Luis Carrera sold cocaine to a confidential informant, and he brought his brother, David Carrera, with him to the sale. As a result, Luis and David Carrera were both charged with conspiring to possess cocaine with intent to distribute. Luis ultimately pleaded guilty to the indictment, and David was found guilty by a jury. In this consolidated appeal, David and Luis Carrera both raise a number of issues regarding their respective convictions and sentences. Because we find no errors requiring reversal, we affirm.

On July 27, 1999, Francisco "Cisco" Soto made arrangements through drug broker Caesar Salazar to sell five kilograms of cocaine for $19,500 per kilogram to one of Salazar's customers. Unbeknownst to Soto, Salazar had become a confidential informant, and his "customer" was actually Investigator Calderon, an undercover agent. Because Soto was unavailable to deliver the cocaine that night, the parties agreed that Luis would make the delivery, and that they would share the responsibility for his fee. Through a series of recorded telephone conversations, Salazar and Luis agreed to meet at the Holiday Inn in Hillside, Illinois at 9:00 p.m. to complete the sale.

About 8:00 p.m. on July 27, Luis and his brother David1 were on their way to buy a garage door opener for a garage door they had purchased earlier in the day when Luis informed David that he needed to meet a friend before they ran their errand. David, a construction worker by trade, knew that his brother was involved in dealing drugs and did not ask any questions. At approximately 9 p.m., David and Luis pulled into the parking lot of the Holiday Inn in a pick-up truck. Luis instructed David to tell Salazar and Calderon, who were waiting in the parking lot, to come over to the truck. David then exited the truck and walked towards the two men. After speaking briefly with Calderon and Salazar, David proceeded about thirty feet from the truck to the front of the hotel and sat on a brick ledge.

Upon reaching the truck, the undercover agent and the informant had a conversation with Luis, which was recorded by the agent's body microphone. Luis opened his backpack and displayed five bricks of cocaine. Calderon opened one of the packages and determined that the substance was, in fact, cocaine. He then suggested that Luis's "friend" count the money. Luis agreed that David would count the money, and the men decided that they would exchange the cocaine for the money inside the buyer's hotel room. Luis, carrying the backpack containing the cocaine, exited his truck and began walking toward the hotel with Salazar and Calderon. As they approached the entrance, Luis instructed his brother to join them. David got up and followed the three men into the hotel. After the men entered the hotel elevator, agents arrested Luis and David and pretended to arrest Salazar. The agents also recovered the backpack, which was later found to contain 4,975 grams of cocaine.

B. The Post-Arrest Statements of David and Luis Carrera

After their arrests, Luis and David Carrera were transported to the Hillside Police Department and placed in a cell together. Subsequently, Luis was taken to a conference room and interviewed by Investigator Calderon, Investigator Woytko, and Special Agent Ohlin. Luis admitted that he had obtained the cocaine the week before by traveling to Mexico and arranging for five kilograms to be delivered to him in Laredo, Texas. He explained that he had purchased the cocaine for $10,000 per kilogram and that he expected to personally make a $35,000 profit on the deal. According to Luis, the rest of the money was to go to others involved in the deal, but not to his brother David. He admitted that David knew that he sold drugs, but he maintained that David had only come with him as a favor to help him count the money. After Luis gave his statement, one of the agents prepared a typewritten statement for Luis to sign. According to the agents, Luis admitted that the statement was true but refused to sign it until David saw it.

David was then brought into the room. Before the agents had a chance to say anything, David allegedly blurted out, "what my brother told you guys is true." The agents proceeded to tell David what Luis had said, and they gave him the typewritten statement to read. David agreed that the typewritten statement was true, and the agents repeated their request for Luis to sign it. Luis again replied that the statement was true, but he still refused to sign it. The agents then removed Luis from the room and proceeded to interview David alone. During this interview, David admitted that he knew that his brother sold cocaine, and that he assumed that Luis was going to do a drug deal that night. According to the agents, he also stated that he had accompanied Luis to the hotel to help him "take care of business."

