
    UNITED STATES of America, Plaintiff-Appellee, v. Roberto GONZALEZ, Roberto Ramirez, Angel M. Amejeiras, Vicente Chao, Luis Gonzalez, and Rafael Izquierdo, Defendants-Appellants.
    Nos. 88-2281, 88-2282, 88-2283, 88-2284, 88-2285, 88-2347 & 89-1038.
    United States Court of Appeals, Seventh Circuit.
    Argued April 6, 1990.
    Decided May 1, 1991.
    As Amended May 2, 1991.
    
      Anton R. Valukas, U.S. Atty., Steven A. Miller, Scott D. Levine, David J. Stetler, Asst. U.S. Atty., Office of the U.S. Atty., Crim. Receiving, Appellate Div., Chicago, Ill., for plaintiff-appellee.
    Rick Halprin, Chicago, Ill., for defendant-appellant in No. 88-2281.
    Donald I. Bierman, Bierman, Shohat & Lowey, Miami, Fla., for defendant-appellant in No. 88-2282.
    Walter Jones, Jr., Curiel & Jones, Chicago, Ill., for defendant-appellant in No. 88-2283.
    Rafael Izquierdo, pro se.
    James W. Reilley, Christine P. Curran, Reilley & Associates, Des Plaines, Ill., for defendant-appellant in No. 88-2284.
    Michael D. Monico, Barry A. Spevack, Monico, Pavich & Spevack, Chicago, Ill., for defendant-appellant in No. 88-2285.
    Vicente Chao, pro se.
    Lawrence Rosenthal, DCC, Office of the Corp. Counsel, Appeals Div., Chicago, Ill., for plaintiff-appellee in No. 88-2347.
    Nathan Diamond-Falk, Rick Halprin, Chicago, III, for defendant-appellant in No. 88-2347.
    Thomas M. Durkin, Scott D. Levine, Asst. U.S. Attys., Office of the U.S. Atty., Chicago, Ill., for plaintiff-appellee in No. 89-1038.
    Walter Jones, Jr., Curiel & Jones, Chicago, Ill., for defendant-appellant in No. 89-1038.
    Before COFFEY, MANION and KANNE, Circuit Judges.
   COFFEY, Circuit Judge.

This is the consolidated appeal of six defendants convicted of various federal narcotics crimes. We affirm the convictions of each of the defendants and the sentence of Roberto Ramirez.

I.

PROCEDURAL BACKGROUND

On January 21, 1988, a grand jury returned a three-count superseding indictment charging violations of 21 U.S.C. §§ 841(a)(1) and 846. Count I of the indictment charged Roberto Gonzalez, Roberto Ramirez, Rafael Izquierdo, Angel M. Ame-jeiras, Vicente Chao, and Luis Gonzalez, together with Jose Alexander Peña, Ulises Ortega, Cesar Tobon, Manuel Angel Telle-chea, Alvaro Quintero and Alcides Cruz with conspiracy to possess with intent to distribute and to distribute cocaine in violation of 21 U.S.C. §§ 841(a)(1) and 846. Count II charged that on July 29, 1987, Vicente Chao and Ulises Ortega knowingly and intentionally possessed with intent to distribute approximately 2,265 kilograms of a mixture containing cocaine, a “Schedule II narcotic drug controlled substance,” in violation of 21 U.S.C. § 841(a)(1) and that Roberto Gonzalez, Luis Gonzalez, Ramirez, Amejeiras, Izquierdo, Tellechea, Quintero and Cruz aided and abetted in the commission of this offense. Count III alleged that, also on July 29, 1987, Jose Alexander Peña and Cesar Tobon knowingly and intentionally possessed with intent to distribute approximately 2,248 kilograms of cocaine in violation of 21 U.S.C. § 841(a)(1) and that Roberto Gonzalez, Luis Gonzalez, Ramirez, Amejeiras, Izquierdo, Chao, Telle-chea, Quintero and Cruz, aided and abetted in the commission of the offense.

The appellants, together with Alcides Cruz and Ulises Ortega, proceeded to trial on April 4, 1988. The jury returned a verdict finding the appellants and Alcides Cruz guilty on all counts but finding Ulises Ortega not guilty. The defendants, sentenced to various terms of confinement, appeal their convictions.

II.

FACTUAL BACKGROUND

This case involves a cocaine importation and distribution conspiracy which imported cocaine into Miami, Florida through Honduras during the years 1986 and 1987. The cocaine was concealed in shipments of plantains. From Miami the drugs were distributed to the cities of New York and Chicago. Testimony concerning the conspiracy’s operation was received from the defendant Cesar Tobon, a member of the conspiracy who participated in the cocaine distribution operation. Testimony was also provided by unindicted, co-conspirators Jesus Ortiz and Julio Ortiz, father and son, who participated in the conspiracy’s cocaine importation operations and testified under grants of immunity. Daniel Petroski, a truck driver, who was unwittingly hired to transport the conspiracy’s July 1987 drug shipment also provided testimony.

Jesus Ortiz testified that two shipments of cocaine were made, in August and October 1986 respectively, from Honduras to Miami by a group consisting of Jesus Ortiz, Alcides Cruz, Manuel Angel Tellechea, and Roberto Ramirez. The cocaine was brought to Honduras from Columbia via airplane. In Honduras, the cocaine was hidden in plantain shipment containers placed aboard ships destined for Miami. As a result of one of the airplane shipments of cocaine from Columbia to Honduras being intercepted by the Honduran military in October of 1986, the cocaine importation enterprise was temporarily suspended.

Julio Ortiz testified concerning the conspirators’ efforts to resume the drug importation and distribution activity after the October 1986 incident and described a February 1987 meeting held between Cruz, Tel-lechea, Angel Amejeiras and himself, where Cruz outlined his plans for the future operations of the conspiracy. During this meeting Cruz explained that Julio would be in charge of the import company receiving the cocaine in Miami, Roberto Ramirez would supply the drugs, and that Cruz and Tellechea would be responsible for the transportation and handling of the shipments in Central America.

In late April or early May of 1987, Julio Ortiz commenced the operation of the Miami-based import business, International World Enterprises, to receive the conspiracy’s cocaine shipments from Honduras. A shipment said to contain 1,148 kilograms of cocaine concealed in plantains arrived in Florida on a freighter on June 4, 1987. Shortly thereafter, as a result of a disagreement over money, Julio Ortiz left his position as head of International World Enterprises. Luis Gonzalez became the manager of a new company known as International Palm Products, that replaced International World Enterprises as the outlet for the receiving of cocaine imported into Miami from Honduras.

Cesar Tobon described the New York cocaine distribution operation, responsible for the transportation of the cocaine imported through Miami for the New York area. Tobon spoke of the numerous trips that he and other members of the conspiracy made in June and July 1987 between New York and Florida and within the New York City area. He explained further that Roberto Gonzalez was the recipient of many of these cocaine deliveries.

In mid-July 1987 the conspiracy shipped 2,265 kilograms of cocaine, concealed in a load of plantains, from Honduras to Miami. Unfortunately for the conspirators, the large cocaine shipment was intercepted in Miami on July 23, 1987, by a special team of Customs agents. At this time federal authorities set up a “controlled delivery” of the cocaine.

During the time the cocaine was being intercepted, Tellechea and Amejeiras were at a truck stop in Miami where they met with one Daniel Petroski to hire him to deliver what Petroski believed to be a load of plantains to Las Villas Enterprises in the Bronx, New York. Petroski picked up the load of plantains which, unbeknownst to him contained cocaine, at Miami Cold Storage and left for New York. After departing from Miami Cold Storage, he and his shipment were detained by federal agents in the Miami area. After questioning, he agreed to cooperate in the drug investigation.

Petroski testified that when he met Luis Gonzalez at the Las Villas Enterprises building in the Bronx on July 28, 1987, Gonzalez stated that a mistake had been made as to the destination of the cargo and that it should be delivered to Vicente Chao in Chicago. Petroski further testified that at this time Luis Gonzalez entered the trailer and inspected the cargo with a flashlight.

On the morning of July 29, Rafael Izquierdo, who had traveled from Miami to Chicago with the conspiracy’s cocaine supplier (Roberto Ramirez) went to the Celi-Mar fish, vegetable and fruit dealership in Chicago where Chao was employed. Izquierdo later departed with Celi-Mar’s owner, Matteo Hernandez, to visit area stores in a supposed attempt to generate fish sales. Hernandez testified that this was the first time that he had ever made the rounds of area businesses with Izquier-do. Izquierdo apparently accompanied Hernandez to ensure that Hernandez would not return while the cocaine was being transferred.

Testimony from Petroski and federal agents established that Petroski arrived at the Celi-Mar warehouse in Chicago, Illinois, shortly after noon on July 29, 1987. This testimony, together with a videotape of the cocaine delivery to the Celi-Mar warehouse introduced at trial, revealed that Chao and the defendant Ulises Ortega commenced the unloading of Petroski’s truck. Later, drug couriers Jose Alexander Peña and Cesar Tobon arrived at the Celi-Mar warehouse and conferred with Chao. Chao explained to Pena and Tobon that they could locate the boxes containing the cocaine by placing their fingers in the containers’ air holes and feeling the plastic wrap rather than plantains. During the loading Tobon organized the cargo in the truck while Peña sought to locate a missing box of cocaine. After the cocaine-laden truck departed from the warehouse, law enforcement officers intercepted and confiscated the truck and arrested Peña and Tobon. Chao was also arrested the same day.

Following the arrests of Chao, Peña and Tobon, law enforcement officers conducted a search of the Celi-Mar warehouse. In the aftermath of the arrests other conspirators who had been in the Chicago area awaiting the delivery departed, including Luis Gonzalez and Telleehea who took circuitous routes home in an attempt to confuse pursuers. Steven Bissegger, Special Agent for the DEA, testified that around noon on August 4, 1987, he “received a phone call ... from an individual who identified himself as Gary Sternberg” and “said he was an attorney who represented Mr. Matteo Hernandez.” Bissegger further testified that after he received the phone call, he “proceeded to Celi-Mar” with another DEA agent. When the agents arrived at the cold storage area of the Celi-Mar warehouse, Bissegger stated he met “an individual who identified himself as Mr. Sternberg” who “pointed out a wooden pallet containing some boxes,” and told him “that a box had been found on that pallet that he thought we would be interested in.” Bissegger stated that Sternberg pointed to a particular box. Bissegger went on to testify that when the box was opened he viewed “17 individually wrapped packages.” The contents of the box were submitted to the DEA laboratory where it was determined that the box “contained 17 ... separate packages, weighing a total of 17.-027 kilograms that contained powder that was tested and determined to be 93 percent pure cocaine.”

III.

ISSUES PRESENTED

(1) Was it proper for Ramirez to receive multiple punishments for convictions on two separate counts of possessing cocaine with intent to distribute; (2) Did the trial court properly refuse to sever the trials of Ramirez and Izquierdo from those of their co-defendants; (3) As to all the defendants, did the trial court err in admitting and allowing the jury to view 2,248 kilograms of cocaine in the courtroom; (4) With respect to Chao, did the district court abuse its discretion in admitting expert testimony concerning the unusual length of narcotics-oriented telephone calls; (5) Was Chao's Fifth Amendment privilege against self-incrimination violated when the trial court received in evidence Chao’s affidavit of in-digency; (6) Did the prosecutor’s reference in closing argument to facts not in evidence pertaining to Chao’s alleged theft of a missing box of cocaine deny Chao a fair trial; (7) Did the trial court deny Luis Gonzalez a fair trial in giving the jury a “conscious avoidance” instruction pertinent to its consideration of the evidence against him; (8) Was there sufficient evidence to support Chao’s, Izquierdo’s, Amejeiras’ and Luis Gonzalez’ convictions of (a) conspiracy to possess cocaine with intent to distribute, (b) possession with intent to distribute and (c) aiding and abetting possession of cocaine with intent to distribute; (9) Was the trial court’s refusal to give Roberto Gonzalez’ proffered instruction requiring “membership” in the conspiracy to establish vicarious liability on the two possession with intent to distribute counts proper together with the related question of whether sufficient evidence supported Roberto Gonzalez’ convictions on the substantive counts; and (10) Did the government’s failure to disclose information concerning alleged prior drug activity of government witness Cesar Tobon require that a new trial be granted to Izquierdo, Chao, and Roberto Gonzalez.

IV.

MULTIPLICITY OF INDICTMENT

Defendant Roberto Ramirez argues that the indictment was multiplicitous because the two possession with intent to

distribute counts in the indictment charged the commission of merely one offense. In United States v. Briscoe, 896 F.2d 1476, 1522 (7th Cir.1990), we observed that: “Essentially a claim of multiplicity alleges that separate counts in an indictment charge a single offense. ‘As such the indictment exposes a defendant to the threat of receiving multiple punishment for the same offense.’ ” (Citation omitted) (quoting United States v. Podell, 869 F.2d 328, 330 (7th Cir.1989)). In United States v. Marquardt, 786 F.2d 771, 778 (7th Cir.1986), we set forth the standard utilized in evaluating whether counts are multiplicitous:

“The traditional test of multiplicity ‘determines whether each count “requires proof of a fact which the other does not.” ’ United States v. Kennedy, 726 F.2d 546, 547-48 (9th Cir.), cert. denied, [469 U.S. 965], 105 S.Ct. 365, 83 L.Ed.2d 301 (1984) (quoting United States v. Glanton, 707 F.2d 1238 (11th Cir.1983)). ‘If one element is required to prove the offense in one count which is not required to prove the offense in the second count, there is no multiplicity.’ United States v. Briscoe, 742 F.2d 842, 845 (5th Cir.1984).”

