
213 F.Supp.2d 900 (2002)
UNITED STATES of America, Plaintiff,
v.
William M. PATTERSON and Daryl L. Smith, Defendants.
No. 01 CR 0108.
United States District Court, N.D. Illinois, Eastern Division.
August 8, 2002.
*901 *902 *903 Morris O. Pasqual, United States Attorney's Office, Chicago, IL, for Plaintiff.
Andrea Paula Taylor, Fedeeral Defender Program, Phillip Arnold Turner, Peter John Vilkelis, Michael J. Rovell, Law Offices of Michael J. Rovell, Chicago, IL, Gustavo Munoz, Michael J. McCafferty, Munoz & Wilkes, Ltd., Summit, IL, Peter J. Wilkes, Peter J. Wilkes, P.C., Chicago, IL, for Defendants.

MEMORANDUM OPINION AND ORDER
BUCKLO, District Judge.
William Patterson and Daryl Smith, Chicago Police Officers assigned to the Public Housing South Division, Tactical Unit, were tried on charges of conspiring and attempting to possess with the intent to distribute, and to distribute, approximately five kilograms of cocaine in violation of 21 U.S.C. §§ 841(a)(1) and 846, as well as charges of carrying a firearm in relation to a drug trafficking offense in violation of 18 U.S.C. § 924(c), and theft of government funds in violation of 18 U.S.C. § 641. Patterson was convicted of all the charges against him in the indictment, and Smith was acquitted on all charges except for theft of government funds. Each moves for a new trial under Fed.R.Crim.P. 33 and a judgment of acquittal under Rule 29. Smith also moves for an arrest of judgment under Rule 34. I deny the motions.

I.
The trial evidence, viewed in the light most favorable to the government, demonstrated that, in January 2001, William Patterson, a 28-year veteran of the Chicago Police Department, then a sergeant, devised a plan to steal money and drugs from a drug dealer. Patterson was approached by his long-time friend Arthur Veal, who was cooperating with the government after being arrested for cocaine trafficking. Veal testified that he had identified "rip-off" targets for other friends on the police force in the past, and that Patterson had previously asked Veal to set up a rip-off for him.
On January 13, 2001,[1] after Veal began cooperating with the FBI, he set up a *904 meeting at his office with Patterson. That meeting was unrecorded. Veal testified that he asked Patterson whether he was still interested in doing a rip-off of a drug dealer and Patterson said that he was. Veal told Patterson that he had information from a "Mexican male" who wanted to steal drugs and money from a stash location of the drug dealer for whom he worked. Veal told Patterson that the rip-off would involve five to ten kilograms of cocaine, which would be given to the Mexican male, and $500,000 in cash, which would be split between Patterson, Veal, and anyone whom Patterson recruited to assist him. Patterson said that he was interested and that the only person whom he trusted to help him was Daryl Smith, or "Smitty," also a Chicago Police officer. Patterson and Veal discussed the logistics of the rip-off, including the possibility of killing the Mexican male so that there would be no witnesses.
The January 13 meeting ended at approximately 2:47 p.m., and telephone records demonstrated that, between 9:20 p.m. and 9:40 p.m. that night, there were five telephone calls between Patterson's cellular telephone and Smith's cellular telephone, the last of which lasted eight minutes. On January 14, there were two calls between Smith's and Patterson's cellular telephones, one lasting one minute, the other twenty-three minutes. Smith and Patterson were not on duty on January 13 or 14.
On January 17, Patterson had a recorded telephone conversation with Veal in which Patterson told Veal about Smith's reactions to the plans for the rip-off. Patterson also told Veal that he would contact him later in the week with any "twist" he and Smith might put in the plans for the rip-off. Earlier in the day, there had been six telephone calls between Smith's and Patterson's cellular telephones.
On January 19, Patterson met with Veal at Veal's office, and FBI surveillance recorded the meeting. Veal told Patterson that the Mexican male and the wife of the drug dealer from whom they were supposed to steal would leave the stash apartment empty for a period of time so that Smith and Patterson could break in and take the money and drugs. Veal said that the wife of the drug dealer would believe that police had raided the apartment and confiscated the money and drugs. Patterson asked Veal: "How much work is gonna be in there?" Veal responded that he told the Mexican male that they needed "550 to 600," by which he meant $550,000 to $600,000, and that the drug dealer said there would be "10 keys," or kilograms, of cocaine. Patterson asked "We gonna leave it there? Where you want us to leave it?" Veal told him that he should take both the money and the drugs; Veal would see that the drugs got back to the Mexican male and the money would be split between Patterson, Veal, and Smith.
Patterson and Veal also talked about whether it was necessary to inventory any of the cocaine and turn it in to the police department. Patterson said: "If he [the Mexican male] ain't gonna be there .... ain't got to inventory nothing, unless it goes to plan B." The original plan called for Patterson and Smith to break in to the apartment and take the drugs and money undetected, and for the wife of the drug dealer to believe that there had been a police raid. If Smith and Patterson were detected during the break-in, however, "Plan B" provided that they would inventory some of the drugs and leave without saying anything to the neighbors.
Also during the January 19 meeting, Veal told Patterson to "tell Smitty after you do this gig have to stop sticking up the projects now. Don't be snatching no money out of nobody hand." Patterson responded *905 by telling Veal that, earlier that day, he and Smith and another police officer had stolen drugs and money from hiding places in the Chicago Housing Authority housing projects where they worked, and that they had planted drugs on a suspect. The following day, January 20, there were six telephone calls between Patterson's home telephone and Smith's cellular telephone, one of which lasted ten minutes, and another of which lasted twenty-eight minutes.