C. Proceedings Against Luis and David Carrera

On September 22, 1999, David and Luis Carrera were each charged with one count of conspiring to possess with intent to distribute at least five kilograms of mixtures containing cocaine in violation of 21 U.S.C. sec. 846 and 18 U.S.C. sec. 2, and one count of possession with intent to distribute approximately five kilograms in violation of 21 U.S.C. sec. 846 and 18 U.S.C. sec. 2.

On October 26, 1999, one week before defendants' joint trial was scheduled to begin, Luis's court appointed attorneys, John A. Meyer and Timothy O'Connor,2 filed an emergency motion to withdraw as counsel for Luis. The motion offered two reasons necessitating withdrawal: Luis Carrera's family had retained private counsel, and the rules of professional responsibility required withdrawal as a result of "matters that arose for the first time on October 25, 1999."

The court considered the motion the next day during a pretrial hearing. Luis's proposed new counsel was not present. Meyer explained to the court that Luis had informed him the previous day that his family had retained a new attorney, and that he no longer wished to have Meyer and O'Connor represent him. Meyer stated that he had contacted Luis's family and was told that the new counsel would be in court for the start of trial on November 1. He told the court that he had advised Luis and Luis's family that this was unacceptable, and that the new attorney needed to be in court that day to ask the court's permission to substitute. Meyer did not know the name of Luis's new attorney, and neither he nor the government had been contacted by anyone claiming to be Luis's new attorney.

After listening to this explanation, the district judge stated, "[a]ll right, then, I'm going to have to deny your motion." Meyer then reminded the court that the motion to withdraw was based not only on Luis's desire for new counsel but also on professional responsibility considerations. At that point, the following colloquy took place:

The Court: Well, that presents a problem. I'll think about that problem. But has Mr. Carrera disclosed to you who this attorney is?

Mr. Meyer: No he hasn't Judge. And perhaps he could, if he knows the name.

Luis Carrera: Your Honor, I spoke to my attorney and stuff and, ah, things aren't--things aren't working the way, you know that I--you know that I assume they would have been and I'm just not happy with the stuff that is going on. So I requested, you know, to get some other attorneys.

The Court: Well,--

Luis Carrera: And my family is looking into it. I just-- I just told him yesterday that I didn't want them to represent me.

The Court: Well they are appointed by the court to represent you. And they weren't just appointed yesterday, they were appointed quite some time ago. And Mr. Meyer has done quite a bit of trial preparation, we had a pretrial conference, we're ready to try the case on Monday. And absent some kind of compelling good reason for a substitute of counsel, I cannot authorize them to withdraw at this point. If you had counsel here ready to go to trial, or would be ready to go to trial by next week, and somebody who's admitted to the bar, qualified to do so, of course I would grant the motion. But that's not the case. So the motion is denied.

Luis Carrera: Well, your honor, like I said, I just advised them yesterday that I was going to have an attorney come to speak to me today. But, you know, I was rushed over here. I was barely arraigned less than a month ago, I don't know if you can take that into consideration.

The Court: ... The motion is denied.

Tr. of Emergency Mot. Hr'g. at 5-6.

The joint trial of Luis and David began six days later, on November 2, 1999, with Meyer and O'Connor serving as counsel for Luis. On the morning of the first day of trial, Victor Ciardelli, the attorney retained by Luis's family, attempted to file some sort of emergency motion to postpone the trial. The exact sequence of events is a bit unclear, but Ciardelli was not permitted to enter his appearance on behalf of Luis at that time. The court proceeded with the trial, and the government completed its case-in-chief that afternoon. The next morning, Ciardelli informed the court that he had spoken to Luis over the weekend, and that Luis wished to change his plea to guilty. The district court allowed Ciardelli to enter his appearance as additional counsel for the purposes of the plea hearing. Warning Luis that "there are no economies to either the government or to the Court... for a guilty plea at this stage," the district court proceeded to conduct the guilty plea hearing.

The district court proceeded with David's trial, and it ended in a mistrial when the jury was unable to reach a verdict on either count. A few days later, David was tried again, and this time, the jury found him guilty on both counts.