Ramirez was convicted of the two counts of possession with intent to distribute cocaine based upon the vicarious liability theory of Pinkerton v. United States, 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946). In order for Ramirez to be liable for Chao or Ortega’s possession of cocaine with intent to distribute under Pinkerton, the government was required to demonstrate that Chao or Ortega possessed cocaine with intent to distribute in furtherance of or as a natural consequence of the conspiracy and that Ramirez was a co-conspirator with either Chao or Ortega. Conviction on the second count of possession with intent to distribute required proof that Peña or Tobon (rather than Chao or Ortega) had possessed cocaine with intent to distribute in furtherance of or as a natural consequence of the conspiracy and that Ramirez was a co-conspirator with Peña or Tobon. The record establishes that these two separate crimes of possession of cocaine with the intent to distribute in conjunction with the conspiracy occurred and that Chao (the jury absolved Ortega) possessed the cocaine with the intent to distribute it at the time he and Ortega unloaded it at the Celi-Mar warehouse, and Ramirez is vicariously liable for Chao’s crime under Pinkerton in Count II. Likewise, under Count III Ramirez is vicariously liable for Peña’s and Tobon’s possession of the cocaine with the intent to distribute it, which occurred when they conveyed the cocaine from the warehouse in a truck. Since the government was required to prove the element of Peña’s and Tobon’s possession of cocaine with the intent to distribute under Count III that was immaterial to Count II, it was proper that the two counts be individually charged and that Ramirez receive separate punishment for each count.

V.

SEVERANCE

Ramirez and Izquierdo both sought to separate the trials of their cases from the joint trial of the co-defendants. Ramirez argued that severance was necessary because two of his co-defendants, Vicente Chao and Rafael Izquierdo, might have provided testimony favorable to Ramirez in a separate trial. Izquierdo argued that his case should be severed because there was a great disparity between the degree of evidence against him as compared with the stronger case against the co-defendants, Roberto Gonzalez, Luis Gonzalez, Roberto Ramirez, Angel Amejeiras, Alcides Cruz and Vicente Chao.

In United States v. Moya-Gomez, 860 F.2d 706, 754 (7th Cir.1988), cert. denied, 492 U.S. 908, 109 S.Ct. 3221, 106 L.Ed.2d 571 (1989), we summarized the standard utilized in reviewing a district court’s severance decision:

“Rule 14 permits the trial court in the exercise of its discretion to grant separate trials when the interests of justice so require. A district court’s ruling on a Rule 14 severance motion will be overturned only upon a showing of abuse of discretion. Because the balancing of the cost of conducting separate trials and the possible prejudice inherent in a single trial is best conducted by the trial court, the defendant bears an extremely difficult burden of showing on appeal that the district court abused its discretion. In order to appeal successfully the denial of a severance motion, a defendant must establish actual prejudice resulting from the denial. Actual prejudice means that the defendant could not have a fair trial without severance, ‘ “not merely that a separate trial would afford him a better chance of acquittal.” ’ [United States v. Peters, 791 F.2d 1270, 1301 (7th Cir.), cert. denied, 479 U.S. 847, 107 S.Ct. 168, 93 L.Ed.2d 106 (1986)] (quoting United States v. Papia, 560 F.2d 827, 836 (7th Cir.1977)) ....”

(Footnotes and citations omitted). We have also noted the strong public interest in joint trials in conspiracy cases:

“ ‘In considering a motion for severance, the trial judge should give deference to the “strong public interest in having persons jointly indicted tried together, particularly where, as here, a conspiracy is charged and may be proved by evidence that arises out of the same act or series of acts.” ’ United States v. Percival, 756 F.2d 600, 610 (7th Cir.1985) (quoting Papia, 560 F.2d at 836-37)....”

Briscoe, 896 F.2d at 1516.

A. Ramirez’ Severance Claim — Presentation of Testimony of a Co-Defendant in a Severed Trial

Ramirez alleges that his trial should have been severed from his co-defendants’ in order that he might be permitted to present exculpatory testimony of co-defendants Vicente Chao and Rafael Izquierdo. In support of his pretrial motion for severance, Ramirez supplied an affidavit of Vicente Chao stating that Chao would testify in a separate trial of Roberto Ramirez that Ramirez had traveled to Chicago during the time period of the conspiracy in furtherance of legitimate business dealings. Ramirez also furnished a pretrial affidavit of Rafael Izquierdo which stated that Izquierdo would testify that Ramirez traveled to Chicago on legitimate business during the conspiracy’s time frame and that one of the purposes of Ramirez’ trip to Chicago was to discuss financing of a transaction that would permit Izquierdo to purchase Ramirez’ business, Agromar Enterprises. It is interesting to note that neither of the affidavits contained statements that excluded the possibility that Izquierdo also traveled to Chicago on drug-related business on other occasions during the conspiracy nor specifically discussed, much less detailed with any specificity, Ramirez’ July 1987 trip to Chicago. The government relied upon Ramirez’ July 1987 trip to Chicago in establishing his guilt.

In United States v. Studley, 892 F.2d 518, 525 (7th Cir.1989), we held that:

“When a defendant seeks a severance to avail himself of allegedly exculpatory testimony from a co-defendant, a trial court should consider three factors:
‘(1) whether the co-defendant’s testimony would be exculpatory; (2) whether the co-defendant would in fact testify; and (3) whether the testimony would bear on defendant’s case.’
United States v. Melton, 689 F.2d 679, 686 (7th Cir.1982) (citations omitted).”

As detailed above, the problem with Ramirez’ severance claim is that the content of the statements presented in the affidavits of Chao and Izquierdo would not exculpate Ramirez from allegations that Ramirez took a trip to Chicago for drug-related purposes. They merely state that Ramirez took a legitimate trip to Chicago. Thus, the district court did not abuse its discretion in denying Ramirez' severance motion.

B. Izquierdo’s Motion for Severance — ‘ ‘Spillover” Effect of Evidence

Izquierdo alleges that the trial court should have severed his trial because the evidence presented against his co-defendants was much stronger than the evidence introduced against Izquierdo. In United States v. Diaz, 876 F.2d 1344, 1357 (7th Cir.1989), we summarized the legal principles applicable to a severance claim of this nature:

“ ‘Denial of a motion for severance may be an abuse of discretion if there is a great disparity of evidence between the moving defendant and [his] codefend-ants.' Moya-Gomez, 860 F.2d at 765. But, ‘the fact that the evidence against [his] co-defendants might have been proportionally greater than the evidence against [him] is not itself grounds for a severance.’ United States v. Hendrix, 752 F.2d 1226, 1232 (7th Cir.1985). ‘In such situations, the relevant inquiry is whether it is within the jury’s capacity to follow the trial court’s limiting instructions requiring separate consideration for each defendant and the evidence admitted against [him].’ Moya-Gomez, 860 F.2d at 765. ‘Juries, however, are presumed capable of sorting through the evidence and considering the cause of each defendant separately.’ United States v. Williams, 858 F.2d 1218, 1225 (7th Cir.1988).”

876 F.2d at 1357-58.

In this case the district court provided the jury with the following instruction:

“Although the defendants are being tried jointly, you must give separate consideration to each defendant. In doing so, you must analyze what the evidence in the case shows with respect to each defendant, leaving out of consideration any evidence admitted solely against some other defendant or defendants. Each defendant is entitled to have his case decided on the evidence and the law applicable to him.”

The district court further instructed the jury that:

“Where two or more persons are charged with the commission of a crime, the guilt of one defendant may be established without proof that each of the defendants performed every act constituting the crime charged. However, you must give separate consideration to each individual defendant and to each separate charge against him. Each defendant is entitled to have his case determined from his own conduct and from the evidence which may be applicable to him.”

Izquierdo, despite all the evidence against him, asserts that this proof is less probative than the facts presented against the other defendants. But in previous cases involving allegations of disparate evidence, limiting instructions of the nature enumerated above have been held sufficient to eliminate any prejudice resulting from alleged “spillover” of evidence applicable to other defendants. See United States v. Briscoe, 896 F.2d at 1517-18; United States v. Diaz, 876 F.2d 1344, 1358 (7th Cir.1989). Because the jury was properly instructed and directed to give individual consideration to each and every element of each crime charged against a particular defendant and because “juries ... are presumed capable of sorting through the evidence and considering the cause of each defendant separately,” we are convinced that a jury, following these instructions, was able to give separate consideration to Izquierdo’s case. Izquierdo, thus, did not suffer prejudice as a result of the evidence introduced at the trial.

VI.

PHYSICAL DISPLAY AND ADMISSION INTO EVIDENCE OF 2,248 KILOGRAMS OF COCAINE SEIZED FROM DEFENDANTS

Each of the defendants argues that the trial court acted improperly in admitting and displaying the 2,248 kilograms of cocaine seized from the defendants Peña and Tobon before the jury. The admission and display of this large volume of cocaine was the subject of repeated objections at trial. When the prosecution announced at the opening of the trial that it intended to exhibit this amount of cocaine to the jury, the defendants objected, stating that this would result in a “sideshow” and that it was an “attempt to inflame the jury with the quantity of cocaine_” The defendants went on to state that they would not object to the government’s introduction in evidence of one or two kilograms of cocaine and would stipulate only that this cocaine was part of a shipment of 2,260 kilograms, that it was in fact cocaine and that there was an uninterrupted chain of physical custody. The defendants also suggested that photographs or videotape could adequately portray the quantity of cocaine to the jury. The court, after hearing argument, overruled the objection and allowed the admission of the cocaine and the display of the quantity to the jury for a limited period of time stating that this case involved the transportation of a large volume of cocaine:

“Well, I think that in view of the fact that a fair amount of testimony in this case is going to involve moving it [the cocaine] from one place to another and in this, out of that and so forth, that they’re entitled to indicate to the jury what kind of volume they are talking about. But as far as I am concerned, we do it once, they take a look so that the jury has an idea of the kind of volume that we are talking about, because there is going be a lot of testimony to some logistics of it, and then we get it out of here, and we never see it again.”

After the cocaine was put on display before the jury, the defendants moved for a mistrial. In denying the motion, the court stated: “I will say, again, it seems to me that it is relevant, and the jury has a right to know what kind of actual volume was involved that somebody had to transport in the center of a shipment of plantains.” The next morning several of the defense attorneys requested the court examine each of the jurors to determine whether the introduction and display of this evidence had a prejudicial effect upon them. The judge denied this request, but stated that he was willing to give the jury a limiting instruction. A number of the defendants requested this instruction and, when the jury returned, it was instructed that:

“This is a case where nobody has ever disputed that a large amount of cocaine was imported into the United States by somebody. What the case is all about is whether the government can prove its charges against each of these defendants. We ended up yesterday with all the cocaine being brought in, which, obviously, was a lot of cocaine. It was brought in solely for the purpose of acquainting you with the kind of bulk that was involved and for no other purpose.”

The defendants argue that the admission and display of this amount of cocaine to the jury resulted in prejudice outweighing the probative value of the evidence. Rule 403 of the Federal Rules of Evidence provides that:

“Although relevant, evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence.”

“It is well established that ‘a trial judge’s assessment of relative probative value and unfair prejudice is generally accorded great deference because of his first-hand exposure to the evidence and his familiarity with the course of the trial proceeding.’ ” Briscoe, 896 F.2d at 1498 (quoting United States v. Liefer, 778 F.2d 1236, 1244 (7th Cir.1985) (citation omitted)). Furthermore, it is recognized that any evidence of a crime carries with it a degree of prejudice. See United States v. Sophie, 900 F.2d 1064, 1076 (7th Cir.1990) (“[A]ll probative evidence is prejudicial to the party against whom it is introduced.”).

The amount of cocaine seized (2,248 kilograms) certainly was relevant to establish the magnitude of the conspiracy as well as that the quantity of cocaine could not have been intended for personal use rather than for the purpose of possession with intent to distribute cocaine on a large scale. The jury was given an opportunity to view the drugs in the courtroom for a limited period of time. Furthermore, at the beginning of the following day the jurors were given an instruction that specifically reminded them of the very limited purpose for which the cocaine was introduced (“acquainting [the jury] with the kind of bulk that was involved and for no other purpose”). Thus, we hold that the trial court’s exercise of discretion in admitting into evidence and permitting display of the 2,248 kilograms of cocaine was proper.

VII.

ADMISSION OF EXPERT TESTIMONY CONCERNING LENGTH OF NARCOTICS-RELATED TELEPHONE CALLS

DEA Agent Francis Tucci testified that usually “narcotic-related phone calls or phone calls which deal with narcotic conversations are short. They are against the law, and, therefore, anytime you are committing the crime you make it as short as possible. They are brief.” Chao asserts that Agent Tucci’s statement was “mere speculation” that should not have been admitted into evidence as expert testimony.