On January 22, Veal and Patterson had a recorded telephone conversation. Patterson asked whether Veal had set up the rip-off yet, and Veal responded that "everybody is straight with what everybody wanna do. We just gotta get right ... with the right numbers." Patterson said that Smith told him that the rip-off "looks like retirement." Veal told Patterson to tell Smith that they would each end up with "$2.00," or $200,000, apiece. Veal also told Patterson to "tell Smitty just follow the program ... go along for the ride." Patterson said that Smith asked him "why can't we just be you and me with the program? I said man you ask a lot of questions about stuff man.... I said because that ain't, because there's more things involved.... Yeah he [Smith] saying he wants to, he wants the equation to be as least complicated as possible, man."
On January 30, Patterson took a day off from work while Smith reported to work, and Patterson purchased a large black duffel bag. There were six telephone calls between Patterson's home telephone and Smith's cellular telephone, one lasting eighteen minutes and another lasting twenty-seven minutes. In an unrecorded conversation on January 30, Veal informed Patterson that the date for the rip-off would be February 1. This four-minute telephone call from Veal's business telephone to Patterson's home telephone was followed by three telephone calls from Patterson's home telephone to Smith's cellular telephone. Patterson also stayed home from work on January 31, and there were three telephone calls that morning between his home telephone and Smith's cellular telephone, lasting from one to nine minutes.
Just after noon on January 31, Patterson had a recorded telephone conversation with Veal. Veal asked Patterson "Smitty, he say, he's all cool for tomorrow ain't he?" Patterson responded "Oh yeah man ... You know but ... just make sure, you know, that this, this stud is straight, man?" Veal told Patterson that the Mexican male would meet them after the rip-off at the parking lot of the Jewel grocery store at 50th Street and Kedzie Avenue in Chicago. Veal said that he would park his Chevy Tahoe truck there so that Patterson would recognize it, and said that Patterson should throw the drugs in the Tahoe and take the money himself. Veal said that the drugs would be in one bag and the money in another in the apartment. Veal told Patterson that there would be approximately $600,000 in one bag, and that Patterson would not need to look around for the money.
Also during the January 31 conversation, Patterson told Veal that he and Smith planned to use a key, provided by Veal, to go in the front door of the apartment, and that they would break the lock on the back door to make it look like a forced entry. Immediately after the telephone call with Veal ended, there were two short calls from Patterson's home telephone to Smith's cellular telephone. Later that evening, Veal called Patterson at home in a recorded conversation. Patterson asked if Veal had everything set for the rip-off, and Veal said he did not have they key, but that he would meet Patterson at a pancake house on Hyde Park Boulevard at *906 9:30 the next morning to give him the key and the address.
At 10:15 a.m. on February 1, Veal and Patterson met at the pancake house. The recording of this meeting is mostly unintelligible. Veal testified that he brought an envelope with him, provided by the FBI, with the address of an undercover FBI apartment on West 58th Street in Chicago. He gave this envelope to Patterson along with two keys, one for the front door of the apartment building and one for the door of the apartment itself. Veal told Patterson that there would be five kilograms of cocaine in one bag, which he should put in Veal's truck in the Jewel parking lot, and money in the other bag, which Patterson should keep. Veal said that he would meet with Patterson later to split up the money. After Veal and Patterson left the pancake house, Veal told Patterson that the drugs would be in one place, but that the money might be scattered throughout the apartment. This portion of the tape was audible.
The undercover FBI apartment was equipped with video and audio surveillance. An FBI agent placed in the apartment a black plastic garbage bag wrapped in duct tape, which contained $20,000 in United States currency, and a red gym bag with five one-kilogram-sized bricks of sham cocaine.
A few minutes after noon on February 1, Patterson and Smith drove an unmarked Chicago Police Department car with municipal license plates to the undercover apartment. They entered the apartment through the front door with the key provided by Veal. Both Smith and Patterson were on-duty and were armed. Each wore a mask that completely concealed his face, although Chicago Police Department policy forbade officers from concealing their faces during official police department searches. Neither Smith nor Patterson sought permission from their supervisor to conduct a raid of the apartment, although it was outside of their assigned beat at public housing.
Smith entered the undercover apartment, walking slowly. He carried his gun in one hand and a battering ram in his other hand. Patterson and Smith searched the kitchen cabinets. Patterson found the package of money in a wall cabinet in the kitchen, and then found the red gym bag with the sham cocaine in a cabinet under the kitchen counter. He took both bags into the living room and unzipped the red duffel bag and looked inside. He then placed both bags in the black duffel bag he had brought with him.
After finding the two packages, Patterson went back into the kitchen and whispered something to Smith. Before leaving, Smith and Patterson quickly searched the apartment again, then moved furniture to make the apartment look as if it had been ransacked. In the living room, Patterson placed the television on the floor and tipped the television stand on the floor, and he tossed a chair cushion on the floor. Smith picked up a lamp and gently tilted it so that it rested on the arm of the couch. In the kitchen, Patterson strewed garbage on the floor and Smith emptied the contents of a cabinet on the floor. Patterson and Smith kept their masks on for the duration of the search, and spoke very little. Patterson used hand signals at one point to communicate with Smith.
