the sources of cash available to him. The Government attempted to challenge that testimony by introducing evidence regarding Sidney Collins’s tax returns. Gregory Collins never suggested that his father could have rebutted the accuracy or authenticity of information from his tax returns. He merely wanted his father to supplement earlier testimony concerning his access to cash. Nothing prevented the defense from extracting everything Sidney Collins had to say on that subject during its case-in-ehief. District courts have authority to exercise reasonable control over the mode and order of presenting evidence so as to make the presentation of evidence effective for the ascertainment of truth and avoid needless consumption of time. *United States v. Chapman,*954 F.2d 1352, 1374 (7th Cir.1992), citing FRE 611(a). The trial judge did not abuse his discretion in exercising that authority here.

Appeal of Kenneth Dale Collins, a/k/a “Kent”

The jury acquitted Kenneth Collins of possessing cocaine with intent to distribute, 21 U.S.C. § 841(a)(1); 18 U.S.C. § 2, but convicted him of conspiring to distribute and possess with intent to distribute cocaine base in excess of fifty grams, 21 U.S.C. §§ 841(a)(1), 846. He argues that the Government characterized him as a heavy user who hung around drug dealers, but never proved that he joined the conspiracy.

Conspiracies present a greater danger than individual action because they, among other things, reduce the transaction costs of accomplishing criminal objectives. *United States v. Townsend,*924 F.2d 1385, 1394-95 (7th Cir.1991). Conspirators reduce their transaction costs by agreeing to organize what would otherwise be market transactions. *Id.,*citing Ronald Coase, *The Firm, the Market, and the Law*6-7 (1988). Joining a conspiracy involves joining in such an agreement.

Joining a distribution conspiracy does not require an agreement to distribute personally. For example, an agreement to further the conspiracy’s efforts to obtain drugs for distribution may constitute the type of cost-reducing agreement at which the law of conspiracy aims. *Townsend,*924 F.2d at 1394. See also *United States v. Young,*954 F.2d 614, 619 (10th Cir.1992) (joining a *745conspiracy to distribute marijuana does not require intent to personally distribute marijuana so long as defendant knowingly joined a conspiracy that has the objective and intent of distributing). The alleged co-conspirators’ conduct may be diverse and far-ranging, although it must be interdependent in some way. *United States v. Horn,*946 F.2d 738, 740 (10th Cir.1991). Moreover, the crime of conspiracy focuses on agreements, not groups. The Government need not prove with whom a defendant conspired, and failure to prove that a defendant conspired with every alleged co-conspirator is not fatal to the Government’s case. *Townsend,*924 F.2d at 1389. The Government must prove that the defendant joined the agreement, not the group. *United States v. Narvaez,*995 F.2d 759, 762 (7th Cir.1993).

“After a jury convicts, the question becomes whether any sensible person could find, beyond a reasonable doubt, that the defendant committed the crime.” *United States v. Brigham,*977 F.2d 317, 319 (7th Cir.1992). That burden is steep, more so because conspiracies, like other crimes, may be proved entirely by circumstantial evidence, *Townsend,*924 F.2d at 1390. Thus, if sensible jurors could infer, beyond a reasonable doubt, that a defendant shared a mutual purpose to achieve the conspiracy’s goals, the jury may convict. *Id.*at 1392-95 (discussing the limits of conspiracy law).

Anthony Davis testified that he met Kenneth Collins in August of 1988 and sold him an ounce of cocaine. Kenneth told Davis the ounce was for his brother, Gregory Collins, who wanted to check out the quality of Davis’s goods. The evidence at trial showed that Gregory was at the center of the alleged conspiracy, having distributed cocaine to most of his co-defendants for processing into crack and retail distribution. Kenneth subsequently told Davis that Gregory “liked the package” and wanted to purchase nine ounces — one quarter of a kilogram. He introduced Davis to Gregory, and, according to Davis, “[t]hat is when we started dealing.” Davis sold Gregory Collins the nine ounces he wanted, initiating a relationship that produced a series of wholesale level transactions between Gregory Collins and Davis and between Gregory Collins and Larry Miller, Davis’s associate “in charge of distribution.”1 There was no direct evidence that Kenneth Collins knew of these subsequent transactions.

Evidence of lesser calibre implicated Kenneth Collins as well. Illinois State Police Sergeant Gregory Fernandez participated in a surveillance operation outside Gregory Collins’s residence at No. 1 Kingston Drive in Belleville, Illinois on 12 August 1990. From a location across the street, Sergeant Fernandez saw Sylvia Ann Lipson and Gregory Collins pull into the front driveway of No. 1 Kingston Drive in a gray Audi. At the same time, Kenneth Collins arrived in a maroon Escort. Gregory and Kenneth ran upstairs to Gregory’s apartment. Kenneth came back down a couple of minutes later, went to the Audi, with Lipson in the driver’s seat, and handed her something he took from “his beltline or a pocket area high up.” Based on his training and experience, but without any explanation of the criteria he considered, Sergeant Fernandez testified that, in his opinion, the object Kenneth Collins handed Sylvia Lipson was cocaine. Kenneth Collins testified that it was a badminton birdie.

Special Agent Kenneth Etchison of the Drug Enforcement Administration also participated in the surveillance of No. 1 Kingston Drive. On 14 August 1990, he observed and photographed Kenneth Collins handing over a half-inch thick stack of currency to Gregory Collins. Later that same day, Et-chison observed Kenneth come down from Gregory’s apartment, approach a vehicle on the passenger side, stay there for a short time, return to the top of the stairs in the area of the apartment, return moments later with a beer in one hand and something *746cupped in the other that he delivered to the vehicle’s driver. Agent Etchison admitted that he had not seen what Kenneth held in his cupped hand, but based on his testimony the jury could reasonably have inferred that Kenneth was delivering drugs.

Of course, Kenneth could not have joined a conspiracy unless he knew about it. *Townsend,*924 F.2d at 1390. But the evidence showed that Kenneth’s brother, Gregory, who supplied Kenneth with cocaine, was the ringleader of this conspiracy, that Kenneth regularly received cocaine and crack cocaine from Gregory’s co-conspirators and distributors Andrea Ward2 and Montuella Wright3 and from Gregory’s supplier, Anthony Davis.4 A defendant cannot be convicted of conspiracy simply because he had close personal relationships with the conspirators. *United States v. White,*569 F.2d 263 (5th Cir.1978). But where such relationships exist, the defendant frequently obtained drugs from several co-conspirators, and appears to have run errands in furtherance of the conspiracy’s objectives, his knowledge of the conspiracy may be inferred. This amply supported inference, plus evidence that Kenneth Collins assisted the conspiracy by helping Gregory obtain his stock-in-trade, provided the jury with a sufficient basis for convicting Kenneth Collins of joining the conspiracy. See *United States v. Williams-Hendricks,*805 F.2d 496 (5th Cir.1986) (“when inferences drawn from the existence of a family relationship or ‘mere knowing presence’ are combined with other circumstantial evidence, there may be sufficient evidence to support a conspiracy conviction”).

The scope of his agreement is a different matter and goes to sentencing rather than conviction. The Government must prove sentencing factors by a preponderance of the evidence, *United States v. Rossy,*953 F.2d 321, 325 (7th Cir.1992), and we review a district court’s factual determinations on sentencing issues only for clear error, *United States v. Schuster,*948 F.2d 313, 315 (7th Cir.1991).