We have recognized that federal agents trained and experienced in drug-related transactions, crimes and prosecution are qualified to give expert testimony concerning the practices of those engaged in this type of criminal activity. In United States v. Rollins, 862 F.2d 1282, 1292 (7th Cir. 1988), we permitted a federal agent to provide expert testimony concerning the meaning of narcotics code words and phrases, observing:

“In our view, the district court properly concluded that the meaning of narcotics code words and phrases is not within the common understanding of most jurors. We therefore agree with a number of courts that have addressed this question, that narcotics code words and the operations of drug dealers are generally an appropriate subject for expert testimony. See United States v. Ginsberg, 758 F.2d 823, 830 (2d Cir. 1985) (‘The operations of narcotics dealers are a proper subject for expert testimony under Rule 702.’); United States v. Ramirez, 796 F.2d 212, 216 (7th Cir.1986) (FBI agent properly qualified as an expert to testify to the meaning of code words used during drug transaction); United States v. Martino, 664 F.2d 860, 864 n. 3 (2d Cir. 1981), cert. denied, 458 U.S. 1110, 102 S.Ct. 3493, 73 L.Ed.2d 1373 (1982) (admission of expert testimony regarding the meaning of certain code words used during drug transaction was appropriate). The district court did not abuse its discretion in permitting Agent Wright to give his expert testimony on the meaning of the code words that Wells and Slaughter used to set-up their drug transactions.”

See also Briscoe, 896 F.2d at 1497 (“It is well settled that the meaning of narcotics code words are an appropriate subject for expert testimony”). We stated in United States v. Vega, 860 F.2d 779, 795 (7th Cir. 1988):

“As we observed in United States v. Zanin, 831 F.2d 740, 744 (7th Cir.1987): ‘Conversations regarding drug transactions are rarely clear. A fact-finder must always draw inferences from veiled illusions and code words.’ In this case the jury was confronted with conversations which contained ‘code words’ that when considered in isolation, might seem unclear, veiled and almost nonsensical, but when analyzed properly, in the context of the totality of the evidence, can be clearly be seen to be ‘code words’ for drugs. See generally United States v. Abascal, 564 F.2d 821, 827 (2nd Cir.1977) (‘The conversing conspirators frequently discussed non-narcotic related matters at the beginning of conversations, and often resorted to jargon and code words, a frequent practice in narcotics dealings’); United States v. Chavez, 533 F.2d 491, 494 (9th Cir.1976) (‘Jargon and code words are commonly used by those dealing in elicit drugs and were employed here’) (citation omitted). It is true that, advisedly, no explicit mention was ever made of cocaine or other drugs in any of Vega’s conversations with the Zambra-nas. However, a case was made, which was more than strong enough to convince the jury, the trier of fact, that Vega used terms like ‘chickens,’ ‘roosters,’ and ‘it’ as code words for drugs. Not only are code words always used by drug conspirators when they realize as they do in today’s drug culture, that their telephone conversations are frequently intercepted, such terms were obviously used by the conspirators in this case.”

Furthermore, we have permitted the admission of expert testimony concerning the operation and use of beepers in drug trafficking. See United States v. Solis, 923 F.2d 548, 550-51 (7th Cir. 1991) (“The government was entitled to demonstrate through the use of expert testimony that someone traveling with two kilograms of cocaine under the conditions we have described would find access to beepers a useful means of effectuating the transportation and eventual distribution of her deadly cargo”).

In the same manner that a well trained investigator may properly enlighten a lay jury concerning drug conspirators’ actions including the use of “code words,” he can also inform them of the conspirators’ other practices concerning telephone conversations. The investigator and the expert witness both serve as a link to the drug culture in providing the jury with understanding of the intricate patterns and mo-dus operandi of those participating in drug conspiracies. Furthermore, any questions or problems concerning the expert’s opinion and testimony may be thoroughly explored during the cross-examination of the expert witness. Our examination of the record convinces us that Agent Tueci’s testimony, based upon his experience as a federal drug agent, would be helpful to a jury considering the intricate and clandestine activities of a narcotics conspiracy and, thus, the expert opinion testimony was properly admitted in evidence.

VIII.

ADMISSION OF CHAO’S AFFIDAVIT OF INDIGENCY

Following the completion of the defendants’ cases, the government announced that it would introduce Chao’s affidavit of indigency, prepared for the purposes of obtaining appointed counsel, in its rebuttal case against co-defendants Ramirez and Izquierdo. The reason for this decision was that evidence had been offered in Ramirez’ case that in the summer of 1987 Chao was going to provide financing for Izquierdo to purchase Ramirez’ business, Agromar, and Chao’s indigency would be useful in rebutting this contention. Chao argues that the affidavit of indigency should not have been admitted against his co-defendants because evidence that Chao was indigent would cast doubt upon Chao’s credibility. Specifically, Chao believes that the admission of this evidence against his co-defendants would demonstrate that Chao was “a liar, because he claimed indi-gency when in fact he had a lot of money, or a person who did not want the Government to know about the illegal funds he had acquired.”

Although Chao objected to the admission of the evidence at the time of its introduction and in a post-trial motion, he failed to delineate a specific ground for his objection. “To preserve an issue for appellate review, a party must make a proper objection at trial that alerts the court and opposing party to the specific grounds for the objection.... Neither a general objection to the evidence nor a specific objection on other grounds will preserve the issue for review.” United States v. Wynn, 845 F.2d 1439, 1442 (7th Cir. 1988). Thus, Chao “has waived this issue on appeal unless the admission of [the affidavits] was plain error.” Id. In United States v. White, 903 F.2d 457, 466-67 (7th Cir.1990), we explained the “plain error” standard as follows:

“As we observed in United States v. Silverstein, 732 F.2d 1338, 1349 (7th Cir. 1984): ‘To be plain, an error must be conspicuous, at least in hindsight....’ As we have also noted:
‘A plain error is an error that is “not only palpably wrong but [is] also likely to cause the outcome of the trial to be mistaken.” United States v. Kehm, 799 F.2d 354, 363 (7th Cir. 1986). “A reversal on the basis of plain error can be justified ‘only when the reviewing court is convinced that it is necessary in order to avert an actual miscarriage of justice.’ ” [United States v. Requarth, 847 F.2d 1249, 1254 (7th Cir. 1988)] (quoting United States v. Silverstein, 732 F.2d 1338, 1349 (7th Cir. 1984), cert. denied, 469 U.S. 1111, 105 S.Ct. 792, 83 L.Ed.2d 785 (1985)).’ United States v. Dietrich, 854 F.2d 1056, 1060 (7th Cir.1988).”

“The plain error doctrine allows an appellate court to correct errors that were not objected to at trial if the defendant can demonstrate that he or she probably would have been acquitted but for the erroneously admitted evidence.” Wynn, 845 F.2d at 1443.

Chao asserts that his Fifth Amendment privilege against self-incrimination was violated when his affidavit of indigency was offered against Ramirez and Izquierdo but we fail to understand why, for he has failed to demonstrate how admission of this affidavit in the government’s rebuttal case against his co-defendants served to incriminate him. But, this does not end our discussion, for Chao asserts in his appellate brief that the affidavit’s admission was prejudicial because it questioned his credibility. Nonetheless, as discussed in section V-B of the opinion, the court took the precaution to thoroughly instruct the jury concerning its duty to consider the evidence of Chao’s indigency only against Izquierdo and Ramirez, the specific defendants against whom the evidence had been offered. The Supreme Court has observed: “To say that the jury might have been confused amounts to nothing more than an unfounded speculation that the jurors disregarded clear instructions of the court in arriving at their verdict. Our theory of trial relies upon the ability of a jury to follow instructions.” Opper v. United States, 348 U.S. 84, 95, 75 S.Ct. 158, 165, 99 L.Ed. 101 (1954). Because we are convinced the jury was able to follow the specific instructions to consider evidence solely against the parties concerning whom it was introduced, we conclude that the trial court did not commit plain error in receiving the affidavit of indigency in evidence.

IX.

THE GOVERNMENT’S CLOSING ARGUMENT

Chao asserts that his due process right to a fair trial was violated when the prosecutor, during rebuttal closing argument, stated that Chao had stolen the box containing 17 kilograms of cocaine that was missing when the government seized the truck driven by Peña and Tobon. Chao asserts that there was nothing in the record to support this statement and, thus, the government’s statement violated his right to a fair trial.

In United States v. Stillwell, 900 F.2d 1104, 1112 (7th Cir.1990), we set forth the law applicable to a defendant’s claim that his rights were violated by an improper government closing argument:

“Defendants are entitled to a new trial only if the government’s comments were improper ones that prejudiced the defendants’ rights to a fair trial. It is, of course, improper to suggest that opposing counsel’s objection was not proper or to rely on information not in evidence. It is also improper to inform the jury that there is information not in evidence that supports the government’s case. In determining whether comments prejudiced the defendants’ right to a fair trial, however, the comments must be viewed in the context of the entire trial.”

(Citations omitted). In determining whether a defendant’s right to a fair trial was violated as a result of prosecutorial misconduct, we have observed that:

“This court’s review of a claim of pros-ecutorial misconduct follows a bifurcated analysis. First, this court examines the challenged remark in isolation to determine whether it was improper. If the court concludes that the remark was improper, the remark is evaluated in light of the entire record to determine whether it deprived the defendant of a fair trial.”

United States v. Spivey, 859 F.2d 461, 465 (7th Cir.1988).

Initially, we turn to an examination of “the challenged remark in isolation.” Spivey, 859 F.2d at 465. During oral argument the government asserted that the evidence in the record was sufficient to allow the inference that Chao stole the box containing cocaine. The government contends that since Chao had control over the boxes in the warehouse prior to his arrest, he could have removed the box from the shipment before his arrest and might very well have instructed someone to return it subsequent to his arrest. We have been unable to find proof sufficient to support this inference. In United States v. De Geratto, 876 F.2d 576, 586-87 (7th Cir.1989), we determined that a prosecutor presented an argument that when considered, in isolation, was improper where he “went beyond the evidence and stated that the missing record ‘had obviously been suppressed and are sitting in an ashtray somewhere,’ ” and when he accused the defendant “without proof, in the prosecutor’s words, of ‘deep sixing’ the records.” De Geratto, 876 F.2d at 587. Based upon this precedent, reference to Chao’s supposed theft of a box containing 17 kilograms of cocaine was improper in isolation.

Under the bifurcated analysis set forth in Spivey, this is only the first step of the two-step process to determine whether there is reversible error. “[T]he remark [must be] evaluated in light of the entire record to determine whether it deprived the defendant of a fair trial.” Spivey, 859 F.2d at 465. In addressing the issue of whether the constitutional right to a fair trial was interfered with as a result of improper prosecutorial comments in United States v. Pirovolos, 844 F.2d 415, 426 (7th Cir.1988), we drew

“guidance from the Supreme Court’s ... decision in Darden [v. Wainwright ], 477 U.S. 168, 106 S.Ct. 2464 [91 L.Ed.2d 144 (1986)]. In that case the Court discussed several criteria that may be helpful in our inquiry. They include: (1) the nature and seriousness of the prosecuto-rial misconduct, (2) whether the prosecutor’s statements were invited by impermissible conduct by defense counsel, (3) whether the trial court instructed the jury to disregard the statements, (4) whether the defense was able to counter the improper arguments through rebuttal, and (5) the weight of the evidence against the defendant. Id. at 181-83, 106 S.Ct. at 2472-73.”

Just as we refused to reverse on the basis of an improper closing argument in Pirovolos, here, as in Pirovolos, there are factors that weigh in favor of the defendant, while others tip the scales in favor of the government. Certainly the inclusion of an improper, uninvited statement in the prosecution’s closing argument on rebuttal limited Chao’s opportunity to counter the argument without intervention by the court on proper motion. But, it is important to note that immediately following Chao’s objection to the closing argument, the trial court provided the jury with the following instruction: “It’s argument. If a lawyer makes an argument that isn’t supported by reasonable inference and the evidence, then the jury should disregard it.” Furthermore, at the conclusion of the case the court instructed the jury that:

“Opening statements of counsel are for the purpose of acquainting you in advance with the facts counsel expect the evidence to show. Closing arguments of counsel are for the purpose of discussing the evidence....
“The evidence consists of the sworn testimony of the witnesses, the exhibits received in evidence, and stipulated or admitted facts....
“You are to consider only evidence received in this case. You should consider this evidence in the light of your own observations and experiences in life. You may draw such reasonable inferences as you believe to be justified from proved facts.
“You are to disregard any evidence to which I sustained an objection or which I ordered stricken_
“You should decide this case solely on the evidence presented here in the courtroom.

(Emphasis supplied). Thus, the court provided adequate limiting instructions to the challenged argument both immediately after the objection was made and again in the formal jury instructions given prior to the jury retiring for deliberation.