Patterson and Smith left the undercover apartment through the front door, and Patterson carried the large black duffel bag. They used something to break the lock on the front door; a bashing noise was audible on the tape as Patterson and Smith left the apartment. Patterson drove the unmarked police car, with Smith as a passenger, to the Jewel at 50th and Kedzie, using alleys and side streets rather than a direct route. While they were *907 driving, an FBI surveillance agent saw Smith leaning over the passenger seat into the back seat of the car and doing something with his hands in the back seat.
Patterson drove up to Veal's Tahoe in the Jewel parking lot. Smith got out of the unmarked police car and placed a black plastic garbage bag, later discovered to contain the red gym bag with the sham cocaine, into Veal's Tahoe. An FBI agent took surveillance photographs, which showed Smith moving between the two vehicles. Patterson and Smith did not inventory either the money or the drugs, although police department policy required them to do so.
Patterson and Smith then drove to Patterson's home at 11138 South Loomis Street in Chicago, again taking an indirect route. The unmarked police car was spotted, unoccupied, in Patterson's driveway, and a few minutes later Smith and Patterson got in the car and drove away. Patterson and Smith were arrested later that day. A search of Patterson's home revealed the package of money from the undercover apartment. Patterson gave a post-arrest statement in which he stated that he was involved in a custody battle with his ex-wife over his six-year-old daughter, and that he had arranged the rip-off with Veal because he needed the money. He admitted that he expected to find as much as $800,000 in cash and four to five kilograms of drugs.
Patterson testified at trial. He admitted the content of the recorded conversations, but testified that there were other unrecorded conversations in which he and Veal discussed the rip-off. Patterson testified that Veal had lent him money several times for his custody fight, and that he owed Veal a favor, so he agreed to go into an apartment and retrieve money that he believed to belong to Veal. He testified that he did not expect there to be drugs, and that Veal threatened him and told him not to look in the bags. Patterson also testified that Smith did not know anything about any drugs that may have been involved.
Smith did not testify, but his attorneys argued, during closing argument, that Smith believed he was involved in a legitimate raid of a drug-dealer's apartment. In rebuttal argument, the government said "Daryl Smith? Well his defense attorney just said that Smith's version now is that he believed he was conducting a legitimate narcotics investigation."

II. Patterson

A. Count 1 (Conspiracy)
Patterson argues that his conspiracy conviction must be vacated because his conviction is inconsistent with Smith's acquittal on that charge, and because the jury instructions and special verdict forms constructively amended the indictment.

1. Inconsistent Verdicts
"A conspiracy under 21 U.S.C. § 846 requires that (1) two or more people agreed to commit an unlawful act and (2) the defendant knowingly and intentionally joined in the agreement." United States v. Gardner, 238 F.3d 878, 879 (7th Cir. 2001). I instructed the jury that the defendants could not, as a matter of law, conspire with Veal because he was a government agent. Jury Instruction 24. Patterson argues that, because the indictment charged Smith and Patterson with conspiring "with each other" and there was no evidence presented of other coconspirators, a verdict convicting him but acquitting Smith is inconsistent and cannot stand.
In 1974, the Seventh Circuit held that "it is clear that a conspiracy requires at least two participants, and it has repeatedly been said that the acquittal of all but one of the alleged conspirators should operate as an acquittal of that defendant as well." *908 United States v. Fleming, 504 F.2d 1045, 1055 (7th Cir.1974). It did so despite its acknowledgment that, where the record demonstrated that the acquitted defendants actually did conspire with the convicted defendant, "it is not at all clear in view of the well-settled rule that verdicts in criminal cases need not be consistent." Id. (citing Dunn v. United States, 284 U.S. 390, 52 S.Ct. 189, 76 L.Ed. 356 (1932)).
Ten years later, the Supreme Court held that "[i]nconsistent verdicts ... present a situation where `error,' in the sense that the jury has not followed the court's instructions, most certainly has occurred, but it is unclear whose ox has been gored." United States v. Powell, 469 U.S. 57, 65, 105 S.Ct. 471, 83 L.Ed.2d 461 (1984). In that case, the defendant charged with drug conspiracy and possession, and with the use of the telephone to facilitate the conspiracy and possession, was acquitted of the conspiracy and possession counts but convicted of the use of the telephone counts. Id. at 59-60, 105 S.Ct. 471. She challenged her verdicts as inconsistent on the ground that the jury acquitted her of the crimes that she was convicted of facilitating. Id. at 61, 105 S.Ct. 471. The Supreme Court noted that no provision of the Constitution requires consistent verdicts, id. at 63, 105 S.Ct. 471, and noted that its decision in Dunn "establish[ed] `the unreviewable power of a jury to return a verdict of not guilty for impermissible reasons.'" Id.[2]
Juries may reach inconsistent verdicts for a variety of reasons, including mistake, compromise, or lenity. 469 U.S. at 63, 105 S.Ct. 471. The Powell Court reasoned that, because the government has no right to appeal an inconsistent acquittal, because the inconsistency may be the result of lenity, and because it is "imprudent and unworkable" to inquire into the individualized, subjective reasons for the jury's verdict, inconsistent verdict are not reviewable. Id. at 66, 69, 105 S.Ct. 471. Although acquittal against the law and the evidence is an unlawful exercise of the power of lenity by a jury, it is unreviewable by the government. Id. at 66, 105 S.Ct. 471. The Court held that review for sufficiency of the evidence was a sufficient safeguard against a defendant's wrongful conviction, independent of any inconsistency in the jury's verdict, and that "no further safeguards against jury irrationality are necessary." Id. at 67, 105 S.Ct. 471.