Sentencing in drug conspiracy cases depends primarily on the amount of drugs imputable to each defendant. While a conspiracy conviction does not depend on proof that the defendant conspired with each alleged co-conspirator, a defendant may not be held responsible for the total quantity of drugs distributed through an organization simply because he conspires with the organizer and knows the organizer runs a large-scale operation. *Narvaez,*995 F.2d 759, 763 (7th Cir.1993).

Under our precedents, “conspiratorial liability cannot exceed the scope of a defendant’s agreement to further criminal activity.” *United States v. Edwards,*945 F.2d 1387, 1396 (7th Cir.1991). Under the United States Sentencing Commission’s Guidelines, “those convicted of conspiracy may be sentenced only on the basis of acts committed in furtherance of the conspiracy that were reasonably foreseeable.” *Id.*These formulations illuminate each other in determining the base offense level for a drug distribution conspirator. “[T]he appropriateness of the base offense level turns on the quantity of drugs that was reasonably foreseeable to each defendant. This determination depends upon the scope of the conspiracy that each defendant entered into.” *Id.*at 1397. In other words, “[bjefore concluding that a given quantity of drugs was foreseeable for sentencing purposes, the district judge should make clear that he has considered the *747evidence of the individual’s agreement to join a conspiracy of the scope alleged by the Government.” *Id.*at 1399. Because eo-con-spirators do not necessarily enter into agreements of the same scope, the scope of each defendant’s agreement must be determined individually. *Id.*at 1400.

The trial judge sentenced Kenneth Collins to life in prison based on finding that “this conspiracy involved amounts greatly in excess of 15 kilograms of crack cocaine, and the amount that the Court finds was reasonably foreseeable by the Defendant Kenneth Collins was also in excess of 15 kilograms of crack cocaine.” This finding corresponds to a base offense level of 42. USSG § 2Dl.l(c)(l). The judge added two points for possession of a firearm during the course of the conspiracy5 and thus arrived at a total offense level of 44, which requires a life sentence.

The judge found that Kenneth knew of his brother’s affiliation with Montuella Wright, Mark Nicholson, and Andrea Ward, but made no finding that Kenneth knew of the scope of their activities or that he conspired with them directly. The judge found also, however, that Kenneth had first-hand knowledge of his brother’s attempt to purchase 15 kilograms of cocaine from Andrew Chambers, a paid confidential informant working for the Drug Enforcement Administration.

This finding seems clearly erroneous. During Chambers’s testimony, several tapes of conversations between him and Gregory Collins were played for the jury. Speaking of Kenneth Collins, the trial judge said, “His voice appears on tapes of the telephone conversations with Chambers. It was clear that the defendant knew who Chambers was and what those calls were about. They were the attempted sale to, or purchase by, Gregory Collins of 15 kilograms of cocaine.” We have found nothing in the record to support this finding. Chambers identified the voices on each tape played while he was on the stand and never once mentioned Kenneth Collins. And while it is possible that we have missed a needle in a haystack, we are emboldened in our conclusion that the evidence does not exist by the following: (1) the Government’s brief on appeal cites only to the judge’s finding on this point, rather than to the trial transcript; (2) in neither its sentencing memorandum nor its oral argument at the sentencing hearing did the Government suggest that Kenneth Collins participated in Gregory Collins’s attempt to purchase 15 kilograms of cocaine from Andrew Chambers; (3) the pre-sentence report contains no such finding.

Moreover, if the judge erred, the reason is obvious. While Chambers’s testimony indicated that only Gregory Collins’s voice appears on the tapes of conversation with him, other evidence suggested that Kenneth Collins’s voice appeared on a tape presented as evidence of a much more modest drug transaction between him and Marlon Crockett. Two defendants named Collins plus two tapes of drug transactions, mixed into fifteen days of testimony, seems like a recipe for confusion.

As the Government concedes in its brief, “[t]he most telling incident of [Kenneth’s] role in the conspiracy is the attempted purchase of 15 kilograms of cocaine from confidential informant Chambers.” That is so because all of the other evidence against Kenneth is consistent with his being Gregory’s errand boy and a user whose knowledge of the cocaine business in general and this conspiracy in particular may have been quite limited, making much less reasonably foreseeable to him than to the others. The district judge might well conclude that the truth is otherwise; we do not mean to preempt his role as fact-finder. But absent some indication of how the judge inferred Kenneth’s involvement in the 15 kilogram deal with Chambers, we think it best that he have an opportunity to reconsider the record and supplement his findings. We therefore vacate the sentence of Kenneth Collins and remand to the district court for further consideration.

Appeal of Sylvia Ann Lipson, a/k/a Sylvia Lipscomb

The jury convicted Lipson of conspiring to distribute and possess with intent *748to distribute, 21 U.S.C. §§ 841(a)(1), 846, and of establishing a drag manufacturing and storage operation, 21 U.S.C. § 866. She seeks reversal of the conspiracy conviction, arguing that the Government established nothing more than that Gregory Collins was her boyfriend. She rightly asserts that no court could tolerate such a basis for conviction.

But that did not happen here. Co-conspirator Montuella Wright testified that Lipson knowingly allowed Gregory Collins to store drags at her home. Other witnesses corroborated this. Wright also identified Lipson as a distributor for Gregory Collins, and testified that he obtained small amounts of cocaine for re-sale from Lipson and Anthony Smith up to seven times a day during March of 1989. Co-conspirator Clifford Douglas testified to purchasing cocaine from her. Lipson does not confront any of this testimony in her brief. It amply supports her conviction for conspiracy.

Lipson also charges the district judge with abuse of discretion in denying her motion to sever her trial from the trial of Gregory Collins. Without any citation to the trial transcript, she argues that the Government introduced “tapes on which conversations were made by Gregory Collins indicating that indeed a conspiracy to deliver drags may have taken place.” Since Gregory Collins asserted his Fifth Amendment rights, Lipson could not call him as a witness. Her sole citation in support of her argument, *United States v. Bruton,*391 U.S. 123, 88 S.Ct. 1620, 20 L.Ed.2d 476 (1968), makes clear that Lipson is alleging a violation of her Sixth Amendment right to confront witnesses against her.

Lipson’s argument fails on its face. She has not claimed that any evidence she complains of implicated her directly, but merely indicated the existence of a conspiracy. See *United States v. Briscoe,*896 F.2d 1476, 1501 (7th Cir.1990) *(Bruton*does not come into play unless a co-defendant’s extrajudicial statement directly implicates the defendant).

Next, Lipson argues the trial judge erred by not submitting her proposed jury instructions numbered 4, 5, 9, 10, and 14. According to Lipson, the jury needed these instructions to determine whether she had been coerced into the illegal actions with which she was charged. As evidence of the jury’s need for guidance, Lipson points to a question the jury asked the judge during deliberation:

> Your Honor, we need your assistance on interpretation of a point charged to willingness, Sylvia Ann Lipson. In your instructions definition of conspiracy first that the alleged conspiracy existed. Second that she was a willing participant. We feel she was a willing participant only because of love, fear, and concern for her children. We feel she was willing in much the same way one would be with a knife to their throat. Is this sufficient cause for reasonable doubt?

After reading this note to the lawyers, the trial judge suggested a “standard response:” “Ladies and gentlemen, the Court has furnished you with instructions, which when considered as a whole will provide the answer to our [sic] question. Please read these instructions carefully.” Lipson’s counsel agreed to this procedure, without objection.