The most important factor to be considered in determining whether the closing statement violated Chao’s rights is that the proof of Chao’s guilt was more than sufficient. As we noted in Pirovolos:

“Most important, though, the evidence of Pirovolos's guilt was truly overwhelming. Such strong evidence of guilt ‘eliminates any lingering doubt that the prosecutor’s remarks unfairly prejudiced the jury’s deliberations.’ [United States v. Young, 470 U.S. 1, 19, 105 S.Ct. 1038, 1048, 84 L.Ed.2d 1 (1985) ]; see also Darden, 477 U.S. at 182, 106 S.Ct. at 2472 (overwhelming evidence of guilt a factor in affirming conviction despite serious prosecutorial misconduct); Berger v. United States, 295 U.S. 78, 89, 55 S.Ct. 629, 633, 79 L.Ed. 1314 (1935) (overwhelming evidence of guilt justified affirming verdict even in the face of highly improper conduct by prosecutor).”

Pirovolos, 844 F.2d at 427. The evidence against Chao was overwhelming. Chao was actively involved in the operations of the Chicago warehouse business (Celi-Mar), the cocaine delivery point in July of 1987. Chao supervised and even participated in the unloading and loading of the drug cargo. Furthermore, Chao made statements at the time of this delivery to Peña and Tobon concerning what they might do to locate the boxes containing cocaine, the efforts the co-conspirators expended to keep Matteo Hernandez, the owner of the business, away from the premises during the cocaine delivery and expressed concern that the drug transfer be completed prior to Hernandez’ return. In addition, a search of the Celi-Mar warehouse following Chao’s arrest resulted in the discovery of a business card that Alvaro Quintero had instructed Peña to hand to Chao as a signal to Chao that he was to turn the cocaine delivery over to Peña. This card was probative because the evi-denee clearly established that Chao did, in fact, deliver cocaine to Peña as Quintero had contemplated when Peña exhibited the business card (signal). Even though it directly reflects on Chao’s credibility, the question of whether Chao stole a box of cocaine did not bear upon the central questions of whether Chao was an active and knowledgeable member of the conspiracy and further that he knowingly possessed cocaine with intent to distribute in July 1987. The overwhelming evidence of Chao’s guilt beyond a reasonable doubt is sufficient for us to conclude that the prosecutor's improper comments did not rise to the level of a violation of the defendant’s due process rights and thus deprive him of a fair trial. See Pirovolos, 844 F.2d at 427 (prosecutorial misconduct was not constitutional error in light of overwhelming evidence of defendant’s guilt).

Likewise, the strong evidence of Chao’s guilt detailed in our consideration of the issue of constitutional error also leads us to the conclusion that Chao has failed to demonstrate “that any error here may have substantially influenced the jury’s verdict.” Pirovolos, 844 F.2d at 427. Thus, we hold that the prosecutor’s closing argument does not require reversal.

Although we do not reverse Chao’s conviction, neither do we approve of the prosecutor’s conduct in closing argument. We strongly suggest that prosecuting attorneys thoroughly prepare their closing arguments before delivery and thus avoid such reckless and unsupportable comments and/or supposed legitimate inferences. “The prosecutor’s office is an entity [of the government] and as such it is the spokesman for the Government.” Giglio v. Unit- ed States, 405 U.S. 150, 154, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972). “The United States Attorney is the representative not of an ordinary party to a controversy, but of a sovereignty whose obligation to govern impartially is as compelling as its obligation to govern at all; and whose interest, therefore, in a criminal prosecution is not that it shall win a case, but that justice shall be done.” Berger v. United States, 295 U.S. 78, 88, 55 S.Ct. 629, 633, 79 L.Ed. 1314 (1935). “It is well understood in the realm of ethical and proper conduct of a criminal trial, that the prosecutor ‘may prosecute with earnestness and vigor — indeed, he should do so. But, while he may strike hard blows, he is not at liberty to strike foul ones.’ ” United States v. Chaimson, 760 F.2d 798, 809 (7th Cir.1985) (quoting Berger v. United States, 295 U.S. 78, 88, 55 S.Ct. 629, 633, 79 L.Ed. 1314 (1935)). Prosecutors must remember to live up to the code of professional ethics and fair play at all times or the American system of justice cannot endure, and ultimately our nation will lose confidence and trust in its rendering of justice, but, we refuse to reverse a conviction when we are convinced that the improper argument did not rise to the level of a constitutional violation of the defendant’s rights. As we concluded in Pirovo-los:

“In closing, we emphasize that we do not reverse convictions to punish prosecutors. ‘It is better to punish the prosecutor directly; there is no lack of sanctions for a lawyer’s misconduct of which improper advocacy is a well recognized species.’ United States v. Mazzone, 782 F.2d 757, 763 (7th Cir.1986); See also Young, 470 U.S. at 7-11, 105 S.Ct. at 1042-44. When the seriousness of prose-cutorial misconduct and the weakness of evidence of guilt causes to question a trial’s fairness, we will not hesitate to reverse the resulting conviction and order a new trial. See, e.g., Mauricio v. Duckworth, 840 F.2d 454 (7th Cir.1988); Williams v. Lane, 826 F.2d 654 (7th Cir. 1987); United States v. Shue, 766 F.2d 1122 (7th Cir.1985). Here, however, ‘[t]he evidence against the appellant was overwhelming; it included substantial eye-witness evidence ... as well as physical evidence_ It is almost inconceivable that if the prosecutor had refrained from making the remarks that he did, the appellant [ ] would have been acquitted.’ Mazzone, 782 F.2d at 764. As the Supreme Court often has reminded us, the Constitution guarantees a fair trial, not a perfect one. See, e.g., Delaware v. Van Arsdall, 475 U.S. 673, 681, 106 S.Ct. 1431, 1436, 89 L.Ed.2d 674 (1986); United States v. Hasting, 461 U.S. 499, 508-09, 103 S.Ct. 1974, 1980-81, 76 L.Ed.2d 96 (1983); Bruton v. United States, 391 U.S. 123, 135, 88 S.Ct. 1620, 1627, 20 L.Ed.2d 476 (1968).”

Pirovolos, 844 F.2d at 427.

X.

CONSCIOUS AVOIDANCE INSTRUCTION

Luis Gonzalez asserts that the trial court erred when it provided a “conscious avoidance” jury instruction, alleging that the evidence “offered no reasonable basis for the inference that Gonzalez knew or should have suspected that something foul was afoot relating to the [July 1987 cocaine] shipment.” The trial court gave the following instruction:

“You may infer knowledge from a combination of suspicion and indifference to the truth. If you find that a person had a strong suspicion that things were not what they seemed or that someone had withheld some important facts, yet shut his eyes for fear of what he would learn, you may conclude that he acted knowingly, as I have defined that word.”

We have approved the above formulation of the “conscious avoidance” or “ostrich” instruction in a number of previous cases. See United States v. Valencia, 907 F.2d 671, 679 (7th Cir.1990); United States v. Paiz, 905 F.2d 1014, 1022-23 (7th Cir.1990); United States v. Defazio, 899 F.2d 626, 635-36 (7th Cir.1990); United States v. Herrero, 893 F.2d 1512, 1537-38 (7th Cir.), cert. denied, — U.S. -, 110 S.Ct. 2623, 110 L.Ed.2d 644 (1990); United States v. Talkington, 875 F.2d 591, 595-96 (7th Cir. 1989); United States v. Diaz, 864 F.2d 544, 549-51 (7th Cir.1988), cert. denied, 490 U.S. 1070, 109 S.Ct. 2075, 104 L.Ed.2d 639 (1989). In United States v. Bigelow, 914 F.2d 966, 970 (7th Cir.1990), we set forth the law currently applicable to the review of a conscious avoidance instruction:

“At the outset, we note that in assessing the district court’s determination to give this instruction, we must review the evidence and any reasonable inferences that can be drawn from that evidence in the light most favorable to the government. See United States v. Talkington, 875 F.2d 591, 596 (7th Cir.1989); United States v. Johnson, 605 F.2d 1025, 1028 (7th Cir.1979). In addition, we do not review instructions in lonely isolation, but rather in the context of the trial as an integrated whole. See United States v. Herrero, 893 F.2d 1512, 1536 (and cases cited therein).
“While we have warned that ‘this instruction should be given only when it addresses an issue reasonably raised by the evidence,’ [United States v. Diaz, 864 F.2d 544, 549 (7th Cir.1988) ], an ostrich instruction is appropriate when ‘the defendant claims a lack of guilty knowledge and there are facts and evidence that support an inference of deliberate ignorance.’ Talkington, 875 F.2d at 596 (quoting United States v. White, 794 F.2d 367, 371 (8th Cir.1988)) (and cases cited therein).”
“In Diaz, we stated:
‘The ostrich instruction has been principally employed where there is evidence that the defendant is associated with a group, but where there is also evidence that the defendant consciously was avoiding knowledge of the illegal nature of the group’s activity. In most cases, the defendant acknowledges his association with the group, but, despite circumstantial knowledge to the contrary, denies knowledge of the group’s illegal activity.’ 864 F.2d at 550.”

Viewing the evidence in the light most favorable to the government, on the challenge of the conscious avoidance instruction, there are a number of facts that lead us to the conclusion that Luis Gonzalez was aware of the illegal activities of the conspiratorial group. Daniel Petroski, who transported the cocaine in his truck, from Miami to New York and then to Chicago, identified Luis Gonzalez as the individual who met him at the Las Villas Warehouse in New York on July 28, 1987, entered his trailer and inspected his cargo with a flashlight. Gonzalez gave Petroski a yellow sheet of paper with the address and phone number of the Celi-Mar warehouse, told him to contact Chao and informed him that the load was misdirected and should have gone to Chicago. Gonzalez’ meeting with Petroski occurred during a trip Gonzalez made with co-conspirator, Tellechea, tracking the cocaine from Miami to New York and then to Chicago. In Chicago Tellechea and Gonzalez stayed at the same hotel and records of telephone calls between Telle-chea’s room and cocaine supplier Roberto Ramirez’ hotel room, as well as between Tellechea’s room and the Celi-Mar warehouse were received in evidence. When Gonzalez and Tellechea left Chicago, following Chao’s arrest, they flew together to Detroit and then on to Miami, in what Tellechea described to Julio Ortiz as an effort to erase trails. Luis Gonzalez’ activities relative to the July 1987 cocaine shipment took place following his appointment as manager of International Palm Products, the outlet for receiving the cocaine imported from Honduras. As reflected in his trial testimony, Julio Ortiz, a knowledgeable member of the conspiracy, formerly managed the business which received the imported cocaine. Although Gonzalez had headed International Palm Products for only two weeks, it is quite reasonable to believe that the person entrusted with taking over the role as head of a drug conspiracy’s importation outlet would be well aware of the conspiracy’s illegal activities. In light of the clandestine nature of a drug conspiracy and the control conspirators exercise over the organization’s membership, no conspiracy would place an individual at the very heart of its million-dollar drug import business if he was not well known and knowledgeable of its activities as well as trusted by the members of the organization.

Based upon the totality of the evidence presented, a reasonable jury could have properly come to the conclusion that Luis Gonzalez was aware of the conspiracy and its illicit purposes. Despite the clear evidence of this association with members of the conspiratorial group, Luis Gonzalez asserts that he lacked knowledge of the conspiracy’s drug related activity. We have recognized that: “Such a scenario, one in which ‘the defendant acknowledges [his] association with the group but, despite circumstantial evidence to the contrary, denies knowledge of the group’s illegal activity,’ is a paradigm case for the use of the ‘ostrich’ instruction.” United States v. Paiz, 905 F.2d 1014, 1022 (7th Cir.1990) (quoting Diaz, 864 F.2d at 550). The conscious avoidance instruction also appropriately implements the legal rule that

“with respect to the question of knowing participation in a conspiracy, it is well settled that ‘[i]f the facts indicate the defendant must have known something ... then a jury may be able to find beyond a reasonable doubt that [he] did know it, especially since the requirement of knowledge is satisfied by proof that the defendant willfully shut [his] eyes for fear of what [he] might see if [he] opened them, United States v. Josefik, 753 F.2d 585, 589 (7th Cir.1985).’ ”

United States v. Diaz, 876 F.2d 1344, 1354 (7th Cir.1989) (quoting United States v. Cerro, 775 F.2d 908, 911 (7th Cir.1985)). We are convinced that the evidence in the record of Luis Gonzalez' involvement in the conspiracy demonstrates that his alleged lack of knowledge could only have resulted from his “cutting off of [his] normal curiosity” and thus is more than sufficient to uphold the trial court’s conscious avoidance instruction.

XI.

SUFFICIENCY OF THE EVIDENCE— THE CHALLENGES OF IZQUIERDO, AMEJEIRAS, LUIS GONZALEZ AND CHAO

Izquierdo, Amejeiras, Luis Gonzalez and Chao challenge the sufficiency of the evidence to support their convictions on the conspiracy count (Count I). Chao alleges that there was inadequate proof that he knowingly possessed cocaine with intent to distribute (Count II), and Izquierdo, Ame-jeiras and Luis Gonzalez each argue that the insufficient documentation of their knowing participation in the conspiracy precludes their conviction under either a vicarious liability theory or an aiding and abetting theory for each of the two counts of possession of cocaine with intent to distribute (Counts II and III) alleged in the indictment. Chao claims that the evidence against him lacked the quantum of proof required to demonstrate that he possessed cocaine with intent to distribute (Count II). He further alleges that the insufficient evidence of his knowing participation in the conspiracy requires the conclusion that there was no basis for his conviction on the remaining count of possession of cocaine with intent to distribute (Count III) under either an aiding and abetting or vicarious liability theory.