The Seventh Circuit has strongly suggested that it would extend the reasoning of Powell to cases like Fleming, where all defendants but one are acquitted of conspiracy. See United States v. Mancari, 875 F.2d 103, 104 (7th Cir.1989), cert. denied, 499 U.S. 924, 111 S.Ct. 1320, 113 L.Ed.2d 253 (1991). In Mancari, two defendants were charged with conspiring with each other and "others known and unknown to the Grand Jury"; one defendant was acquitted and the other was convicted. Id. at 103-04. The court noted that, "[a]lthough Powell and Dunn are cases where the inconsistent verdict was rendered against one defendant, their reasoning applies with undiminished force to a case in which the jury has treated codefendants inconsistently." Id. at 104 (citing Standefer v. United States, 447 U.S. 10, 25, 100 S.Ct. 1999, 64 L.Ed.2d 689 (1980) ("While symmetry of results may be intellectually satisfying, it is not required.") (citing Dunn and holding that, based on the legislative history of the aiding and abetting statute, a conviction for aiding *909 and abetting could stand even though the principal was acquitted)). As in a single-defendant case, "[t]he acquittal of a codefendant may have been motivated by sympathy for that defendant[,] but the government can do nothing about it." Id. The Seventh Circuit stated that, "after Powell there can be no presumption that the jury acquitted [one defendant] because the government had failed to prove him guilty beyond a reasonable doubt, and convicted [the other defendant] lawlessly." Id. (emphasis in original). "[I]f there is overwhelming evidence of conspiracy, the jury will be assumed not to have convicted lawlessly but instead to have acquitted the other(s) lawlessly." Id.
Nonetheless, the Seventh Circuit did not rely on Powell in reaching its decision in Mancari because the government in that case conceded that the rule of consistency applied and that the conviction could not be upheld on the basis of evidence that the convicted defendant conspired with the acquitted defendant. Instead the government argued that the conviction could be upheld on the basis of the charge that the defendant also conspired with "others known and unknown to the Grand Jury." 875 F.2d at 104, 106. Patterson contends that Mancari should be limited to cases in which there is evidence that the defendant conspired with someone other than the acquitted co-defendant named in the indictment, but the Mancari opinion does not support that limitation. The court stated that the government's concession to the rule of consistency, and its reliance on the existence of "others known and unknown to the Grand Jury," was "unwarranted," id. at 104, and "improvident," id. at 107. These are strong indications that the court would have relied on Powell if the government had not conceded the point.[3]
Six circuits have expressly rejected the rule of consistency in "lone conspirator" cases like Mancari. See United States v. Zuniga-Salinas, 952 F.2d 876, 878 (5th Cir.1992) (en banc) ("An inconsistent verdict should no longer be a bar to conviction where all other co-conspirators are acquitted."); United States v. Thomas, 900 F.2d 37, 40 (4th Cir.1990) (applying Powell and holding that there was sufficient evidence of conspiracy between convicted defendant and acquitted co-conspirator to uphold verdict); United States v. Bucuvalas, 909 F.2d 593, 597 (1st Cir.1990) ("[T]he `rule of consistency' exception to the Dunn rule [in multi-defendant conspiracy cases] is no longer viable in light of Powell."); United States v. Dakins, 872 F.2d 1061, 1065 (declining to adopt rule of consistency in multi-defendant case in light of Powell); United States v. Valles-Valencia, 823 F.2d *910 381, 382 (9th Cir.1987) ("[T]he acquittal of all conspirators but one does not necessarily indicate that the jury found no agreement to act .... The fact that the conflict in this case involves charges against different defendants, rather than different charges against the same defendant does not affect the rationale."); United States v. Andrews, 850 F.2d 1557, 1561 (11th Cir. 1988) ("Consistent verdicts are unrequired in joint trials for conspiracy: where all but one of the charged conspirators are acquitted, the verdict against the one can stand.").[4]
In light of Powell and Mancari, the inconsistency of the conviction of Patterson and the acquittal of Smith, standing alone, provides no basis for vacating Patterson's conspiracy conviction. Instead, I consider only whether there was sufficient evidence of an agreement between Smith and Patterson to sustain the conviction. Because the Seventh Circuit in Mancari stated that "if there is overwhelming evidence of conspiracy, the jury will be assumed not to have convicted lawlessly ...", Patterson argues that the government must demonstrate that the evidence against him was overwhelming. However, the Supreme Court clearly held that review for sufficiency of the evidence was the only safeguard necessary, and required no more exacting review. See Powell, 469 U.S. at 67-68, 105 S.Ct. 471. See also Thomas, 900 F.2d at 40 (applying sufficiency of the evidence standard). Sufficiency of the evidence review is very limited:
[t]he evidence and all reasonable inferences that can be drawn from it must be viewed in the light most favorable to the government. [I] do not weigh the evidence or second-guess the jury's credibility determinations. The test is whether, when the evidence is viewed in a light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.
United States v. Gardner, 238 F.3d 878, 879 (7th Cir.2001).