We give the trial court substantial discretion in crafting the language of jury instructions, *United States v. Mitan,*966 F.2d 1165, 1177 (7th Cir.1992), and a defendant is entitled to a particular instruction only if failing to give it denies the defendant a fair trial, *United States v. Pedigo,*12 F.3d 618, 626 (7th Cir.1993). Here, the trial judge used this circuit’s Pattern Jury Instruction on conspiracy, No. 5.11, modified in light of *United States v. Caliendo,*910 F.2d 429, 433 (7th Cir.1990). In addition to instructing the jury that the Government must prove knowledge and intent, 5.11 instructs that “[t]he Government must prove beyond a reasonable doubt that [the defendant] was aware of the common purpose [of the conspiracy] and was a willing participant.”

Defendant’s proposed instruction No. 5 discusses the knowledge requirement only and is therefore irrelevant to the issue of coerced participation. Defendant’s proposed instruction No. 9 discusses intent primarily, but concludes with the sentence, “An act or failure to act is ‘knowingly’ done, if done *749voluntarily and intentionally, and not because of mistake or accident or other innocent reason.” This sentence seems more confusing than helpful and is inconsistent with Pattern Jury Instruction 6.04 (given by the trial judge), which defines “knowingly” without reference to intent or volition. Similarly, Defendant’s proposed instruction No. 10 defines “intentionally” as “knowingly, willfully and purposely,” thus threatening to create a confusing spiral of circular definitions. Defendant’s proposed instruction No. 14 addresses intent only and has nothing to do with Lipson’s claim of coercion.

The defendant’s proposed instruction No. 4 defines “willfully” as “voluntarily and intentionally and with the specific intent to do something the law forbids; that is to say, with bad purpose either to disobey or to disregard the law.” The definition can be found in Pattern Jury Instruction 6.03. But what does it add to the instructions given by the trial judge? The actual instructions informed the jury that the Government had to prove Lipson was a “willing participant” in the conspiracy. Lipson’s proposed instruction would have added, at most, that her actions had to be “voluntary.” Frankly, “willing participant” seems a more favorable locution for Lipson than “voluntary.” In any case, “voluntary” does not illuminate or clarify “willing participant” in such an obvious way that a trial judge’s refusal of this proposed instruction can be called “clear error.” Moreover, our pattern jury instructions expressly discourage trial courts from defining “willfully” for the jury unless the defendant has been charged under a statute containing that word precisely because “the concept of willfulness will be adequately explained in other instructions defining “knowingly,” “intentionally,” or “deliberately.” None of the statutory sections under which Lipson was charged contain the word “willfully,” and the elements of that concept are adequately contained in the pattern instructions given by the trial judge. See *Mitan,*966 F.2d at 1177 (the trial court may refuse a proposed instruction if the essential points are covered by those given). The judge’s rejection of her proposed instructions certainly did not deny Lipson a fair trial.

Finally, Lipson challenges her sentence. For reasons unknown to us, she was neither present nor represented at her scheduled sentencing hearing, and the transcript of whatever proceedings took place on that date has not been included in the record on appeal. The district court’s judgment against Lipson states that the trial judge “adopts the factual findings and guideline application in the presentence report.” The presentence report found that the conspiracy trafficked in more than 15 kilograms of crack cocaine and that Lipson’s involvement was sufficient to conclude that the conspiracy’s scope was reasonably foreseeable to her. Lipson’s written objections to this report were before the court prior to sentencing.

Lipson’s brief does not clearly state the basis of her sentencing appeal. To the extent that she believes the judge should not have sentenced her without a hearing, we point out that any right she had to an allocution or hearing under the Federal Eules of Criminal Procedure or the Sentencing Guide-fines, see *United States v. Cantero,*995 F.2d 1407, 1412-13 (7th Cir.1993), was lost by her failure to appear at the scheduled hearing and failure to request re-scheduling.

To the extent that Lipson believes the presentence report’s findings were clearly erroneous, she offers no argument or analysis to support this claim. In fact, the evidence that more than 15 kilograms of crack cocaine passed through the Collins distribution operation is overwhelming, so overwhelming that Gregory Collins has not challenged his sentence, and Kenneth Collins and Anthony Smith have challenged only the judge’s finding on the scope of their individual agreements. As for the scope of Lipson’s agreement, the presentenee report quotes from the Government’s sentencing memorandum:

> As to Sylvia, it was shown that she was a main source of storage for the cocaine. She was Gregory Anthony Collins’s girlfriend and accompanied him on various shopping sprees, dinner engagements, nights on the town and deliveries of cocaine. As such, it could hardly be argued that she was not aware of the scope and nature of the conspiracy of which she had *750been found to be a member. Because of the intimacy and the interrelationship between all of the members of this conspiracy, it could not be argued that these members were not aware of the scope, means and direction of the conspiracy. As such, all should be accountable for the entire amounts of drugs in this conspiracy.

While this finding seems a bit conclusory and vague given the individual sentencing requirements of *Edwards,*it actually stands on a strong evidentiary foundation.

Lipson not only had an intimate relationship with Gregory Collins, the conspiracy’s kingpin, according to Wright she was also a distributor who worked closely with him and Smith.6 Moreover, according to Clifford Douglas, who says he made numerous purchases from Lipson, she stored drugs for Mark Nicholson in her Belleville apartment, and the testimony of Sharon Wren7 and Erica Scott showed that Nicholson and Andrea Ward sold drugs supplied by Gregory Collins from a trailer owned by Sylvia Lip-son. Clifford Douglas testified that Nicholson’s daily revenue from drug sales was between $10,000 and $15,000 per day. Douglas also placed Lipson at a Halloween party in 1990, attended by him, Gregory Collins, Mark Nicholson, Montuella Wright, and Marlon Mason. In sum, the trial judge’s finding, adopted from the presentence report, that Lipson was so deeply involved and familiar with a closely knit conspiracy that her knowledge of its scope and agreement to participate fully may fairly be inferred cannot be called clear error.

Appeal of Anthony Angelo Smith, a/k/a Tony Montana

The grand jury charged Smith with just one count, conspiring to distribute and possess with intent to distribute, 21 U.S.C. §§ 841(a)(1), 846, and the petit jury convicted him of that charge. Smith challenges his conviction and sentence under a variety of theories.

A. Testimony of Anthony Davis

Anthony Davis, who supplied wholesale quantities of cocaine to Gregory Collins, testified that Smith sold cocaine for Collins out of Melina Miller’s apartment in Centreville. Smith argues that this testimony lacked foundation — that it was based on hearsay, rather than personal knowledge.

Smith’s lawyer had an opportunity on direct to object for lack of foundation, but waited until cross-examination to explore this issue. On cross, he asked Davis whether he had based his testimony on what someone else told him. Davis replied, “I seen him selling dope down there,” meaning at the Centreville projects. When counsel pressed for clarification, Davis said, “I seen people going to his house. You know what I am saying. He asked me about drugs a few times, but I never did deal with him.” No other conversation was mentioned during the cross-examination of Davis by Smith’s attorney.

Counsel nevertheless approached the bench and moved to strike portions of Davis’s testimony on direct because “[o]n cross examination he admitted that his knowledge of that was based upon what someone told him. That is testimony based on hearsay.” The trial judge denied the motion, stating that the jury could evaluate Davis’s testimony and that instructing the jury to disregard the earlier testimony would put the court in the position of commenting on the evidence. The motion merited denial on another ground. Davis had not admitted that his knowledge was based on hearsay. His testimony on cross indicates that based on having discussed drugs with Smith, whose out-of-court statements are not hearsay, and on observations of people going into Smith’s house, Davis, an admitted drug dealer, inferred that Smith was dealing inside. Smith’s motion to strike Davis’s testimony as hearsay was thus properly denied.