We have summarized our standard of review for sufficiency of the evidence as follows:

“ ‘In evaluating [Haro’s] sufficiency of the evidence challenge, we note that [he] bears a heavy burden. Initially, we “review all the evidence and all the reasonable inferences that can be drawn from the evidence in the light most favorable to the government.” ’ United States v. Nesbitt, 852 F.2d 1502, 1509 (7th Cir. 1988) (quoting United States v. Pritchard, 745 F.2d 1112, 1122 (7th Cir.1984)). ‘The test is whether after viewing the evidence in the light most favorable to the government, “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” ’ Pritchard, 745 F.2d at 1122 (quoting Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979) (emphasis in original)).”

United States v. Herrero, 893 F.2d 1512, 1531 (7th Cir.1990). As we observed in United, States v. Caudill, 915 F.2d 294, 297 (7th Cir.1990): Thus the appellants carry a heavy burden in asking us to reverse their convictions for lack of evidence. United States v. Caudill, 915 F.2d 294, 297 (7th Cir.1990).

“A verdict will withstand a sufficiency of the evidence challenge unless there is no evidence from which the jury could find guilt beyond a reasonable doubt. See United States v. Beverly, 913 F.2d 337, 360 (7th Cir.1990); United States v. Durrive, 902 F.2d 1221, 1225 (7th Cir. 1990). In appeals of jury trials such as this case, we are obliged to ‘ “defer to reasonable inferences drawn by the jury and the weight it gave to the evidence. Likewise, we leave the credibility of witnesses, solely to the jury’s evaluation, absent extraordinary circumstances.” ’ Beverly, at 360 (quoting United States v. Hogan, 886 F.2d 1497, 1502 (7th Cir.1989) (citation omitted)). To sustain the conspiracy charge against [the defendants], the government need only prove the existence of the conspiracy and a participatory link with the defendants. Durrive, 902 F.2d at 1225, United States v. Missick, 875 F.2d 1294, 1297 (7th Cir.1989). Substantial evidence must support both the existence of the conspiracy and the defendants’ participation in it. Durrive, 902 F.2d at 1229. Nonetheless, we ‘view the evidence in the light most favorable to the government and accept circumstantial evidence as support, even sole support, for a conviction.’ Id.”

A. Existence of a Single Conspiracy as Alleged in the Indictment — Variance

Initially, Chao and Izquierdo argue that the evidence did not establish their participation in a single overall conspiracy with the remaining defendants as alleged in the indictment. Rather, Chao and Izquierdo assert that the evidence demonstrates that they participated in a conspiracy only with respect to the July 1987 drug delivery. Thus, they assert there was an improper variance between the proof offered at trial and the allegations in the indictment that they participated in an ongoing narcotics importation and distribution conspiracy that took place from October 1986 to July 1987.

In United States v. Briscoe, 896 F.2d 1476, 1505 (7th Cir.1990), we reiterated the “various elements necessary to establish a single conspiracy” set forth in United States v. Varelli, 407 F.2d 735, 742 (7th Cir.1969):

“ ‘Various people knowingly joining together in furtherance of a common design or purpose constitute a single conspiracy. While the conspiracy may have a small number of co-conspirators, other parties who knowingly participate with these co-conspirators and others to achieve a common goal may be members of an overall conspiracy.
“ ‘In essence, the question is what is the nature of the agreement. If there is one overall agreement among the various parties to perform different functions in order to carry out the objectives of the conspiracy, the agreement among all parties constitutes a single conspiracy.’ ”

Briscoe, 896 F.2d at 1505 (quoting Varelli, 407 F.2d at 742). As we emphasized in United States v. Paiz, 905 F.2d 1014, 1020 (7th Cir.1990):

“A single conspiracy exists ‘[i]f there is “one overall agreement among the various parties to perform different functions in order to carry out the objectives of the conspiracy.” ’ [U.S. v.] Sababu, 891 F.2d [1308] 1322 [(7th Cir.1989)] (quoting United States v. Varelli, 407 F.2d 735, 742 (7th Cir.1969)). ‘[Multiple] conspiracies exist when each of the conspirators’ agreements has its own end, and each constitutes an end in itself.’ Id. (citing Blumenthal v. United States, 332 U.S. 539, 558-59, 68 S.Ct. 248, 257-58, 92 L.Ed. 154 (1947)).”

Paiz, 905 F.2d at 1020. As we observed in Briscoe, 896 F.2d at 1507:

“It is well settled that a single conspiracy may consist of ‘a small core of people with whom other conspirators knowingly participate to achieve the common purpose of the conspiracy.’ United States v. Noble, 754 F.2d 1324, 1329 (7th Cir.), cert. denied, 474 U.S. 818, 106 S.Ct. 63, 88 L.Ed.2d 51 (1985). It is equally well established that the parties involved in a single conspiracy need not know one another or participate in every aspect of the conspiracy, id. at 1329.... In any case, as long as the evidence demonstrates that the ‘coconspirators ... “knowingly embraced a common criminal objective,” ’ this is sufficient to establish the existence of a single overall conspiracy among the coconspirators.”

(Quoting United States v. Boucher, 796 F.2d 972, 975 (7th Cir.1986)). Although we scrutinize the conspiratorial agreement in our determination of whether the facts support a conclusion of single or multiple conspiracies, we realize the limited scope of our review of the jury’s determination of this issue:

“In performing a variance review we do not comb the evidence de novo, as the appellants might like. Our review is second-hand. The jury gets first crack at deciding ‘whether there is one conspiracy or several when the possibility of a variance appears.’ United States v. Percival, 756 F.2d 600, 609 (7th Cir.1985). This is so because a question of variance is a question of fact, which is something especially within the jury’s realm of expertise .... At this stage the question for us simply is whether the evidence is sufficient to support the jury’s determination. We must view the proof at trial in the light most favorable to the prosecution, and we must uphold the jury’s single conspiracy determination if any rational trier of fact could have found beyond a reasonable doubt the one conspiracy. ‘We give deference to the jury’s weighing of the evidence and its drawing of reasonable inferences.’ [United States v. Sababu, 891 F.2d 1308, 1322 (7th Cir.1989)]. This deference is significant: Given the nature of conspiracies, juries often must infer their existence and scope from circumstantial evidence and ‘the reasonable inferences drawn therefrom.’ ”

Paiz, 905 F.2d at 1019 (quoting United States v. Whaley, 830 F.2d 1469, 1473 (7th Cir.1987), cert. denied, 486 U.S. 1009, 108 S.Ct. 1738, 100 L.Ed.2d 202 (1988)) (footnote and citations omitted) (emphasis added).

In this case a core group of Miami-based conspirators led by Manuel Angel Telle-chea, Alcides Cruz and Roberto Ramirez imported cocaine from Honduras to Miami. Ramirez obtained cocaine for the conspiracy, while Tellechea and Cruz supervised the transportation of drugs from Columbia to Honduras and then to Miami. Also involved in the conspiracy’s importation operation were Julio Ortiz and Luis Gonzalez, who managed the conspiracy’s Miami import business at different times during 1987, Angel Amejeiras, who performed a variety of tasks in assisting the conspiracy’s Miami operation; Rafael Izquierdo, who worked for Ramirez and was involved in the July 1987 cocaine transportation operation; Vicente Chao, who received the July 1987 cocaine shipment in Chicago; Jesus Ortiz, who handled the cocaine shipments in Honduras; and Miguel Garin and Manuel Garcia, Hondurans who played small roles in the conspiracy’s Honduran operations. The conspiracy’s New York-based domestic distribution network was overseen by Alvaro Quintero and utilized Jose Alexander Peña and Cesar Tobon as couriers. Roberto Gonzalez received shipments that Peña and Tobon delivered from Miami to New York and within the New York area. Both the importation and domestic distribution branches were active from August 1986 to July 1987, although there was a brief cessation of operations following the Honduran military’s interception of a plane containing a shipment of the conspiracy’s cocaine in October 1986. Because we view “an ongoing drug conspiracy involving core members who buy and sell to various suppliers and dealers who may change over time — as a single conspiracy rather than a series of smaller conspiracies,” United States v. Sophie, 900 F.2d 1064, 1081 (7th Cir.1990), and because “parties involved in a single conspiracy need not ... participate in every aspect of the conspiracy,” Briscoe, 896 F.2d at 1507, it is immaterial whether Chao or Izquierdo were involved in cocaine transactions with other members of the ongoing conspiracy prior to July 1987. When we view the evidence in a light most favorable to the prosecution, it is clear that a rational trier of fact could and did find beyond a reasonable doubt a single conspiracy based upon Izquierdo and Chao’s dealings with the core group of importers and distributors in the ongoing conspiracy during July 1987.

B. Izquierdo’s, Amejeiras’, Luis Gonzalez’ and Chao’s Participation in a Single Overall Conspiracy

Having determined that there was substantial evidence to establish the existence of a single overall conspiracy as alleged in the indictment, we now proceed to determine whether the record contains substantial evidence to support the jury’s verdicts that Izquierdo, Amejeiras, Luis Gonzalez and Vicente Chao knowingly participated in the conspiracy. In United States v. Briscoe, 896 F.2d 1476, 1505 (7th Cir.1990), we observed:

“The government may establish a defendant’s knowing participation in a single conspiracy by offering evidence that:
‘[t]he parties to the agreement were aware that others were participating in the scheme. The co-conspirators must have “knowingly embraced a common criminal objective.” ... However, there is no requirement that the participants in the plan “personally know the individuals involved ... [a]s long as the conspiracy continues in its goals to achieve a common objective.” ’
United States v. Boucher, 796 F.2d 972, 975 (7th Cir.1986) (citations omitted). In other words, the government may establish that a defendant knowingly became a member of a single narcotics conspiracy ‘ “if each [defendant retailer] knew or had reason to know, that other retailers were involved with the ... organization in a broad project for smuggling, distribution and retail sale of narcotics, and had reason to believe that their own benefits derived from the operation were probably dependent upon the success of the entire venture ... ” ’ United States v. Cerro, 775 F.2d 908, 911 (7th Cir.1985) (emphasis in Cerro and citation omitted).”

In addressing the question of whether substantial evidence supports a conclusion of knowing participation in the single overall conspiracy we have recognized that, as an appellate court: “Our job is not to weigh the evidence or assess the credibility of the witnesses. Our job is merely to determine if the evidence introduced is sufficient to support the jury’s finding of knowing participation, a finding that may arise from circumstantial evidence and the reasonable inferences derivable therefrom.” Paiz, 905 F.2d at 1021 (citations omitted).

1. Rafael Izaquierdo’s Participation in the Conspiracy

Rafael Izquierdo asserts that the evidence was insufficient to demonstrate his participation in a single overall conspiracy with the other defendants. He further contends that because the government failed to establish by a preponderance of the evidence that Izquierdo was a member of a conspiracy including Vicente Chao, testimony of Cesar Tobon dealing with the hearsay statement that someone was keeping the owner of the Celi-Mar warehouse away from the business on the day of the cocaine delivery should not have been admitted into evidence.

Izquierdo traveled to Chicago on July 16, 1987, immediately prior to the cocaine delivery, with the conspiracy’s cocaine supplier, Roberto Ramirez. Ramirez and Izquierdo traveled on airline tickets Izquierdo had purchased for them with Izquierdo’s charge card. Telephone records documented frequent telephone contacts during the time period of the conspiracy between Izquierdo and Vicente Chao, the conspirator who received the cocaine delivery. Shortly before Izquierdo’s arrival in Chicago, toll records reflected calls between Izquierdo’s home and Celi-Mar and from Izquierdo’s residence to Chao. The record of frequent telephone contacts, including the telephone calls between Izquierdo’s home and Celi-Mar on the day prior to the arrival of the June 1987 cocaine shipment in Miami is just another part of the evidence establishing a relationship between Izquierdo and Chao. After arriving in Chicago, Izquierdo kept the Celi-Mar warehouse’s owner, Matteo Hernandez, away from the warehouse premises on the day of the cocaine delivery by taking him on a series of calls ostensibly designed to generate fish sales. The importance of Izquierdo’s conduct to the conspiracy and the knowledge he had of the drug ring’s purposes is confirmed in the apprehension enunciated in Vicente Chao’s statement to Pena and Tobon concerning the possibility of Matteo Hernandez, the owner of the Celi-Mar warehouse, returning before the drug shipment left the Celi-Mar warehouse. When Izquierdo took Hernandez away from the Celi-Mar warehouse, he allowed the conspirators to transfer the cocaine shipment without Hernandez’ knowledge. The jury had evidence of the role Izquierdo played in the prevention of Hernandez’ returning to the Celi-Mar warehouse, which helped to insure the success of the July 1987 cocaine delivery. The jury also had before it evidence of Izquierdo’s travel to Chicago in the company of Roberto Gonzalez, an individual involved in arranging the purchase of the cocaine that the conspirators shipped to Miami and of Izquierdo’s frequent contact with conspirator Vicente Chao during the time of the conspiracy’s cocaine shipments in the summer of 1987. Based upon these facts, the jury could conclude beyond a reasonable doubt that Izquierdo was a knowing participant in a single overall cocaine importation and distribution conspiracy that included Vicente Chao.