Patterson does not dispute the strength of the evidence against him, but he argues that there was insufficient evidence of Smith's knowing and voluntary agreement to participate in the rip-off to find that there was a conspiracy. To establish the existence of a conspiracy between Patterson and Smith, the government had to prove that there was an agreement between them, and that Smith and Patterson knowingly and intentionally joined in the agreement. See Gardner, 238 F.3d at 879. "No overt act is required. Guilt can be inferred by the circumstances and the conduct of the parties." Id. (citations omitted).
Patterson argues that there were no conversations in which Smith indicated his agreement. However, Veal's testimony showed that Patterson talked several times about conversations with Smith, and that Smith said that the rip-off "look[ed] like retirement" to him. Patterson also said that Smith wanted the "equation," or split of the proceeds, to be as simple as possible. The telephone records also showed that Smith and Patterson talked on the telephone after most of Patterson's meetings or conversations with Veal. Direct evidence of agreement is unnecessary; "[c]onspiracies, like other crimes, may be *911 proved entirely by circumstantial evidence." United States v. Townsend, 924 F.2d 1385, 1390 (7th Cir.1991). The statements attributed to Smith establish his stake in the venture, and a reasonable jury could infer from Patterson's statements about what Smith said that Smith knew of and agreed to the goal of the conspiracy.
But there is more; a jury could infer knowing agreement from Smith's participation in the ripoff. Although "a defendant's mere knowledge of, approval of, association with, or presence at a conspiracy standing alone is insufficient to establish membership in the conspiracy," United States v. Collins, 966 F.2d 1214, 1220 (7th Cir.1992), an agreement to conspire may be demonstrated by "circumstantial evidence and reasonable inferences drawn therefrom concerning the relationship of the parties, their overt acts, and the totality of their conduct," United States v. Larkins, 83 F.3d 162, 166 (7th Cir.1996). Smith entered the apartment wearing a ski mask and carrying a battering ram, moved furniture in the apartment to make it look as if it had been raided or ransacked, and placed the drugs in Veal's Tahoe in the Jewel parking lot. His participation in the theft and delivery of the goods goes "beyond mere presence," and, together with Patterson's statements to Veal, is, at a minimum, sufficient evidence to sustain a conviction.[5]See Collins, 966 F.2d at 1220 (holding that cumulative circumstantial evidence of membership in conspiracy was sufficient where the defendant was present and participated in overt acts and placed and received telephone calls from key coconspirators in the days before the transaction).
It is also reasonable to infer that Smith, a Chicago police officer for ten years, would know that evidence seized, without a warrant, from a purported drug dealer's apartment should not be placed in an unlocked truck in a parking lot, and that by placing the bag in Veal's Tahoe, Smith knowingly and intentionally joined in the criminal purpose of the plan. See United States v. Hunte, 196 F.3d 687, 691 (7th Cir.1999) (holding that evidence of participation in drug transaction was sufficient to establish defendant's knowing and intentional link to conspiracy even where there was no evidence that defendant had helped to plan transaction or expected to share in proceeds). A rational jury could also infer that Patterson, who admitted to planning and carrying out the theft, would not bring another veteran police officer along for the ride unless that officer knew of the plan and agreed to it. There was sufficient evidence of Smith's agreement and participation to sustain a conviction for conspiracy, so although the jury did not convict Smith, Patterson's conviction stands.

2. Constructive Amendment
"Under the Grand Jury Clause of the Fifth Amendment, the possible bases for conviction are limited to those contained in the indictment." United States v. Soskin, 100 F.3d 1377, 1380 (7th Cir. 1996). The indictment charged Patterson with conspiracy and attempt to possess "approximately five kilograms of cocaine." The jury was instructed that, if it found Patterson guilty of conspiracy and attempt, it had to determine, beyond a reasonable doubt, the amount of cocaine involved. The options given to the jury tracked the statutory penalties in 21 U.S.C. § 841(b): "5 kilograms or more," "500 grams or more, but less than 5 kilograms," *912 or "less than 500 grams." Jury Instruction 42 and Special Verdict Forms. The jury unanimously convicted Patterson of conspiring and attempting to possess more than 500 grams but less than five kilograms of cocaine. Patterson argues that the special verdict form and the instruction to the jury constituted a constructive amendment.
"A constructive amendment to an indictment occurs when either the government ... or the court ... or both, broadens the possible bases for conviction beyond those presented by the grand jury." United States v. Trennell, 290 F.3d 881, 888 (7th Cir.2002) (emphasis added). However, no constructive amendment occurs where the evidence, arguments, or jury instructions narrow the bases for conviction. Soskin, 100 F.3d at 1380. "Such an occurrence is typically labeled a variance and is subject to harmless error review." United States v. Willoughby, 27 F.3d 263, 265 (7th Cir.1994). "[T]he essential question [in the case of a variance] is whether the initial statement of that offense [in the indictment] was so obfuscated by the breadth of the charging instrument that [the defendant] was unfairly surprised or otherwise prejudiced in the conduct of his defense (or a risk of double jeopardy was created)." Id. at 265-66. Patterson does not argue that he was prejudiced in this manner, so the only question is whether the difference between the indictment and the special verdict forms and jury instructions constituted a permissible variance or an impermissible constructive amendment.