However, on re-direct, the Government attorney asked Davis how he knew Smith sold drugs, and Davis replied, “James Harris had a house in Centreville projects on one end, *751and Tony Montana on the other end, and they was selling drugs. James told me. I never knew the man sold drugs.” At this point, Smith’s lawyer said, “I’m going to renew my objection. He’s testifying to what someone else told him.” The judge agreed and sustained the objection. At that moment, counsel did not renew the motion to strike the earlier testimony on direct; he simply thanked the judge and sat down. His objection applied only to contemporaneous testimony — Davis’s statement that James Harris had told him Smith was dealing.

The next day, defense counsel did renew his motion to strike the testimony elicited from Davis on direct examination. The Government attorney argued “if the Court would at all entertain the motion [to strike], the proper way to do it would be to call Mr. Davis back to the stand and ask him questions to see if he does have the basis.” The trial judge denied Smith’s motion on finding that Davis’s testimony rested on sufficient foundation. We review a district court’s evidentiary rulings for abuse of discretion. *United States v. Briscoe,*896 F.2d 1476, 1490 (7th Cir.1990).

On direct examination, Davis’s testimony that Smith sold crack from his girlfriend’s apartment in the Centreville projects almost certainly rested on an insufficient foundation under FRE 602. Nor could FRE 701 have saved the testimony on direct, because Davis did not offer it in the form of an opinion or inference. But the defense did not object. And by the time defense counsel made a motion to strike, he had established, through his own questioning, that Davis had actually inferred Smith’s distribution activity based on conversations with Smith about drugs and Davis’s observations of traffic patterns in and out of Smith’s house. In other words, having set out to discover whether Davis’s testimony had a sufficient basis under FRE 602, defense counsel established that the proper test for the testimony was FRE 701.

FRE 701 allows non-expert witnesses to give “testimony in the form of opinions or inferences” when “those opinions or inferences [ ] are (1) rationally based on the perception of the witness and (b) helpful to a clear understanding of the witness’s testimony or the determination of a fact in issue.” The rule “places great reliance on a party’s ability to cross-examine an opponent’s witness and present any weaknesses in the witness’s testimony to the trier of fact.” *United States v. Allen,*10 F.3d 405, 414 (7th Cir.1993). The trier of fact can normally be depended upon — with the aid of counsel — to pick up the nonverbal signals which, although absent from the record, indicate fairly clearly when the witness is describing what he saw and when he is describing what he thinks happened; the trier of fact should also generally be depended upon to give whatever weight or credibility to the witness’ opinion as may be due.” *Id.,*quoting Jack B. Weinstein and Margaret Barger, 2 *Weinstein’s Evidence,*¶ 701 [02] at 701-32 (1993).

Under this liberal standard, Davis’s testimony was admissible. The judge might have instructed the jury to disregard Davis’s testimony on direct — phrased as a matter of perception — and consider only his testimony on cross — phrased as a matter of inference. But such commenting on the evidence might have been more confusing than helpful. Especially since the whole situation arose only because defense counsel failed to make a timely objection during direct examination, the judge certainly had no obligation to provide such commentary.

Davis’s testimony on re-direct does not affect the analysis. Davis testified that until James Harris told him Smith sold drugs, Davis had not known that he did. That does not contradict the inference, amply supported in Davis’s testimony on cross, that he also acquired an additional and independently sufficient basis for believing that Smith sold drugs: his conversations with Smith and his observation of traffic patterns at Smith’s house. Defense counsel had the opportunity to challenge the adequacy of these perceptions on cross-examination. While it may have been poor strategy, defense counsel could have asked what statements by Smith led Davis to believe Smith was selling drugs and could have asked for more precise accounts of the traffic patterns Davis observed at Smith’s house in Centreville.

Even if there had been an evidentiary error here, it would not require reversal in *752the face of the overwhelming evidence against Smith. The next section discusses this evidence in addressing Smith’s claim that the Government failed to prove its case.

B. Sufficiency of the Evidence

The testimony of Montuella Wright, Melina Miller, and Albert McClendon sufficiently supports Smith’s conspiracy conviction; Davis’s testimony simply frosted the cake. Wright, an indicted co-conspirator, identified all of the appellants as participants in a distribution operation headed by Gregory Collins. He specifically described Smith as a distributor for Collins. According to Wright, Gregory Collins introduced him to Smith in 1988—a meeting at which Collins provided Wright and Smith with cocaine to sell on the street. Wright testified that he saw Smith take his portion of the cocaine to a tree in Centreville, where he sold it off in amounts worth $10, $15, and $20. At the time, Wright was “trying to do the same, competing, having fun.” Later in the summer, Wright began acquiring larger quantities of cocaine, up to full ounces, in transactions in Chicago and East St. Louis that sometimes involved Collins and Smith together.

Then in December of 1988, Wright moved into Melina Miller’s residence, where both Miller and Smith resided. He did so at Gregory Collins’s request; Collins asked Wright to “watch over” Smith, whose use of cocaine had become an operational problem for the business. Wright’s mission was to control the flow of cocaine to Smith because Smith “had a very bad habit of smoking the cocaine he was supposed to be distributing at that time.” Nevertheless, when Smith’s attorney asked Wright whether Wright had been Collins’s “right hand man,” Wright testified that although he was “close” to Collins, perhaps Smith was even closer because he was “a better distributor of cocaine.”

In March of 1989, Wright acquired cocaine from Smith, Gregory Collins, and Sylvia Lip-son in an apartment at 128 Arlington, in Belleville, “five, six, seven times a day or whatever I needed.” Wright and Smith, “and every so often Mr. Gregory Anthony Collins,” would process crack cocaine together in that apartment. Wright also testified that when Collins was not there, he could transact business with Lipson or Smith.

Melina Miller testified that in April 1988 she had a romantic relationship with Smith, that he lived with her in Centreville, and sold drugs from her apartment. When asked whether Gregory Collins had a role in Smith’s dealing, Miller answered that Collins would “just come and drop off the stuff.” She confirmed that Wright lived there for a time with her and Smith. She never testified, as Smith now suggests, that he did not know there was cocaine in the apartment. She said that she was paid to babysit the cocaine and Smith did not know where in the apartment it was kept, a situation entirely consistent with Wright’s characterization of Smith as a distributor who consumed his own stock.

Albert McClendon testified that he met Gregory Collins and Smith simultaneously in 1988 in Melina Miller’s residence in the Cen-treville housing project and that Collins and Smith “had what you call a crack house in the back of the [Centerville] projects that they operated.” McClendon had been in that crack house on two or three occasions in December 1988, had seen Smith with various amounts of crack, and once saw Smith “cooking up” dope. He never saw Smith selling drugs in the apartment, but on two or three occasions he did see Smith working what McClendon knew to be a “crack strip where people pull over in the cars and they run up there and sell them crack.” From about two hundred feet away, McClendon could see Smith run up to cars along this crack strip and make hand-to-hand exchanges with people in the cars. He saw money pass in these exchanges; he could not see drugs, but he saw that something was being exchanged for the money each time and, given his familiarity with the area and his “street knowledge,” he recognized these exchanges as drug transactions.