Because we are of the opinion that the evidence set forth above established beyond a reasonable doubt Izquierdo’s knowing participation in the conspiracy, it also follows that there was certainly more than a preponderance of the evidence upon which the trial judge could conclude that Izquierdo was a member of the conspiracy for the purpose of determining the admission of the co-conspirator hearsay. Thus, the trial judge properly received in evidence Chao’s statement, as co-conspirator hearsay, that someone was keeping Celi-Mar’s owner away from the Celi-Mar warehouse on the day of the July 1987 cocaine delivery.

2. Angel M. Amejeiras’ Participation in the Conspiracy

Angel M. Amejeiras alleges that the evidence demonstrated that he was merely an “errand boy” for the other conspirators and thus not a knowing participant in the conspiracy. We disagree.

Amejeiras was one of the persons present at the conspirators’ February 1987 planning meeting. As to the July 1987 drug shipment, Amejeiras was one of the individuals who met with Daniel Petroski in the successful attempt to hire him to deliver cocaine from Miami to New York and on to Chicago. Julio Ortiz testified that Ame-jeiras demonstrated familiarity with the circumstances of the July 1987 cocaine shipment in a conversation with Ortiz concerning the diversion of the cocaine. In addition, telephone records established that during the time Tellechea, a consistent participant in the conspiracy, was trailing the cocaine shipment from Miami to New York and then on to Chicago a number of calls were made from the hotel rooms where Tellechea was staying to Amejeiras’ residence and from Amejeiras’ home to Telle-chea’s hotels. Furthermore, after Amejeir-as received a telephone call from Julio Ortiz informing him that the burglar alarm had been tripped at the offices of International Palm Products, Amejeiras drove to International Palm Products where he was met by federal agents conducting a search of the premises. The above evidence provided the jury with a sufficient basis to conclude that Amejeiras was a knowledgeable participant in the drug conspiracy enterprise.

3. Luis Gonzalez’ Participation in the Conspiracy

Luis Gonzalez asserts that the evidence was insufficient to demonstrate that he knowingly participated in the cocaine importation and distribution conspiracy. We detailed the evidence supporting Gonzalez’ knowledgeable participation in the conspiracy in our discussion of the conscious avoidance instruction in Section X, supra.

Gonzalez was identified as the individual who personally inspected the cocaine shipment in New York and who advised Petro-ski, the truck driver, that the shipment should have been delivered to Chicago rather than New York.

After Gonzalez traveled with a co-conspirator to follow the cocaine from Miami to New York to Chicago, he attempted to confuse his pursuers by flying from Chicago to Detroit and later on to Miami rather than proceeding on a direct flight from Chicago to Miami.

Gonzalez exercised control over the conspiracy’s reception center designated for the receiving of cocaine from Honduras. It is beyond comprehension and ridiculous to expect one to believe that conspirators, concerned with the secrecy of a clandestine business where killing is a frequent occurrence to prevent information from reaching authorities and/or to enforce debts, would entrust an individual with a major role in the conspiracy if he lacked knowledge of the conspiracy. Thus, a jury could reasonably find that although Gonzalez was managing the conspiracy’s business for only two weeks, his position in the management and control of the conspiracy’s enterprise for receiving cocaine through Honduras exposed him to the intricate business of cocaine importation and distribution.

Based upon all the evidence of Gonzalez’ participation in the conspiracy before and after his advancement to the managerial position recounted in this section, as well as in Section X, supra, a reasonable jury could very easily reach the conclusion that Luis Gonzalez was a knowing participant in the conspiracy. This is especially true because “with respect to the question of knowing participation in a conspiracy, it is well settled that ‘[i]f the facts indicate the defendant must have known something ... then a jury may be able to find beyond a reasonable doubt that [he] did know it, especially since the requirement of knowledge is satisfied by proof that the defendant willfully shut [his] eyes for fear of what [he] might see if [he] opened them, United States v. Josefik, 753 F.2d 585, 589 (7th Cir.1985).’ ” United States v. Diaz, 876 F.2d 1344, 1354 (7th Cir.1989) (quoting United States v. Cerro, 775 F.2d 908, 911 (7th Cir.1985)). Thus, we conclude that the jury’s verdict that Luis Gonzalez knowingly participated in the drug importation and distribution conspiracy was proper.

4. Vicente Chao’s Participation in the Conspiracy and Chao’s Possession of Cocaine with Intent to Distribute

Vicente Chao asserts that the evidence was insufficient to demonstrate either that he knowingly participated in the single overall drug importation and distribution conspiracy or that he knowingly possessed cocaine with intent to distribute the same on July 29, 1987, when he accepted delivery of the cocaine shipment at the Celi-Mar warehouse and transferred the cocaine to Peña and Tobon for further distribution.

The evidence reveals that when Petroski arrived with the cocaine shipment on July 29 at the Celi-Mar warehouse, Chao participated in the unloading of the plantains and cocaine. After Tobon and Peña arrived at the warehouse, Chao explained the proper procedure for locating the boxes containing the cocaine. He suggested that they stick their fingers through the boxes’ air holes, and that upon touching plastic wrapping without plantain fruit, they would ascertain that the box contained cocaine. He further informed Peña and Tobon that Ulises Ortega was available to load their truck. While cocaine was being loaded in Tobon and Peña’s truck, Chao, Peña and Tobon discovered that one of the boxes containing cocaine rather than plantains was missing. While Peña, Tobon and Chao searched for the cocaine, Chao informed them that the owner was being kept away from the premises and that they must complete the loading of the cocaine and remove it from the premises before his return. In addition, during the search of the Celi-Mar warehouse following Chao’s arrest a business card was found with Izquierdo’s hotel room number that Quintero had instructed Peña to give to Chao as the identifying signal that Peña was the individual to receive the cocaine shipment.

Thus the events described above of July 29, 1987, demonstrate both that Chao had knowledge of and participated in the importation and distribution of the cocaine and knowingly possessed a cocaine shipment with intent to distribute the same. Chao’s statement to Peña and Tobon concerning how they could locate the cocaine by inserting their fingers through the air holes of the boxes to find plastic wrappings without plantain fruit together with his declaration that someone was keeping the owner away, established that he had knowledge of the shipment and its contents. Beyond doubt, after reviewing this evidence, a reasonable fact finder could very well determine not only that Chao knowingly possessed cocaine with an intent to distribute the same in July of 1987 but was also guilty of conspiring to possess this large quantity of cocaine with intent to distribute.

C. The Convictions for Possession with Intent to Distribute of Rafael Izquier-do, Angel Amejeiras, Luis Gonzalez and Vicente Chao

Izquierdo, Amejeiras and Luis Gonzalez challenge their convictions of aiding and abetting Peña’s and Tobon’s possession of cocaine with intent to distribute as well as Chao’s possession of cocaine with intent to distribute. Vicente Chao challenges his conviction for aiding and abetting Peña’s and Tobon’s possession of cocaine with intent to distribute.

In this case the jury received the following instruction on the theory of vicarious liability established in Pinkerton v. United States, 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946):

“A conspirator is responsible for offenses committed by his fellow conspirators if he was a member of the conspiracy when the offense was committed and if the offense was committed in furtherance of or as a natural consequence of the conspiracy. Therefore, if you find a defendant guilty of the conspiracy charge in Count I of the indictment, and if you find beyond a reasonable doubt that while he was a member of the conspiracy, his fellow conspirators committed the offenses charged in Counts II and III of the indictment [possession of cocaine with intent to distribute] in furtherance or as a natural consequence of the conspiracy, then you should find the defendant guilty as charged in Counts II and III of the indictment.”

We approved a very similar Pinkerton instruction in United States v. Troop, 890 F.2d 1393, 1399 (7th Cir.1989). As we observed in Troop, 890 F.2d at 1399:

“Under the Pinkerton doctrine established in Pinkerton v. United States, 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946), a conspirator can be found guilty for a co-conspirator’s crimes but the jury must be instructed on this theory of guilt. The doctrine is based on the idea that conspirators are agents of each other and just as a principal is bound by the acts of his agents within the scope of the agency, so is a conspirator bound by the acts of his co-conspirators.”

(Citations omitted).

As demonstrated in Section XI-B, supra, the evidence was sufficient to support Izquierdo, Amejeiras, Luis Gonzalez and Chao’s convictions on the conspiracy count. As noted in the language of the Pinkerton instruction, “a conspirator is responsible for offenses committed by his fellow conspirators if he was a member of the conspiracy when the offense was committed and if the offense was committed in furtherance of or as a natural consequence of the conspiracy.” A jury after convicting Izquierdo, Amejeiras, Luis Gonzales and Chao on the conspiracy count could find each of these four conspirators guilty of the substantive counts of possession with intent to distribute cocaine committed by their co-conspirators if they found beyond a reasonable doubt that the substantive counts were committed in “furtherance of or as a natural consequence of the conspiracy.” Thus, the defendants were properly found guilty under a Pinkerton vicarious liability theory.

We now turn to the question of whether the actions of Izquierdo, Amejeiras, Luis Gonzalez and Chao also could be found to constitute possession of cocaine with intent to distribute under an “aiding and abetting” theory. In United States v. Valencia, 907 F.2d 671, 677 (7th Cir.1990), we set forth our standard for determining whether a defendant is guilty of aiding and abetting another defendant’s possession of drugs with intent to distribute:

“In defining the elements of aiding and abetting liability, this court has adopted Judge Learned Hand’s well-known formulation in United States v. Peoni, 100 F.2d 401, 492 (2d Cir.1938). In order for Mr. Martinez to be convicted for aiding and abetting Mr. Valencia’s attempted possession with intent to distribute cocaine, all the evidence need show is that Mr. Martinez 1 “in some sort associate[d] himself with the venture, that he participate^] in it as in something he wishe[d] to bring about, [and] that he s[ought] by his action to make it succeed.” ’ [United States v. Piño-Perez, 870 F.2d 1230, 1235 (7th Cir.) (en banc), cert. denied, [— U.S. -,] 110 S.Ct. 260 [107 L.Ed.2d 209] (1989) ] (quoting Peoni, 100 F.2d at 402). As this court stated in United States v. Beck, 615 F.2d 441, 448 (7th Cir.1980), the aiding and abetting standard has two prongs — association and participation. To prove association, the state must prove that the defendant had the state of mind required for the statutory offense; to prove participation, ‘[a] high level of activity need not be shown_ Instead, “there must be evidence to establish that the defendant engaged in some affirmative conduct; that is, there must be evidence that [the] defendant committed an overt act designed to aid in the success of the venture.” ’ Id. at 449 (citations omitted) (quoting United States v. Longoria, 569 F.2d 422, 425 (5th Cir.1978))-”

We initially examine whether Izquierdo, Amejeiras, Luis Gonzalez and Chao satisfied the participation prong of the aiding and abetting test. As demonstrated in the previous discussion of their respective activities in the conspiracy, they all played an important role in facilitating the possession of cocaine with intent to distribute crimes that took place on July 29, 1987. Izquier-do’s activity in keeping Hernandez away from the premises permitted the drugs to be loaded on the truck and removed from the Celi-Mar warehouse without Hernandez becoming aware of the shipment. The importance of Izquierdo’s conduct in the conspiracy and the knowledge he had of the conspiracy is confirmed in the problems Vicente Chao noted in his statement to Peña and Tobon concerning the possibility of Celi-Mar’s owner returning before the drug shipment was transferred out of the Celi-Mar warehouse. As observed above, Amejeiras assisted in the hiring of the truck driver who transported the cocaine to each of the principals who possessed the cocaine with intent to distribute and maintained telephone contact with Tellechea who was monitoring the delivery from Miami to New York and on to Chicago. Luis Gonzalez traveled with Tellechea, surveil-ling the transfer of the cocaine shipment, as pointed out earlier, directed the truck driver in New York to deliver the cocaine to Chao in Chicago, and conducted a personal flashlight inspection of the cocaine in the truck. Finally, Vicente Chao delivered the cocaine to Tobon and Peña at the Celi-Mar warehouse, explained to Peña and To-bon how to locate the boxes containing cocaine and further assisted in the unloading and loading of the trucks containing the drugs. Thus, Izquierdo, Amejeiras, Chao, and Luis Gonzales clearly participated in efforts to “aid in the success of the venture.” Beck, 615 F.2d at 449.

With respect to the question of association, there must be a demonstration that Izquierdo, Amejeiras, Chao, and Luis Gonzalez “either knowingly or intentionally aided or abetted ... the possession of cocaine with the intent that the cocaine be distributed.” Valencia, 907 F.2d at 680 (emphasis in original). “Knowledge and intent in narcotics cases often must be proved largely by circumstantial evidence. The intent to distribute drugs has been inferred from the possession of a vast quantity of drugs larger than needed for personal use....” Id. at 678 (citations omitted). Based upon the participation of Izquierdo, Amejeiras, Chao, and Luis Gonzalez in the conspiracy and the activities of each of them contributing to the success of the large July 1987 cocaine delivery detailed in the preceding paragraph, it can reasonably be inferred that Izquierdo, Amejeiras, Luis Gonzalez and Chao, through their individual and collective conduct, knowingly and intentionally aided each of the principals’ possession of cocaine with the intent to distribute. Izquierdo, Amejeiras, Luis Gonzalez and Chao’s participation in facilitating the cocaine shipment that resulted in Chao, Peña and To-bon possessing over two thousand kilograms of cocaine with intent to distribute supports their conviction under an aiding and abetting theory. Thus, we conclude that under either a Pinkerton vicarious liability theory or under an aiding and abetting theory, Izquierdo, Amejeiras and Luis Gonzalez’ convictions of the possession of cocaine with intent to distribute of Chao, Tobon and Peña were proper and that Chao was appropriately convicted of the possession of cocaine with intent to distribute of Peña and Tobon.