"In order to demonstrate constructive amendment, the crime charged in the indictment must be `materially different or substantially altered at trial, [so that] it is ... impossible to know whether the grand jury would have indicted for the crime actually proved.'" Trennell, 290 F.3d at 888. In Trennell, the indictment did not refer to any particular quantity, but charged the defendants with a conspiracy involving "wholesale quantities of cocaine." The court held that "[t]his language was broad enough to include the quantity of drugs for which [the defendant] was convicted, namely 5 kilograms of cocaine ...." Id. at 889. If the evidence here had demonstrated that the amount involved was significantly more than five kilograms, and the jury had found Patterson guilty of conspiring and attempting to possess an amount in excess of five kilograms, there may have been a constructive amendment, but I need not reach that question. Patterson's conviction for conspiring and attempting to possess more than 500 grams but less than five kilograms of cocaine "was fully contained within the indictment," viz., "approximately five kilograms," and is thus an acceptable variance, not a constructive amendment. See id.
Patterson argues that the Supreme Court's recent decision in Ring v. Arizona, ___ U.S. ___, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), limits the Seventh Circuit's holding in Trennell. Ring, however, only expanded on the Court's earlier decision in Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), and held that "[i]f a State makes an increase in a defendant's authorized punishment contingent on a finding of fact, that factno matter how the State labels it[, whether sentencing factor or element of the offense]must be found by a jury beyond a reasonable doubt." ___ U.S. at ___, 122 S.Ct. at 2439. The rule announced in Apprendithat, "[o]ther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt, 530 U.S. at 490, 120 S.Ct. 2348 does not relate to the question of constructive *913 amendments except to the extent that `[i]n federal prosecutions, such facts [increasing the penalty beyond the statutory maximum] must also be charged in the indictment.'" United States v. Cotton, ___ U.S. ___, ___, 122 S.Ct. 1781, 1783, 152 L.Ed.2d 860 (2002).
Patterson does not expressly argue that there was an Apprendi error in the indictment, which charged him with conspiring and attempting to possess "approximately five kilograms of cocaine." A search of post-Apprendi case law turned up no case finding that the language "approximately five kilograms of cocaine," which straddles the penalties in 21 U.S.C. § 841(b)(1)(A)(ii) ("5 kilograms or more" of cocaine) and § 841(b)(1)(B)(ii) ("500 grams or more" of cocaine), runs afoul of Apprendi. "Approximately five kilograms" could be somewhat more than five kilograms or somewhat less. But no matter what "approximately five kilograms" means, the jury found Patterson guilty of a lesser amount. Even if there was an Apprendi error, it was rendered harmless by the jury's determination, beyond a reasonable doubt and after proper instruction, that Patterson was guilty of conspiring and attempting to possess 500 grams or more but less than five kilograms of cocaine. See Trennell, 290 F.3d at 890.
Patterson argues that the government did not prove the amount involved because the Special Agent did not testify that the bricks of sham cocaine recovered from the Tahoe were the same as the ones placed in the undercover apartment by the FBI. However, there was ample evidence from Patterson's conversations with Veal that the conspiracy involved an amount ranging from five to ten kilograms of cocaine, and Patterson even confessed to a conspiracy involving between four and five kilograms of cocaine. This is sufficient evidence to prove that the amount involved was more than 500 grams but less than five kilograms.

B. Count 2 (Attempt)
Patterson argues that his conviction for attempt should be vacated for the same reasons as his conspiracy conviction, but I have rejected those arguments above. He makes one additional argument, however, that I address separately. Patterson argues that there was no evidence that Patterson knew he had drugs in his possession when he took the bag of sham cocaine out of the apartment. But knowledge of the content of the bag, though necessary to sustain a conviction for actual possession, is unnecessary for attempted possession, of which he was convicted. See United States v. Pulido, 69 F.3d 192, 206 (7th Cir.1995) ("The offense of attempting to possess with intent to distribute is complete when a defendant has been active in negotiating a drug transaction and has actually taken physical steps to obtain possession of a drug."). There was sufficient evidence that Patterson negotiated the drug transaction with Veal; there was extended discussion of whether any of the drugs taken from the apartment ought to be inventoried, and Veal told Patterson that the amount of drugs involved would range from five to ten kilograms. Patterson admitted in his confession that he expected to find a red bag containing four to five kilograms of cocaine, and he admitted to taking the red bag. The break-in and search of the apartment were substantial steps in furtherance of the attempted possession.
Patterson does not dispute this evidence, though he argues that the government overstates the evidence when it says that Patterson unzipped the bag containing the sham cocaine. As I have explained, however, actual knowledge of the content of the bag is unnecessary to sustain a conviction *914 for attempted possession. Nonetheless, I have viewed the videotape again, and I agree with the government that there is evidence that Patterson unzipped the bag and looked inside. The tape shows Patterson yanking his arm back at the same time as a zipping noise can be heard on the tape, and he appears to look inside the red bag before placing it the large black bag he brought with him. A rational jury could believe that Patterson looked in the red bag and saw the bricks of sham cocaine. Even without this evidence, however, Patterson's conviction for attempt may be sustained.

C. Count 3 (Carrying a firearm in relation to a felony)
Patterson argues that his firearm conviction is invalid because the predicate offense was the conspiracy, which he says must be vacated. However, the conspiracy conviction stands, so I consider his other argument, namely, that there was insufficient evidence that he was carrying his firearm "in relation to" the conspiracy. 18 U.S.C. § 924(c) punishes any person who "uses or carries a firearm" "during and in relation to any crime of violence or drug trafficking crime." Patterson does not dispute that there was sufficient evidence that he "carried" a weapon, but he argues that there was no evidence that he did so "in relation to" a drug crime. "The phrase `in relation to' ..., at a minimum, clarifies that the firearm must have some purpose or effect with respect to the drug trafficking crime; its presence or involvement cannot be the result of accident or coincidence." Smith v. United States, 508 U.S. 223, 238, 113 S.Ct. 2050, 124 L.Ed.2d 138 (1993). "[T]he gun at least must `facilitat[e], or ha[ve] the potential of facilitating,' the drug trafficking crime." Id.