On January 20, 2000, the district court sentenced Luis Carrera to 121 months imprisonment, four years supervised release, and a $2,000 fine. David Carrera was sentenced to 78 months imprisonment and four years supervised release. In imposing these sentences, the district court found that Luis qualified for a two-level enhancement under United States Sentencing Guidelines (U.S.S.G.) section 3B1.1(c) for playing a leadership role in the offense and did not qualify for an acceptance of responsibility reduction under U.S.S.G. section 3E1.1. Similarly, the district court found that David qualified for an upward enhancement for obstruction of justice under U.S.S.G. section 3C1.1. Both defendants timely filed notices of appeal.

On appeal, Luis and David each raise a number of issues. Luis argues that the district court: 1) violated his right to counsel of choice by denying a continuance in order to allow him to obtain new counsel; 2) improperly added two levels to his offense level for playing a leadership role in the offense; and 3) inappropriately denied a reduction for acceptance of responsibility. David contends that the district court erred by: 1) admitting the contents of his wallet at the time of arrest into evidence; 2) instructing the jury that he could be guilty of conspiracy to distribute cocaine without knowing the type or quantity of substance that was to be distributed; and 3) increasing his offense level for obstruction of justice without making the required findings. Both defendants argue that the district court committed plain error in imposing four years of supervised release. We will address each of these claims below, beginning with the claims of Luis Carrera.

Luis first claims that the district court erred by arbitrarily refusing to postpone his trial in order to allow him the opportunity to retain his counsel of choice. Before proceeding to Luis's arguments, we must address the proper standard of review in this case. Luis claims that the district court erroneously denied him a brief continuance to secure his attorney of choice. We find this assertion to be disingenuous because neither Luis nor his counsel ever moved for a continuance or asked the district judge to postpone the trial.3 Therefore, because no motion for a continuance was made, our review is for plain error only. See United States v. Olano, 507 U.S. 725, 732, 113 S. Ct. 1770, 123 L. Ed. 2d 508 (1993).

Even under a more stringent standard of review, however, it is clear that the district court did not violate Luis's right to counsel of choice by deciding to proceed with his trial. The right to counsel of one's choice encompassed with in the Sixth Amendment is not absolute. See United States v. Rasmussen, 881 F.2d 395, 401 (7th Cir. 1989). Although a person has the right to be represented by the counsel of his choice, "[t]his right is not absolute, but qualified, and must be balanced against the requirements of the fair and proper administration of justice." United States v. Micke, 859 F.2d 473, 480 (7th Cir. 1988). Therefore, while the denial of a continuance may infringe upon the defendant's right to counsel of choice, see United States v. Santos, 201 F.3d 953, 958 (7th Cir. 2000), "only an unreasoning and arbitrary insistence upon expeditiousness in the face of a justifiable request for delay violates the right to the assistance of counsel." Morris v. Slappy, 461 U.S. 1, 11-12, 103 S. Ct. 1610, 75 L. Ed. 2d 610 (1983) (internal quotation omitted). To determine whether the district court erred in denying a continuance, we "must consider both the circumstances of the ruling and the reasons given by the judge for it." Santos, 201 F.3d at 958.

Luis relies on our decision in Santos for his argument that the district court erred in proceeding to trial. In Santos, defendant's counsel was unavailable for the trial date set by the district court, and the district court refused to grant a continuance. 201 F.3d at 958. In finding that the district court erred, we said:

The salient circumstances here are that the case is not old, the indictment having come down only two and a half months before the scheduled trial date... the government did not oppose the continuance; and the judge had no scheduling conflict that would have led to a further delay had he granted the continuance. Nothing in these circumstances indicated that the grant would pose a hardship to anyone.

Id. Luis argues that the factors we found persuasive in Santos are present and even more compelling in this case. He claims that it is clear that the district court did not properly weigh his right to counsel against concerns of judicial administration because his case was not old, the government did not oppose the continuance, and the judge had no scheduling conflict. While we agree that Luis's case was not old, Luis ignores the fact that, because his attorney never moved for a continuance, we do not know if the government would have opposed the motion, if the judge had a scheduling conflict, or if a continuance would have caused hardship to any of the parties.