XII.

ROBERTO GONZALEZ’ ATTACK ON HIS AIDING AND ABETTING CONVICTIONS

A. The Failure to Give Roberto Gonzalez’ Proposed Jury Instruction

Roberto Gonzalez’ lawyer proposed that the jury be instructed that they could not find Roberto Gonzalez guilty of the substantive counts of possession with intent to distribute if they found only that he “aided and abetted” the conspiracy. In United States v. Galiffa, 734 F.2d 306, 310 (7th Cir.1984), we held that “one can ... aid and abet a conspiracy, which is a separate chargeable offense in and of itself.” We have held that: “In order to aid and abet the evidence must demonstrate that the defendant ‘was associated with a criminal venture, participated in it as something he wished to bring about, and sought by his actions to make it succeed.’ ” Galiffa, 734 F.2d at 311 (quoting United States v. Peoni, 100 F.2d 401, 402 (2d Cir.1938)). Gonzalez argues that “a conviction as an aider and abettor to the conspiracy would have precluded the imposition of Pinkerton liability as to Counts II and III [possession with intent to distribute].”

In United States v. Grier, 866 F.2d 908, 932 (7th Cir.1989), we set forth the ease law applicable to our review of a district court’s determinations regarding jury instructions:

“Turning to the substantive law applicable to review of the jury instructions given in both defendants’ cases, in United States v. Douglas, 818 F.2d 1317, 1320-21 (7th Cir.1987), we held that
‘[a] defendant is entitled to an instruction on his or her theory of defense if: the defendant proposed a correct statement of the law; the defendant’s theory is supported by the evidence; the defendant’s theory of defense is not part of the charge; and the failure to include an instruction on the defendant’s theory of defense in the jury charge would deny the defendant a fair trial.’
(Emphasis added) (citations omitted). We have repeatedly emphasized that when reviewing instructions we consider them as a whole in determining whether or not a court erred in refusing to give a particular instruction.”

Gonzalez’ claim is that “aiding and abetting” a conspiracy differs from membership in a conspiracy and is an insufficient basis to support vicarious liability under Pinkerton for the substantive crimes that a jury determines beyond a reasonable doubt other conspirators have committed “in furtherance or as a natural consequence of a conspiracy.” But, Gonzalez’ proposed jury instruction must be viewed in light of the other instructions the court provided the jury and the trial court’s Pinkerton instruction provided:

“A conspirator is responsible for offenses committed by his fellow conspirators if he was a member of the conspiracy when the offense was committed and if the offense was committed in furtherance of or as a natural consequence of the conspiracy. Therefore, if you find a defendant guilty of the conspiracy charged in Count I of the indictment, and if you find beyond a reasonable doubt that while he was a member of the conspiracy, his fellow conspirators committed the offenses charged in Counts II and III of the indictment [possession of cocaine with intent to distribute] in furtherance of or as a natural consequence of that conspiracy, then you should find that defendant guilty as charged in Counts II and III of the indictment.”

(Emphasis added). The language in the court’s Pinkerton instruction clearly required that there be proof beyond a reasonable doubt of Gonzalez’ membership in the conspiracy in order to convict him of the possession of cocaine with intent to distribute counts of other conspirators under a vicarious liability theory. Gonzalez' proposed instruction sought only to require the jury to find him to be a member of a conspiracy before it found him vicariously liable for the substantive acts of other conspirators. Thus, the Pinkerton instruction the court furnished the jury and Gonzalez’ proposed instruction are in effect the same insofar as they require proof beyond a reasonable doubt of membership in the conspiracy in order to find guilt for the offenses of co-conspirators committed in furtherance or as a natural consequence of the conspiracy.

Furthermore, the last paragraph of Roberto Gonzalez’ proposed instruction, where he stated “if you find [Gonzalez] guilty only of aiding and abetting the conspiracy in Count I, then you must, as a matter of law, find him not guilty of Counts II and III,” was legally improper. This instruction was obviously drafted to benefit Gonzalez and to prevent his conviction on the two possession with intent to distribute counts. Not only would this instruction have prohibited conviction under a vicarious liability theory, it would also have necessarily precluded the jury from finding that Gonzalez aided or abetted the substantive crimes of his co-conspirators. Even if a jury had found only that Gonzalez “aided or abetted” the conspiracy, there is nothing that would have prevented it from also determining that Gonzalez aided or abetted the substantive crimes of his co-conspirators. Thus, the trial court’s action in refusing to give Gonzalez’ proposed instruction was proper.

B. Insufficiency of Evidence Under an Aiding and Abetting Theory

Roberto Gonzalez also argues that his conviction should be reversed because the jury might have based its verdict upon an aiding and abetting theory of liability rather than a theory of vicarious liability under Pinkerton. As noted above, “[i]n order for [a defendant] to be convicted for aiding and abetting ... possession with intent to distribute cocaine, all the evidence need show is that [the defendant] ‘ “in some sort associate^] himself with the venture, that he participate^] in it as in something he wishe[d] to bring about, [and] that he sfought] by his action to make it succeed.” ’ ” Valencia, 907 F.2d 671, 677 (7th Cir.1990) (quoting Piño-Perez, 870 F.2d at 1235, that quoted, in turn, Peoni, 100 F.2d at 402). Gonzalez speculates that the evidence in the record allegedly supporting a theory that he played a role in facilitating the possession of cocaine of Chao, Ortega, Peña or Tobon was by its very nature insufficient to support his conviction under an aiding and abetting theory-

In contrast to Gonzalez’ contention that the evidence was insufficient to convict him on the aiding and abetting theory, he admits there was sufficient evidence to convict him of being a knowing participant in the conspiracy. He also admits that guilt of the substantive offenses could be appropriately premised upon a Pinkerton vicarious liability theory. We believe this admission to be determinative. As discussed in Sections XI-C and XII-A, the jury received a proper Pinkerton instruction which applied to Gonzalez as well as the other defendants. Since Gonzalez admits that the evidence was sufficient to convict him of the possession of cocaine with intent to distribute counts under a Pinkerton theory, there is a proper basis for his conviction. As referred to in our discussion of the severance issue in Section V-B, supra, the Supreme Court observed: “To say that the jury might have been confused amounts to nothing more than an unfounded speculation that the jurors disregarded clear instructions of the court in arriving at their verdict. Our theory of trial relies upon the ability of a jury to follow instructions.” Opper v. United States, 348 U.S. 84, 95, 75 S.Ct. 158, 165, 99 L.Ed. 101 (1954). Where a properly instructed jury had sufficient evidence upon which it could base a verdict of guilt based upon a Pinkerton vicarious liability theory, we refuse to indulge in speculation that the jury relied upon an “aiding and abetting” theory that allegedly was not supported by sufficient evidence.

XIII.

MOTION FOR NEW TRIAL

Izquierdo, Chao and Roberto Gonzalez allege that the district court should have granted a motion for new trial because the government did not disclose prior to trial that government witness Cesar Tobon had allegedly been involved in drug-related activities in the 1970s. Specifically, the government revealed after trial that there was testimony in a Jacksonville, Florida, trial of one Carlos Lehder that Tobon had been involved in the importation of cocaine in the summer of 1976. This was contrary to Tobon’s testimony below when he stated that the first time anyone had asked him to “have anything to do with cocaine” was in the fall of 1986.

“It is within the discretion of the trial court to determine whether a new trial should be granted on the basis of newly discovered evidence. Accordingly, we will only reverse the district court where there has been an abuse of discretion.” Jarrett v. United States, 822 F.2d 1438, 1445 (7th Cir.1987). In United States v. Van Daal Wyk, 840 F.2d 494, 500 (7th Cir.1988), we set forth the standards a district court should apply in analyzing the question of whether newly discovered evidence merits a new trial:

“The general standard for determining whether newly discovered evidence warrants a new trial is the following:
‘The defendant [sic] must show that the evidence (1) came to their knowledge only after trial; (2) could not have been discovered sooner had defendants exercised due diligence; (3) is material, and not merely impeaching or cumulative; and (4) would probably lead to an acquittal in the event of a retrial.’
United States v. Nero, 733 F.2d 1197, 1202 (7th Cir.1984) (quoting United States v. Oliver, 683 F.2d 224, 228 (7th Cir.1982)). This court has formulated a more specific standard in situations where the newly discovered evidence purports to refute false trial testimony:
‘(a) The court is reasonably well satisfied that the testimony given by a ma-ferial witness is false, (b) That the jury might have reached a different conclusion, (c) That the party seeking the new trial was taken by surprise when the false testimony was given and when it was unable to meet it or did not know of its falsity until after the trial.’
Nero, 733 F.2d at 1202 (quoting Larrison v. United States, 24 F.2d 82 (7th Cir.1928)).”

(Emphasis in original).

Under the “general” standard enumerated in Van Daal Wyk, it is clear that the revelation of Tobon’s earlier drug involvement would not merit a new trial as it failed to affect any matter at issue in this case. Its purpose would merely be to impeach Tobon’s testimony. As in Van Daal Wyk: “The new evidence is ‘merely impeaching’ (and impeaching on the most collateral of matters) [over ten year old drug trafficking unrelated to the facts of this case] and thus would not meet the third prong” of the “general standard.” Van Daal Wyk, 840 F.2d at 500. Indeed, if Tobon had been convicted of a drug offense, under Rule 609(b) of the Federal Rules of Evidence, the conviction would have been inadmissible

“if a period of more than ten years has elapsed since the date of the conviction or of the release of the witness from the confinement imposed for that conviction, whichever is the later date, unless the court determines, in the interests of justice, that the probative value of the conviction supported by specific facts and circumstances substantially outweighs its prejudicial effect.”

Federal Rule of Evidence 609(b).

On appeal the defendants argue that a new trial was necessary under the Larri- son standard. However, the defendants did not present arguments under the Lar-rison standard in their challenge of To-bon’s testimony during the attempt to obtain a new trial in the court below.

“We have repeatedly held that a party that fails to press an argument before the district court waives the right to present that argument on appeal. ‘ “It is a well-established general principle that ‘a litigant cannot present to this court as a ground for reversal an issue which was not presented to the trial court and which it, therefore, had no opportunity to decide.’ ” ’ Holleman v. Duckworth, 700 F.2d 391, 394-95 (7th Cir.) (quoting Stern v. United States Gypsum Inc., 547 F.2d 1329, 1333 (7th Cir.) (quoting Desert Palace, Inc. v. Salisbury, 401 F.2d 320, 324 (7th Cir.1968)), cert. denied, 434 U.S. 975, 98 S.Ct. 533, 54 L.Ed.2d 467 (1977)), cert. denied, 464 U.S. 834, 104 S.Ct. 116, 78 L.Ed.2d 116 (1983)_ The district court was not required to investigate the pleadings and evidence for additional arguments that might support [the] petition; it was [the petitioner’s] responsibility to raise the arguments that he seeks to use now on appeal.”

Garlington v. O'Leary, 879 F.2d 277, 282 (7th Cir.1989) (citations and footnote omitted). Thus, the defendants must demonstrate that the trial court’s failure to grant a new trial under the Larrison standard was “plain error” as well as an abuse of discretion. “The plain error doctrine allows an appellate court to correct errors that were not objected to at trial if the defendant can demonstrate that he or she probably would have been acquitted but for the erroneously admitted evidence.” United States v. Wynn, 845 F.2d 1439, 1443 (7th Cir. 1988).

Before a defendant is entitled to a new trial under the Larrison standard, he must demonstrate, “[t]hat the jury might have reached a different conclusion.” Nero, 733 F.2d at 1202. Because our consideration of Larrison in this case is governed by the “plain error” standard, the defendants must further establish that they “probably would have been acquitted” but for any trial court error. The defendants have failed to meet this exacting standard because while knowledge of the fact that Tobon testified falsely concerning the date of his initial drug involvement might have had some impact on the jury’s consideration of Tobon’s testimony, the defendants’ argument that they “probably would have been acquitted” if the jury had been aware of this fact is unconvincing. The evidence against each defendant, discussed in detail, is so overwhelming that it prohibits speculation that a jury would have probably acquitted the defendants had the jury known of Tobon’s false testimony. Thus, we are in agreement with the trial court’s denial of a request for a new trial.

Affirmed. 
      
      . The defendants, Quintero and Tellechea, as of the date of the filing of the government’s brief, were fugitives from justice. Cesar Tobon entered into an agreement to plead guilty and testified at trial.
     