Patterson argues that, as an on-duty police officer, he was required to carry a firearm, and that the fact that he was carrying it during the rip-off was merely coincidental. Although an on-duty police officer has a legitimate reason to carry a firearm, the jury was free to reject this as the only explanation for why Patterson was armed during the break-in. The fact that Patterson was required to carry a firearm as part of his job does not insulate him from liability if he abuses that privilege by committing a crime and he carries or uses the firearm to facilitate that crime. See, e.g., S.Rep. No. 98-225 at 314 n. 10, reprinted in 1984 U.S.S.C.A.N. at 3492 n. 10 (explaining substitution of phrase "in relation to" for "unlawfully" in § 924(c) to encompass cases in which lawfully armed law enforcement officers use or carry weapons in relation to crimes that they commit). The government argues that Patterson carried the firearm for protection and security, but it does not point to any particular evidence in the record to support this theory. Patterson objects that the argument about security was not made at trial and therefore may not be considered here.
Though I am limited to consideration of the evidence presented at trial, I am not limited to the arguments advanced by the government at trial. The question for sufficiency of the evidence is whether any rational jury could have convicted on the basis of the evidence at trial. See United States v. Fort, 998 F.2d 542, 545 (7th Cir.1993). A rational jury could have believed that Patterson carried the gun "in relation to" the conspiracy because "Plan B," discussed by Patterson and Veal prior to the rip-off, involved the ruse of acting in their official capacity as police officers. Under "Plan B," which would have been implemented if Smith and Patterson had been discovered by neighbors in the act of breaking into the apartment, Smith and Patterson would have acted like officers on a legitimate raid and inventoried at least some of the drugs. In that case, a jury *915 could believe that the fact that Patterson carried a firearm during the rip-off had the potential to facilitate the conspiracy by covering it up with the facade of legitimacy, which included carrying a gun. The evidence is sufficient to support his conviction on this charge.

D. Count 5 (Theft of government funds)
Patterson challenges the sufficiency of the evidence on his conviction for theft of government funds. To sustain a conviction for theft or conversion of government funds under 18 U.S.C. § 641, the government must prove: "(1) that the money or property belonged to the government; (2) that the defendant fraudulently appropriated the money or property to his own use or the use of others; (3) and that the defendant did so knowingly and willfully with the intent either temporarily or permanently to deprive the owner of the use of the money or property." United States v. Howard, 30 F.3d 871, 875 (7th Cir.1994). Patterson claims that the evidence showed that he was given a key to the apartment by someone with authority to give it to him (i.e., Veal), and that he was authorized by Veal to remove the package that contained money. He also argues that there was no evidence of forced or unlawful entry and that there was no evidence that he entered the apartment with the intent to steal anyone else's property. This was Patterson's theory at trial, based largely on conversations that Patterson said he had with Veal but which were not tape-recorded.
However, the evidence, and the inferences from it, clearly support the verdict. Patterson confessed that Veal arranged for him to enter the apartment to retrieve a package that contained "a large sum of money" that Patterson hoped to use to pay for his attorney in his custody battle with his wife, and that he took the package that Veal told him would contain the money. The surveillance videotape also showed that Patterson looked into that bag. Veal testified that, in an unrecorded conversation with Patterson on January 13, 2001, he told Patterson that the planned rip-off would be set up by a "Mexican male" who wanted to steal drugs and money from a stash apartment of the drug dealer for whom he worked. The Mexican male expected to keep the drugs, but Patterson and Veal, and anyone recruited by Patterson to help, would split the money up between them. This is sufficient evidence that Patterson intended to steal property belonging to the drug dealer who employed the Mexican male. Faced with Patterson's version that he believed the money to be Veal's and that he was authorized to take it and Veal's version that the money was being stolen from a drug dealerboth unrecorded conversations a rational jury could have believed Veal over Patterson in light of the conversations about what to do with the drugs and money once they were removed from the apartment.
Patterson also objects that the money he was accused of stealing was never introduced into evidence. However, Special Agent Davis testified that the black plastic garbage bag, which Patterson admitted to taking from the apartment and transporting to his home, contained $20,000 belonging to the United States. This is sufficient evidence to establish that Patterson stole the money.

III. Smith
On the charge of theft of government funds in count five, Smith argues that there was insufficient evidence that he had knowledge that there was money in the package that was taken by Patterson. There was no evidence that Smith saw the contents of the package, but knowledge can be proven circumstantially. See United *916 States v. Hammond, 826 F.2d 577, 580 (7th Cir.1987). The tape-recorded conversations between Patterson and Veal demonstrated that Smith knew and expected that money would be taken from the apartment; Patterson conveyed Smith's concern about the split of the proceeds to Veal and said that Smith wanted "the equation to be as least complicated as possible." Gov't Ex. 1-22-01 Tr. at 6. Patterson also said that Smith said that the planned rip-off "looks like retirement." Smith also participated in the break-in, wearing a ski mask, which was prohibited by police department policy during searches, with his weapon drawn, and moved a lamp and emptied a cabinet to create the appearance that the undercover apartment had been ransacked. He also accompanied Patterson into Patterson's home when Patterson deposited the money in a closet. Patterson's testimony about Smith's statements, combined with Smith's actions on the day of the break-in, are sufficient circumstantial evidence that Smith knew that Patterson was taking money out of the apartment.