Smith characterizes all this testimony as boiling down to “a lot of evidence of the Defendant Smith’s drug use and being around drug users” supplemented by answers that do not hold up under cross-examination. But the evidence makes it very clear *753that Smith was a distributor for Collins— indeed, a good distributor, but for his habit of smoking what he was supposed to sell, which is why Coffins asked Wright to move in with Smith and watch over him. A rational jury could easily have concluded beyond a reasonable doubt that Smith had joined the conspiracy as a distributor, perhaps Collins’s favorite.

C. Conspiracy Instruction

Moving on, Smith argues that the district court inadvertently instructed the jury on the elements for aiding and abetting rather than conspiracy because, in Smith’s view, the instruction refers to an agreement “only in terms of conduct.” The Government had not charged Smith with aiding and abetting. The district court gave Seventh Circuit Pattern Jury Instruction 5.11, modified in light of *United States v. Caliendo,*910 F.2d 429 (7th Cir.1990), and *United States v. Martinez de Ortiz,*907 F.2d 629 (7th Cir.1990) (en banc). This instruction states that “[t]he agreement may be inferred from all the circumstances and the conduct of all the alleged participants.” Pattern Jury Instruction 5.11 accurately states the law of conspiracy, including the required element of agreement. *United States v. James,*923 F.2d 1261 (7th Cir.1991). The court’s refusal to give defendant’s proposed instruction No. 6, which stated that “[t]he gist of the offense is a combination or agreement to disobey or disregard the law,” did not deny Smith a fair trial. See *Pedigo,*12 F.3d at 626. While the pattern jury instruction on conspiracy does not automatically assure a fair trial, the defendant’s proposed instruction in this case did not focus on a particular theory advanced by the defense, such as the distinction between a conspiracy and a buyer-seller relationship. Compare *id.*

D. Duplicity

“Duplicity” means, among other things, joining in a single count two or more distinct and separate offenses. *United States v. Orzechowski,*547 F.2d 978, 986 (7th Cir.1977). A guilty verdict on a duplicitous count does not reveal whether the jury’s verdict was unanimous with respect to either offense. Smith argues that Count II of the superseding indictment, the only count against him, was duplicitous because it alleged two conspiracies, one to possess with intent to distribute, and another to distribute crack cocaine.

Section 841(a)(1) of Title 21 of the United States Code makes it 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 846 of the same Title and subehapter makes it unlawful to attempt or conspire to commit “any offense described in this subchapter.”

Possession with intent to distribute and distribution are not separate offenses, but different acts that violate the same statutory provision. So long as the evidence is sufficient with respect to any of the acts charged — and it certainly is here — a guilty verdict on an indictment charging several acts in the conjunctive stands. *Orzechowski,*547 F.2d 978, 987 (7th Cir.1977).

E.The Prosecutor’s Closing Remarks

Still another issue raised by Smith concerns the Government’s closing argument. He claims that the prosecutor’s remarks denied him a fair trial and points to five statements that drew contemporaneous objections.

Our test for challenged prosecutorial statements has two parts. “First, we determine whether, considered in isolation, the challenged remark was improper. If so, we reexamine the improper remark in light of the entire record to determine whether the remark deprived the defendant of a fair trial.” *United States v. Jewel,*947 F.2d 224, 229 (7th Cir.1991), quoting *United States v. Swiatek,*819 F.2d 721, 731 (7th Cir.1987). In addressing the second issue, we consider (1) the nature and seriousness of prosecutorial misconduct; (2) whether impermissible conduct by defense counsel invited the prosecutor’s remarks; (3) whether the trial court instructed the jury to disregard the prosecutor’s improper statements; (4) whether the defense had an opportunity to counter the improper statements through rebuttal; (5) *754the weight of the evidence against the defendant. *United States v. Gonzalez,*933 F.2d 417, 413 (7th Cir.1991).

We will consider in turn each of the statements cited by Smith, but first, some general observations. Nothing in the record suggests flagrant misconduct. Thus, the first factor listed above weighs against finding that the prosecutor’s improper statements denied Smith a fair trial. The fifth factor also weighs against Smith; the Government, as we have seen in assessing the sufficiency of evidence, made a strong ease against him.

*1. [Anthony Davis] told us that he saw Anthony Angelo Smith, Tony Montana, sell drugs on the street.*

In closing, the Government attorney stated that Davis “told us that he saw Anthony Angelo Smith [] sell drugs out on the street.” As our earlier review of Davis’s testimony shows, and contrary to the Government’s contention on appeal, the statement clearly, though not intentionally, misrepresents the evidence.

But this did not make the trial less fair. Explicitly misrepresenting testimony—i.e. telling the jury that this is what a witness told them—differs from implying that evidence not seen by the jury would support a conviction, compare *Phelps v. Duckworth,*757 F.2d 811, 822-23 (7th Cir.1985), or introducing facts on which no evidence has been offered, compare *United States v. Meeker,*558 F.2d 387 (7th Cir.1977). On cross-examination, Smith’s counsel quite clearly established that Davis had not actually seen Smith sell drugs. Counsel thus had both the means and the opportunity to rebut the Government attorney’s representation. The jury, having heard Davis’s testimony, was equipped to determine whether the Government or the defense had provided the more accurate argument. Moreover, we have already concluded that the evidence against Smith was more than sufficient even without Davis’s testimony. Finally, the trial judge’s instructions to the jury included the usual admonition not to treat statements of counsel during opening statements and closing arguments as evidence.

*2. You heard from Anthony*Hues_ *Smith told him, told Anthony Hues, that his source was Gregory Collins.*

The Government all but concedes that Anthony Hues did not testify that Smith told him that Smith’s drug source was Gregory Collins, although the prosecutor claimed just this in his closing argument. But, as the Government points out, whether or not Hues knew it, the trial record contains plenty of evidence that Collins was Smith’s source. And, again, since the jury had heard Hues’ testimony, defense counsel had the opportunity to argue that the Government had misrepresented it.

*3. If [Anthony Hues] was going to lie for the Government, why wouldn’t he say yes, I bought from Anthony Angelo Smith four, five, six, seven, twenty times, ladies and gentlemen?*

Gregory Collins’ lawyer impeached Hues by contrasting his trial testimony that he had never purchased drugs from Smith with his grand jury testimony that he had purchased from Smith three or four times. In his closing argument, Collins’ lawyer characterized the trial testimony on this point as a “bald lie.” The Government attorney, in his rebuttal argument, argued that defense counsel got Hues “scared and rattled” on cross-examination and asked the jury to consider whether Hues had any motive to lie at trial: “If he was going to lie for the Government, why wouldn’t he say yes, I bought from Anthony Angelo Smith four, five, six, seven, twenty times, ladies and gentlemen? It is because he is telling the—” At this point Collins’ lawyer objected: “May it please the court, we have in Court testimony here directly opposing testimony under oath before a grand jury.” The judge sustained this objection and instructed the Government attorney to “move on.”

Smith offers no explanation of how the Government attorney’s statement prejudiced him, and we can think of none. The Government attorney was arguing that Hues’s statement that he never purchased drugs from Smith was *true!*

*755A ... *[Bridget Holton] didn’t know that [Smith] had been convicted of selling drugs.*

The Government attorney argued that Bridget Holton, who testified that Smith never sold drugs, admitted to not knowing that he had been previously convicted of that crime. Actually, Holton testified that she had known Smith for eight years, that Smith worked with her brother at the Club Fantasy, that she knew Smith “pretty well,” and did not know him to be a drug dealer. On cross, the prosecutor asked if she knew whether Smith had been arrested for selling drugs at the Club Fantasy, and Holton said “no.” Then the prosecutor asked whether she knew Smith well enough to know whether or not he was tried and convicted for selling drugs during the eight years she had known him, and she answered that she knew “by the papers that came out” that he had been indicted, but not that he had been convicted.