      
      . Because only Roberto Ramirez challenges his sentence, we need not set forth the sentences of the other defendants. Roberto Ramirez was sentenced to concurrent 20-year terms of imprisonment on the two possession with intent to deliver convictions, 10 years of supervised release consecutive to the imprisonment and was fined $1 million. On his conspiracy conviction Ramirez was sentenced to five years’ confinement to run consecutively to the sentences on the possession with intent to deliver counts.
      We note each appellant’s specific challenges to their convictions and/or sentences in Section III, infra, "Issues Presented.” On August 22, 1988, the government filed materials with the court relating to testimony at the trial of one Carlos Lehder in Jacksonville, Florida, which supported an implication that government witness Cesar Tobon had been involved in drug activities in the 1970s. Tobon had testified during the trial that the first time he had ever been approached about involvement with drugs was in 1986. Izquierdo filed a motion for a new trial based upon this newly discovered evidence (of never being approached about drugs till 1986) which the trial court denied on December 28, 1988. He filed a notice of appeal of the district court’s refusal to grant a new trial on these grounds on January 6, 1989, which we consolidated with the other appeals.
     
      
      .A plantain is “the starchy fruit of the plantain [banana plant] [and] is distinguished in appearance from the ordinary banana by its angular shape and yellowish green color.” Webster’s Third New International Dictionary 1732 (1981).
     
      
      . Prior to trial, Petroski identified Amejeiras as one of the two individuals whom he met at the truck stop and who participated in hiring him to transport the cocaine. At trial he identified Luis Gonzalez, rather than Amejeiras, as one of the two individuals who met with him. However, Petroski’s identification of Luis Gonzalez at trial as one of the two persons who met with him in order to secure his trucking services was at best questionable as he later testified that the first time he saw Luis Gonzalez was when he arrived at Las Villas. According to Julio Ortiz, Amejeiras’ physical appearance had changed after the time he allegedly conferred with Petroski for at the time of trial his hair was long and he no longer wore a mustache. The question of identification was for the jury which could properly choose to accept Petroski’s pretrial identification of Amejeiras rather than his in-court identification of Luis Gonzalez as one of the persons who met with him to hire him to drive the cocaine shipment.
     
      
      . In discussing this issue we will also resolve the related question of whether a co-conspirator’s hearsay statement could be admitted against Izquierdo.
     
      
      . United States v. Williams, 858 F.2d 1218, 1225 (7th Cir.1988).
     
      
      . The cocaine was displayed for a period of only a few hours.
     
      
      . As in Pirovolos, "because we do not find constitutional error, we need not ask whether the error was harmless.” Id. at 427.
     
      
      . Kotteakos v. United States, 328 U.S. 750, 764-65, 66 S.Ct. 1239, 1248, 90 L.Ed. 1557, provides:
      "If, when all is said and done, the conviction is sure that the error did not influence the jury, or had but very slight effect, the verdict and the judgment should stand, except perhaps where the departure is from a constitutional norm or a specific command of Congress. But if one cannot say, with fair assurance, after pondering all that happened without stripping the erroneous action from the whole, that the judgment was not substantially swayed by the error, it is impossible to conclude that substantial rights were not affected. The inquiry cannot be merely whether there was enough to support the result, apart from the phase affected by the error. It is rather, even so, whether the error itself had substantial influence. If so, or if one is left in grave doubt, the conviction cannot stand."
      (Footnote and citation omitted). Here we are confident that the improper comments "did not influence the jury.”
     
      
      . The only difference between the instruction given in this case and the instruction given in the cited cases was the trial court’s use of the word "defined” in the final line of the instruction in the case below, rather than the word “used” found in the instructions in the cited cases. The interchange of these two terms carries no. significance.
     
      
      . See United States v. Talkington, 875 F.2d 591, 596 (7th Cir.1989).
     
      
      . When Julio Ortiz managed the import outlet it was called International World Enterprises.
     
      
      . We are cognizant that in United States v. Giovannetti, 919 F.2d 1223, 1226-29 (7th Cir. 1990); we recently disapproved of an ostrich instruction where there was no evidence that the defendant deliberately avoided knowledge of a tenant's use of a house the defendant owned as a wire room where bets on sporting events were received. The defendant had rented an investment property to a participant in a gambling enterprise and faced charges that his knowing rental of this property aided and abetted a gambling business. In considering this claim, the court stated:
      “The true intermediate case between a clearly proper giving of the ostrich instruction because the defendant did physical acts to insulate himself from knowledge, as in Diaz, and the clearly improper giving of the instruction because the only issues the defendant’s actual knowledge or complete ignorance, is the case of purely psychological avoidance. Josefik was such a case. ‘It is inconceivable that Josefik did not believe that the scotch was stolen, and in context all the challenged instruction [the ostrich instruction] meant is that he could not get off the hook simply by resolutely refusing to find out for sure whether it was stolen.’ 753 F.2d at 589. In other words, the deliberate effort to avoid guilty knowledge that we said is all the guilty knowledge the law requires can be a mental, as well as a physical, effort — a cutting off of one’s normal curiosity by an effort of will. There is no evidence of either sort of effort here."
      
        Giovannetti, 919 F.2d at 1228-29. As contrasted with Giovannetti, the facts of this case establish that if Gonzalez actually was unaware of the illegal activities of the conspiracy (which we do not believe), his ignorance could only have been the result of "a cutting off of [his] normal curiosity by an effort of will.” After taking over the position as manager of the conspiracy’s Miami importation business, Gonzalez, with co-conspirator Tellechea, followed a shipment of cocaine from Miami to New York to Chicago. In New York, Gonzalez personally inspected the drug shipment and diverted it to Chicago. Later, after the drugs were intercepted in Chicago, Gonzalez and Tellechea flew to Detroit and from there to Miami in an attempt to camouflage their trail. These are hardly the actions one would expect from the manager of a legitimate import business. Moreover, it stretches credibility to suppose that a sophisticated drug conspiracy, such as the one at issue, would allow a non-member to supervise its primary site for receiving international shipments of drugs. Thus, Giovannetti presents no obstacle to the approval of the conscious avoidance instruction in Luis Gonzalez’ case.
     
      
      . We summarized the vicarious liability theory in United States v. Troop, 890 F.2d 1393, 1399 (7th Cir.1989), where we stated:
      "Under the Pinkerton doctrine established in Pinkerton v. United States, 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946), a conspirator can be found guilty for a co-conspirator's crimes but the jury must be instructed on this theory of guilt. The doctrine is based on the idea that conspirators are agents of each other and just as a principal is bound by the acts of his agents within the scope of the agency, so is a conspirator bound by the acts of his co-conspirators.”
      (Citations omitted).
      We have set forth the theory of aiding and abetting liability as follows:
      "In defining the elements of aiding and abetting liability, this court has adopted Judge Learned Hand's well-known formulation in United States v. Peoni, 100 F.2d 401, 402 (2d Cir.1938). In order for Mr. Martinez to be convicted for aiding and abetting Mr. Valencia’s attempted possession with intent to distribute cocaine, all the evidence need show is that Mr. Martinez “'in some sort associate^] himself with the venture, that he participate[d] in it as in something he wishe[d] to bring about, [and] that he s[ought] by his action to make it succeed.” ’ [United States v. Piño-Perez, 870 F.2d 1230, 1235 (7th Cir.) (en banc), cert. denied, - U.S. -, 110 S.Ct. 260, 107 L.Ed.2d 209 (1989) ] (quoting Peoni, 100 F.2d at 402). As this court stated in United States v. Beck, 615 F.2d 441, 448 (7th Cir.1980), the aiding and abetting standard has two prongs — association and participation. To prove association, the state must prove that the defendant had the state of mind required for the statutory offense; to prove participation, ‘[a] high level of activity need not be shown.... Instead, "there must be evidence to establish that the defendant engaged in some affirmative conduct; that is, there must be evidence that [the] defendant committed an overt act designed to aid in the success of the venture." ’ Id. at 449 (citations omitted) (quoting United States v. Longoria, 569 F.2d 422, 425 (5th Cir. 1978)).
      
        United States v. Valencia, 907 F.2d 671, 677 (7th Cir.1990).
     
      
      . In view of the fact that circumstantial evidence plays a significant role in this case, we note that in reviewing whether substantial evidence supports the jury’s verdict concerning the existence of a conspiracy and the particular defendants' participation in it, we have specifically spoken to the important role which circumstantial evidence can play:
      "In establishing the existence of an overall conspiratorial agreement, as well as a particular defendant's participation therein, we note that it is perfectly legitimate for the government to offer and for the jury to consider circumstantial evidence. United States v. Vega, 860 F.2d 779, 793 (7th Cir.1988). ‘By its very nature, a conspiracy "is conceived and carried out clandestinely, and direct evidence of the crime is rarely available.”' United States v. Mayo, 721 F.2d 1084, 1088 (7th Cir. 1983) (quoting United States v. Washington, 586 F.2d 1147, 1153 (7th Cir. 1978)). Thus, ‘[n]ot only is the use of circumstantial evidence permissible, but circumstantial evidence may be the sole support for a conviction.’ United States v. Reed, 875 F.2d 107, 111 (7th Cir.1989) (quoting Vega, 860 F.2d at 793-94 (emphasis in original and citations omitted). Although the jury’s verdict may not rest ‘solely on the piling of inference upon inference ..., [t]he view that the prosecution's case must answer all questions and remove all doubts ... of course, is not the law because that would be impossible; the proof need only satisfy reasonable doubt.’ Nesbitt, 852 F.2d at 1511 (emphasis in original and citations omitted). Indeed, '[j]uries are allowed to draw upon their own experience in life as well as their common sense in reaching their verdict. ... While "[cjommon sense is no substitute for evidence, ... common sense should be used to evaluate what reasonably may be inferred from circumstantial evidence.’” Id. (citations omitted).’’
      
        United States v. Briscoe, 896 F.2d 1476, 1505-06 (7th Cir.1990).
     
      
      . Although the telephone in Izquierdo's home was listed in the name of Jose Leon, Izquierdo provided this number as his home number and its address as his home address in a car rental contract he entered in Chicago on July 26, 1987.
     
      
      . As just discussed, Chao was convicted as a principal on the other count of possession of cocaine with intent to distribute.
     
      
      . The instruction given in Troop read:
      "A conspirator is responsible for offenses committed by his fellow conspirators, if he was a member of the conspiracy when this offense was committed, and if the offense was committed in furtherance of or as a natural consequence of the conspiracy. Therefore, if you find a defendant guilty of the conspiracy charge in Count I, and if you find beyond a reasonable doubt that while he was a member of the conspiracy, his fellow conspirators committed an offense alleged in another count of the indictment, in furtherance of or as a natural consequence of that conspiracy, then you should find him guilty of the offense charged in the other count.”
      890 F.2d at 1399.
     
      
      . "Jury instructions are designed to clarify issues for the jury and to educate the jury about what factors are probative on those issues.... The district court, in its discretion, may reject argumentative instructions." Spesco v. General Electric Co., 719 F.2d 233, 239 (7th Cir.1983) (citation omitted). The proposed instruction was obviously drafted to Gonzalez' advantage because it would require acquittal where the jury determined that Gonzalez only aided or abetted the conspiracy. This result would clearly be legally improper if there was sufficient evidence for a jury to convict on Counts II or III without utilizing a Pinkerton vicarious liability theory.
     
      
      . We further observe that a recent decision in United States v. Taglia, 922 F.2d 413, 415-16 (7th Cir.1991), suggests that the fact evidence is merely impeaching may not be an insurmountable obstacle to a new trial under the "general" standard. Taglia notes that "it will be the rare case in which impeaching evidence warrants a new trial, because ordinarily such evidence will cast doubt at most on the testimony of only one of the witnesses,” but asserts that "the practice [to deny new trials where the only newly discovered evidence was impeaching] should not be taken to imply a rule that even if the defendant proves that his conviction almost certainly rests on a lie, the district judge is helpless to grant a new trial." Taglia, 922 F.2d at 415. We are not convinced that the collateral matter of whether Tobon was involved in drug trafficking more than ten years prior to the dates of this conspiracy would have affected the jury’s decision concerning whether to believe the testimony Tobon provided concerning the activities of this group of conspirators during the course of the conspiracy.
     
      
      . The Larrison standard requires a new trial when
      "(a) The court is reasonably well satisfied that the testimony given by a material witness is false.
      “(b) That the jury might have reached a different conclusion.
      "(c) That the party seeking the new trial was taken by surprise when the false testimony was given and when it was unable to meet it or did not know of its falsity until after the trial.”
      
        Nero, 733 F.2d at 1202 (quoting Larrison v. United States, 24 F.2d 82, 87-88 (7th Cir.1928)).
     
      
      . In United States v. Mazzanti, 925 F.2d 1026, 1029-31 (7th Cir.1991), we recently upheld a district court’s denial of a new trial under the Larrison standard where the false "testimony pertained to a transaction that was not specifically charged or referenced in the indictment,” there "was sufficient independent evidence — indeed overwhelming evidence of the conspiracy’s existence and of [the defendant’s] participation in the conspiracy," as well as of "his participation in [all but one of] the possession counts,” and the witness’ "testimony had been subjected to significant other impeachment evidence.” The instant case is an even more compelling one for rejection of a new trial than Mazianti, because the applicable "plain error” standard requires the defendants to demonstrate that they probably would have been acquitted in the absence of the reception of the allegedly false evidence.
     