Smith wanted to use an enlarged chart from the United States Sentencing Guidelines in his cross-examination of Veal. He argues now that I erred by denying him the use of this chart, but he cites no authority and he does not make any argument to support his claim of error. "[P]erfunctory and undeveloped arguments, and arguments that are unsupported by pertinent authority, are waived." United States v. Wimberly, 60 F.3d 281, 287 (7th Cir.1995). Even if the argument were not waived, however, there was no error. What mattered was Veal's understanding of the length of the sentence he faced, not how a judge would have calculated his sentence under the guidelines. I properly excluded the demonstrative exhibit as more prejudicial than probative on the grounds that it was likely to confuse the jury.
In closing rebuttal argument, the government said: "Daryl Smith? Well his defense attorney just said that Smith's version now is that he believed he was conducting a legitimate narcotics investigation. I believe that's what Mr. Vilkelis [Smith's attorney] just said." Smith argues that this statement highlighted the fact that he did not testify and that it improperly suggested that Smith had made some post-arrest statement, not introduced into evidence, that was inconsistent with his counsel's argument.
I must analyze a prosecutor's statement in context to determine whether it violated a defendant's Fifth Amendment right against self-incrimination. See United States v. Mietus, 237 F.3d 866, 871 (7th Cir.2001). The reference to "Smith's version" was clearly a reference to the argument made by Smith's counsel in closing argument, see id. at 872 (holding that statement "the defendants have told you ..." did not improperly highlight failure to testify where, in context, it referred only to arguments advanced by defendant through counsel and defense witnesses), and a jury would not "naturally and necessarily take the remark for a comment on the defendant's silence," id. at 871. See also United States v. Rothman, 567 F.2d 744, 751 (7th Cir.1977) (holding that prosecutor's statement that "[t]he defendant ... argues ..." could not reasonably be construed as a reference to defendant's silence where context suggested it was comment on argument and examination by defense counsel).
Nor does the statement suggest the existence of any post-arrest statement. There was no evidence or direct suggestion that Smith had given any such statement, and the use of the word "now," in context, was no more than a reference to the position that Smith, through his counsel, was taking at the close of all the *917 evidence. There was no error in allowing the statement, so Smith was not prejudiced.

IV. Conclusion
Smith's motion for a new trial, to arrest judgment, and for judgment of acquittal notwithstanding the verdict is DENIED. Patterson's motion for entry of a judgment of acquittal, or, in the alternative, for a new trial, is DENIED.
NOTES
[1]  For the sake of simplicity, I will refer to all subsequent dates in 2001 by month and day only.
[2]  This phenomenon is commonly called "jury nullification." See Andrew D. Leipold, Rethinking Jury Nullification, 82 Va. L.Rev. 253, 253 (1996) ("Nullification occurs when the defendant's guilt is clear beyond a reasonable doubt, but the jury, based on its own sense of justice or fairness, decides to acquit.").
[3]  The Seventh Circuit has since cited Mancari for the proposition that, in a two-man conspiracy, a codefendant's acquittal does not require reversal of the defendant's conviction "as long as the evidence adequately supports a finding that [the defendant] conspired with `others known or unknown to the grand jury' as charged in the indictment." United States v. Byerley, 999 F.2d 231, 234 (7th Cir.1993). Nonetheless, the inclusion of the "others known or unknown" language does not mean that such language referring to or evidence of other co-conspirators is required to sustain the conviction. The Byerley court did not signal retreat from its extension of Powell to multi-defendant cases, and there was evidence of other non-defendant coconspirators to support the verdict in that case that did not require a return to the question.

The First Circuit has expressly declined to consider evidence of "others known and unknown to the grand jury" necessary to uphold a defendant's conviction when the only named co-conspirator is acquitted. See United States v. Bucuvalas, 909 F.2d 593, 594 n. 1 (1st Cir.1990); see also United States v. Andrews, 850 F.2d 1557, 1558, 1561-62 (11th Cir.1988) (applying Powell although indictment named only the two defendants and made no reference to other co-conspirators, named or unnamed).
[4]  Two other circuits, like the Seventh Circuit, have expressed doubt about the continuing vitality of the rule of consistency or have rejected it in dicta. See United States v. Acosta, 17 F.3d 538, 545 (2d Cir.1994); Government of the Virgin Islands v. Hoheb, 777 F.2d 138, 140 n. 4 (3d Cir.1985); see id. at 143 (Garth, J., concurring). Only the Tenth Circuit has expressed continuing support for the rule of consistency. See United States v. Suntar Roofing, Inc., 897 F.2d 469, 475 (10th Cir.1990), criticized by Bucuvalas, 909 F.2d at 596-97.
[5]  Indeed, although Powell does not require overwhelming evidence of a conspiracy, see 469 U.S. at 67-68, 105 S.Ct. 471 (holding that only sufficiency of the evidence was required), I find that the evidence of Smith's agreement and participation in the conspiracy was over-whelming, notwithstanding his acquittal on that charge.