A defendant’s character witnesses may be cross-examined about their knowledge of “relevant specific instances” of the defendant’s conduct. FRE 405(a); *United States v. Alvarez,*860 F.2d 801, 826 (7th Cir.1988). The Government must show a good faith factual basis for inquiry into past acts of misconduct, and it must show relevance, but we review a district court’s decision defining the bounds for cross-examination of a character witness for “clear abuse of discretion.” *Alvarez,*860 F.2d at 826. Smith could have forced the Government to prove-up this impeachment, but has not pointed to an objection in the record preserving a challenge to the Government’s cross-examination of Holton under FRE 405(a); indeed, he has not squarely raised the issue on appeal. The Government accurately summarized its cross-examination of Holton.

5. *I want to make it clear if that were, in fact, the case, they could have called witnesses. They could have shown us. They didn’t. Now, they don’t have to. I want to stress that to you.*

The Government’s rebuttal argument included the following remarks:

> Mr. Black [Sylvia Lipson’s attorney] also challenged the Government. He said well, if Sylvia had all of the clothes as a result of being a member of this conspiracy and working with them and doing all of the things that all of the witnesses said she did, how come the Government didn’t prove it? Well, I think he has asked me to prove something that is impossible. On the other hand, as I have indicated before, the defense may — they don’t have to, they are not required to call witnesses and it is never their burden to call witnesses. I want to make it clear if that were, in fact, the case, they could have called witnesses. They could have shown us. They didn’t. Now they don’t have to. I want to stress that to you.

When defense counsel objected, the judge ruled that this was an “invited response.”

If a defense lawyer invites a comment that does no more than “right the scale,” the response does not warrant reversal. *United States v. DePriest,*6 F.3d 1201, 1210-11 (7th Cir.1993), quoting *United States v. Young,*470 U.S. 1, 12-13, 105 S.Ct. 1038, 1044-45, 84 L.Ed.2d 1 (1985). On the other hand, the Supreme Court has expressed concern that “the idea of ‘invited response’ has evolved in a way not contemplated.” *Young,*470 U.S. at 12, 105 S.Ct. at 1044. The Court has cautioned judges not to read its precedents “as suggesting judicial approval or encouragement of response-in-kind that inevitably exacerbates the tensions inherent in the adversary process.” *Id.*“The issue is not the prosecutor’s license to make otherwise improper arguments, but whether the prosecutor’s ‘invited response,’ taken in context, unfairly prejudiced the defendant.” Lipson’s attorney had urged the jury to consider how difficult it would have been for Lipson to prove herself innocent:

> How can you defend a case where someone says somebody told me that they had drugs, that she kept drugs? What do you do? Line up witnesses at the door and say, well, somebody told me she didn’t, she didn’t, she didn’t, she didn’t. For all of her family members to come take the stand and say Sylvia was a nice person, kept to herself, would that convince you or *756would think that is a family member? It is a heck of a burden.

Did this invite the prosecutor’s remarks concerning the defendant’s legal right to present witnesses? Not really. Defense counsel never suggested that he was legally disem-powered to call witnesses. He merely argued, as our legal system has recognized since its inception, that the burden of proving innocence is too heavy for many innocent defendants to bear, and so judges and juries must focus on whether the Government has proved guilt.

On the other hand, giving due consideration to the heat of the moment, the prosecutor can certainly be excused for misconstruing defense counsel’s point and making an aggressive response. More importantly, given the line of argument selected by defense counsel, which focused the jurors’ attention on Lipson’s failure to offer exculpatory evidence, we can hardly imagine that the prosecutor’s remark had anything more than a de minimis influence on the jury’s consideration of this issue. And even as the prosecutor mentioned the defendant’s failure to call witnesses, he emphasized that it was not her burden to do so. Finally, whatever minimal effect the prosecutor’s remark may have had for its clear target, Lipson, it had even less effect on Smith.

Despite our seriatim analysis of each statement criticized by Smith, we recognize that the conjunction of several improper remarks might have had a cumulative effect warranting reversal, even though none would standing alone. But in this case, the sum of the parts equals not very much—not nearly enough to suggest that Smith was denied a fair trial.

F. Sentencing

Finally, Smith appeals his sentence, claiming that the trial judge relied on clearly erroneous factual findings in determining that his offense involved more than fifteen kilograms of crack cocaine. The judge’s findings do appear to contain some errors, or at least some conclusions that we have not been able to trace back to evidence in the record. But rather than review everything the judge said, we will focus on the testimony of Montuella Wright, Melina Miller, and Mark Nicholson, which, taken together, amply supports the sentence Smith received.

Melina Miller testified that Smith moved into her apartment and started dealing from her apartment in April of 1988 and continued through some point in 1989, but no later than November of that year. Montuella Wright lived with them for roughly two months in the winter of 1988-89. Wright testified that, during his time in the apartment and for several months thereafter, the distribution operation usually generated $10,000 a day or better. Mark Nicholson testified that one-sixteenth of an ounce of crack cocaine brought a price between $80 and $100. Using the higher number, to the defendant’s benefit in this equation, we calculate that an ounce of crack cocaine sold for roughly $1600. A kilogram contains 35.2 ounces, so a kilogram of crack produced roughly $56,320 in revenue.

Wright lived with Miller and Smith at the Centreville location for roughly two months. Let’s call it fifty days. At $10,000 per day, that yields $500,000 in revenue, which represents roughly 8.8 kilograms of crack cocaine sold through Smith’s Centreville operation just during the time Wright lived there. That amount alone results in a base offense level of 40.

The trial judge calculated a base offense level of 42 on finding Smith accountable for more than 15 kilograms of crack cocaine, and then added two levels for Smith’s use of a firearm,8 arriving at a total offense level of 44. Even at 8.8 kilograms, the base offense level is 40 and the two-point enhancement brings the total to 42. That level corresponds to a sentencing range between thirty years and life imprisonment. So the judge could have imposed a life sentence even if the evidence had linked Smith to only 8.8 kilo*757grams — in fact, even if the evidence had linked Smith to only 5.

But the judge sentenced Smith based on 15 kilograms, and that was not clearly erroneous. First, according to Melina Miller’s testimony, Smith sold drugs from their Cen-treville residence for at least eight months. Remember that Wright testified that Smith was a better distributor than he was. Even if Wright accounted for half the sales during his residence in the Centreville apartment, it is reasonable to infer that Smith and Miller in concert processed and sold well over 15 kilograms of crack for Gregory Collins even before Wright moved in.

Add to this Wright’s testimony that from late summer 1988 until he moved in with Smith and Miller, Smith was at least present at cocaine transactions between Wright and Gregory Collins involving amounts ranging from sixteenths of an ounce to full ounces. According to Wright, these quantities “would have to be reformed to crack cocaine,” for retail distribution. Add also Hues’s testimony that Smith was present at several drug transactions between Hues and Gregory Collins. Finally, throw in Wright’s testimony that Smith was Collins’s favorite distributor and that aside from his operation in Centre-ville, Smith also worked with Collins and Lipson at a processing and distribution operation at 128 Arlington in Belleville, where Wright frequently obtained drugs, and consider that Wright himself testified to having comprehensive knowledge of the Collins organization, naming Smith, Lipson, Kent Collins, Ward, Mason, Douglas, and Nicholson as distributors, and the general inference that the full scope of this conspiracy was reasonably foreseeable to Smith becomes quite plausible and certainly beyond the reach of clear error.

The Jury Issue

Now to an issue that cuts across all these appeals: jury impartiality. On the morning of the first full day of deliberation, the trial judge gathered the court reporter, the courtroom clerk, and counsel for all parties in chambers and reported that Juror Rose had told him moments earlier that her former brother-in-law visited her the night before, asked about her involvement in the trial, and said that a member of the Collins family had approached him. Rose was “concerned for her family.” The judge also explained that he had taken precautions to shield the other jurors from Rose’s remarks, but that one had already expressed concern for her safety:

> THE COURT: I have arranged for Miss Rose not to return to the jury room until after we had our discussion. I told her that I did not want her to say anything about [her visitor] to the other jurors. However, independent of all this, one of the jurors this morning said to Sandy what protection—

> COURTROOM CLERK: After we render the verdict, how will we get out of here, protection-wise, who is going to help us out of here.

The judge decided to interview Rose again— on the record, this time, but still absent counsel. In addition to asking questions intended to ascertain her ability to continue as an impartial juror, the judge also asked whether she had discussed the matter with any other juror:

> MRS. ROSE: When I came in, I said I had a visitor last night. That is when you came in, and I said I need to talk to you, I had a problem.9

Upon hearing this information and the judge’s decision to dismiss this juror and proceed with eleven, the defendants all moved for a mistrial on the grounds that the entire jury had been tainted. The judge denied the motion because he lacked sufficient evidence “at this point to come to the conclusion that the jury is tainted by this incident,” but, raised the possibility of a voir dire. The Government opposed this procedure, arguing that it “would emphasize a problem that may not be there.” The defense said nothing; not one of the five defendants’ lawyers asked the judge to voir dire *758the remaining jurors, and none objected when he decided not to.

The judge’s attention then turned to sequestration. Although the defense characterized itself as “a swinging door on this issue,” the judge recognized that sequestration might “cause some concern among the jurors.” Nevertheless, he concluded that he could explain the sequestration in a manner that would “ease their feelings a bit,” by telling the jury that he had excused Mrs. Rose for “personal problems,” that he could accept a verdict from eleven jurors, but not ten, and that he had therefore decided, as a precaution, to sequester them.10 Not only did no defense attorney object, but Smith’s attorney — on appeal, the lead advocate for the defendants on this issue — expressly approved.

' After four days of deliberation, the jury returned its verdicts. The jurors were polled and subsequently dismissed, and no objections or motions were made by defense counsel. Seven days later, Smith served an amended motion for a new trial that included the claim that he had been denied an impartial jury. Neither he, nor any other defendant requested an evidentiary hearing of any kind, nor did they argue that the court had erred by not conducting a voir dire of the eleven jurors who rendered the verdict. On appeal, the defendants claim that the trial court erred by denying the motions for a mistrial and a new trial.

“In a criminal ease, any private communication, contact, or tampering directly or indirectly, with a juror during a trial about the matter pending before the jury is, for obvious reasons, deemed presumptively prejudicial, if not made in pursuance of known rules of the court ... with full knowledge of the parties.” *Remmer v. United States,*347 U.S. 227, 229, 74 S.Ct. 450, 451, 98 L.Ed. 654 (1954) *(“Remmer I”).*Here, only Juror Rose was subject to “private communication, contact, or tampering directly or indirectly,” and the court removed her. But her dismissal leaves behind the possibility that something she did or said prejudiced the remaining jurors.

“If there is a reasonable possibility that a jury’s verdict has been affected by material not properly admitted as evidence, the criminal defendant is entitled to a new trial.” *United States v. Davis,*15 F.3d 1393, 1412 (7th Cir.1994). And “where a bribe or threat to a juror was communicated to other jurors, the trial judge must fully examine the effect of the threat on the remaining jurors.” *United States v. Angulo,*4 F.3d 843, 847 (9th Cir.1993). The Ninth Circuit recently held that in such cases, “without a hearing, a district court does not have the essential facts to properly evaluate a defendant’s motion for a mistrial,” regardless of whether the defendant has requested a hearing. *Id.*at 848. While we are not prepared to embrace the Ninth Circuit’s rule absolutely, district courts in this circuit will rarely have sufficient grounds for straying from it.

In fact, the Ninth Circuit’s rule is a cousin, if not a sibling, of our own: “Once the defendant has made a *sufficient showing that a juror may have been improperly influenced,*the court *must ascertain whether the juror was or was not*tainted.” *Davis,*15 F.3d at 1412 (emphasis in original), citing *Remmer I,*347 U.S. 227, 74 S.Ct. 450; *United States v. Sanders,*962 F.2d 660, 671 (7th Cir.1992). The trial court’s obligation arises not only from the defendant’s right to a fair trial, but also from “proper concern for protecting and preserving the integrity of our jury system,” *Remmer v. United States,*350 U.S. 377, 381, 76 S.Ct. 425, 428, 100 L.Ed. 435 (1956) *(“Remmer II”),*a systemic interest. See also *id.*(“it is the law’s objective to guard jealously the sanctity of the *jury’s*right to operate as freely as possible from outside unauthorized intrusions purposefully made”) (emphasis added).

Post-verdict proceedings generally suffice to determine whether juror impar*759tiality has suffered from extra-judicial contact, *Owen v. Duckworth,*727 F.2d 643, 646 (7th Cir.1984) (per curiam). Although pre-verdict voir dire is generally preferred because Federal Rule of Evidence 606(b) limits the scope of post-verdict interrogation, questioning jurors before a verdict about threats and bribes may so focus their attention that a jury otherwise capable of delivering an impartial verdict no longer can. *United States v. Ruggiero,*928 F.2d 1289, 1301 (2d Cir.1991); *United States v. Williams,*822 F.2d 1174, 1189-90 (D.C.Cir.1987). Such cases, therefore, call for liberal deference to a district court’s decision not to question jurors before the verdict, especially where defense counsel has not requested this procedure.

The jury prejudice issue in this case thus fines itself down: did the trial judge err by not conducting a *post-verdict*hearing even though the defendants failed to request one? Based on his findings and the grounds of his ruling, we think that he did, although the remedy does not necessarily require a new trial or even a hearing.

In *Owen v. Duckworth,*727 F.2d 643, 647 (7th Cir.1984) (per curiam), we noted that a district court faced with a post-verdict question of jury prejudice must find basic facts, such as the nature, content, and extent of extrajudicial contact, and then, infer whether the contact likely affected the jurors’ impartiality. *Id.*We said that the second finding — the one based on inference — merits a more critical review than the basic factual findings. *Id.*Subsequently, in *Haugh v. Jones & Laughlin Steel,*949 F.2d 914 (7th Cir.1991), we held that the basic factual finding is reviewed for clear error and the inference concerning prejudice for abuse of discretion. *Id.*at 916, citing *United States v. Best,*939 F.2d 425, 429 (7th Cir.1991) (en banc). “Abuse of discretion is conventionally regarded as a more deferential standard than clear error, though whether there is any real or consistent difference has been questioned. ... Whatever the standard is called, appellate judges properly give great weight to the trial judge’s assessment of the impact of an improper communication on the jury.” *Haugh,*949 F.2d at 917 (citations omitted). *Haugh*justified this level of deference because the district judge, who had interrogated every juror at a post-verdict hearing, had “the inestimable advantage over the appellate judges of having actually observed the jurors.” *Id.*

In this case, however, the trial judge interrogated only Juror Rose. In fact, the record shows that the judge’s findings had no basis in his observations of the jurors. He reasoned that Rose’s remark about a visitor was subject to so broad á range of interpretation that it did not taint the jury with information that someone had tried to bribe or threaten her: “Another conclusion leaps to mind that the visitor she had last night was the one that visited Mr. Rice a couple of weeks ago, the flu. She became suddenly ill.” A trial court’s perspective for this determination, derived solely from its interpretation of an utterance made outside its presence, has no advantage over ours.

We have previously confronted at least two cases involving claims that knowledge of a threat against one of their number tainted a jury.11 In the first, *Owen v. Duckworth,*727 F.2d 643, 647 (7th Cir.1984) (per curiam) (reversing the district court with instructions to grant petition for habeas corpus where testimony at a post-verdict evidentiary hearing indicated that three jurors “assumed” that the defendant or a friend had threatened another juror and there had been no clear showing the assumption was harmless), we recognized that in addition to knowing what words the jurors heard, “it is equally or perhaps more important to know” how they interpreted those words and what inferences they drew. “Assumptions regarding such matters can affect a juror’s behavior as much as actual knowledge of the facts. Indeed, erroneous assumptions can under circumstances be even more prejudicial than knowledge of the facts.” *Id.*

*760Even accepting as plausible the judge’s interpretation of “I had a visitor,” there is at least a decent chance that one of the eleven remaining jurors understood the phrase as indicating that someone had tried to bribe or threaten Rose. This issue did not arise in a vacuum. Another, unidentified, juror had already expressed concern for her own safety, asking about protection. We are not sure what the judge meant by characterizing the unidentified juror’s remark as “independent of all this,” but if it meant that the remark bore no relation to Rose’s comment, the record lacks any factual finding in support of that inference. If the juror who expressed such concern did so after hearing Rose mention the visitor, any speculation by the court about how “visitor” might be interpreted is beside the point. Such a sequence of events in temporal proximity raises a compelling suggestion of causal connection that no judge could adequately assess without investigation and factual findings beyond what the record reflects.

However, as demonstrated in *United States v. Sanders,*962 F.2d 660, 671 (7th Cir.1992) (affirming a district court’s finding that the jury was capable and willing to decide the case on the evidence properly before it despite the assumption that all jurors knew about a threat against one of them), the questions of what the jurors knew and whether the trial was fair are distinct. We therefore remand this case to the district court with instructions to determine the ultimate issue: whether there is a “reasonable possibility” that the jury’s verdict was affected by material not properly admitted as evidence, in which case there would be a substantial likelihood that the defendants were denied a fair trial. See *Davis,*15 F.3d at 1412, citing *United States v. Balistrieri,*779 F.2d 1191, 1214 (7th Cir.1985).

We see two paths the judge might take. First, he might assume the worst — that every juror knew that the defendants, or their associates, had threatened Juror Rose — and then proceed to determine whether there was a reasonable possibility of prejudice. See *Sanders,*962 F.2d at 673. Alternatively, the court could conduct a hearing, within the confines of FRE 606(b), see *Duckworth,*727 F.2d at 647, to determine what, if anything, the jurors heard Rose say on the morning of the first day of deliberation and whether anything she said, including her demeanor when she said it, gave rise to an inference or assumption that one or more of the defendants or their associates had attempted to bribe, threaten, or otherwise influence her improperly. If the judge finds that one juror did make such an inference or assumption based on a remark by Rose, then the question of a reasonable possibility of prejudice still remains.

In determining whether there was a reasonable possibility of prejudice, the judge may look at an array of factors, including the nature and extent of the evidence against the defendants, admonitions and instructions given to the jury, and the mixed nature of the verdicts. *Sanders,*962 F.2d at 673-74. The judge can also consider the length of deliberations, and any other evidence, such as the content of notes sent to the judge during deliberations, indicating a genuine effort by the jurors to decide the case based on the law and the facts.

Conclusion

The district court’s order denying defendants’ motions for a mistrial or a new trial is vacated and the case is remanded for additional findings regarding the issue of jury prejudice and reconsideration of the defendants’ motions in light of those findings. The sentence of Kenneth Collins is vacated as well, and his sentencing is remanded to the district court for reconsideration.

VACATED AND REMANDED.

1

. Davis and Gregory Collins engaged in two more transactions, involving three-quarters of a kilogram total. Larry Miller testified that from August through October of 1988, he sold quarter and half kilograms of cocaine to Gregory Collins; that from November 1988 through January 1989, he sold half kilograms to Gregory Collins "a couple of times a week sometimes;” that he sold full kilograms of cocaine to Gregory Collins on five to ten occasions; and that in one transaction, Gregory Collins bought two kilograms of cocaine from him.

2

. Ward testified that Kenneth Collins would come to her trailer several times a day, buy a “rock,” take a piece off, and sell the rest outside. While the defense argues, with some merit, that Ward had no basis in personal knowledge for her assertion that Kenneth Collins sold any portion of the drugs he purchased from her, there is no dispute about his purchases or their frequency.

3

. Wright testified that Kenneth Collins "would retrieve or receive cocaine from Gregory Collins, or from us or me personally, and I don't now what he would do with it from there, but he would receive it. I gave him cocaine on numerous occasions. I have seen Mr. Gregory Anthony Collins give him cocaine on numerous occasions and I have seen different parties of our indictment give Mr. Kent Collins cocaine on numerous occasions.”

4

.Kenneth Collins would come four or five times a week to trade expensive clothes for small quantities of cocaine at the drug house Wright ran in East St. Louis. Davis believes that Kenneth was a junkie and did not purchase these quantities for re-sale.

5

. Collins has not challenged the two-level enhancement for possessing a weapon during the conspiracy.

6

. The extent of Smith's distribution operation is discussed in the section addressing his sentence.

7

. Ms. Wren is Melina Miller's sister and another intimate companion of Gregory Collins.

8

. Smith has not raised the firearm-enhancement issue on appeal, but we note that James Harris testified that Smith, displaying a pistol, confronted him in the Centreville projects and warned him not to interfere with Smith’s customers. At sentencing. Smith's attorney argued that the testimony was not credible; the judge found otherwise.

9

. We do not interpret the statement to mean that the judge came into the jury room and discussed the matter with Mrs. Rose. The judge told defense counsel that Sandy, whom we presume to be the courtroom clerk, walked into the jury room to see if all had arrived, and took Mrs. Rose out after Mrs. Rose mentioned that she needed to speak to the judge.

10

. In fact, the judge informed the jury that ”[m]y reason for doing that ... is that while we can accept a verdict from a jury composed of 11 jurors, we cannot accept one from less than that. This morning, as I informed you, I had to excuse one of your members for personal problems, so I am going to order the jury sequestered.” He also told them, “I am sure upon reflection you can understand that after a trial that has gone on this long, we cannot afford to take the possibility that someone may have an accident, become ill, or whatever, overnight."

11

. Both the Government and defense counsel have treated this issue as one of first impression in this circuit, and while in a narrow sense this is so, the principles necessary to resolve this case are fairly patent in our precedents. Moreover, when both sides miss what may be the two cases most on point, one cutting in favor of the Government, the other in favor of the defense, we can only wonder whether the gravity of the appeal has failed to impress the advocates.