Furthermore, Santos is also distinguishable because there was no suggestion that the defendant in that case was invoking her right to counsel of choice in order to delay the trial. See id. at 959. Here, Luis did not timely inform his attorneys that he wanted to replace them, he waited until the trial was a week away. At that point, O'Connor and Meyer had been representing Luis for over a month. The untimely nature of Luis's motion coupled with its close proximity to trial as well as the fact that Luis was unable to name his new counsel made it reasonable for the district court to question whether Luis's motion was an attempt to delay the trial. The right to counsel of one's choice "does not give an accused the power to manipulate his choice of counsel to delay the orderly progress of his case." United States ex rel. Kleba v. McGinnis, 796 F.2d 947, 952 (7th Cir. 1986) (internal quotation omitted).

Based on the surrounding circumstances, we do not think that the district court arbitrarily decided to proceed to trial. The fact that the district court questioned Luis's attorney as well as Luis himself in an attempt to discover whether a new attorney had in fact been retained demonstrates the district court's recognition of Luis's right to counsel of his choice. The district judge also acknowledged this right when she specifically stated, "[i]f you had counsel here ready to go to trial, or would be ready to go to trial by next week, and somebody who's admitted to the bar, qualified to do so, of course I would grant the motion." In addition, when Luis's new attorney did show up on the second day of trial, the district court permitted him to enter his appearance for the purpose of changing Luis's plea. Therefore, there was no plain error in the district court's decision to proceed with Luis's trial as scheduled.

Luis next argues that the district court erroneously concluded that he played a leadership role in the offense and therefore qualified for a two-level upward enhancement under U.S.S.G. section 3B1.1(c). We review the district court's decision to make an upward adjustment based on the defendant's role in the offense for clear error. See United States v. Lemmons, 230 F.3d 263, 265 (7th Cir. 2000), cert. denied, 121 S. Ct. 824, 148 L. Ed. 2d 707 (2001). A finding that a defendant played a leadership role "is clearly erroneous 'only if, after reviewing the entire evidence, we are left with the definite and firm conviction that a mistake has been committed.'" United States v. Matthews, 222 F.3d 305, 307 (7th Cir. 2000), cert. denied, 121 S. Ct. 500, 148 L. Ed. 2d 470 (2000) (quoting United States v. Granado, 72 F.3d 1287, 1290 (7th Cir. 1995)). If the fact finder decides between two permissible interpretations of the evidence, we will not find the decision to be clearly erroneous. See id.

The Application Notes to section 3B1.1 instruct the sentencing judge to consider seven factors in order to determine if an aggravating role enhancement is warranted. See U.S. Sentencing Guidelines Manual sec. 3B1.1, cmt n.4 (1998). These factors include:

the exercise of decision making authority, the nature of participation in the commission of the offense, the recruitment of accomplices, the claimed right to a larger share of the fruits of the crime, the degree of participation in planning or organizing the offense, the nature and scope of the illegal activity, and the degree of control and authority exercised over others.

Id. In adopting the Pre-Sentence Investigation Report's (PSR) recommendation of a two-level increase to Luis's base offense level for playing a leadership role, it is clear that the district court focused on several of the factors listed above. Specifically, the district court found that Luis involved his brother in the offense, had decision making authority, expected a larger share of the profits, and obtained the cocaine himself by traveling to Mexico.

Luis takes issue with the district court's findings. First and foremost, he argues, there is no evidence that he had "the sort of real and direct influence [over David]... that the enhancement was designed to punish." United States v. Mankiewicz, 122 F.3d 399, 406 (7th Cir. 1997) (internal quotation omitted). Second, he claims that he was simply an average participant in a scheme orchestrated by Soto and did not have any realistic expectation of obtaining a larger share of profit from the deal. To support this theory, Luis points to a recorded conversation between Soto and Salazar in which Soto states that they wouldn't have to give Luis "that much" in order to get him to make the delivery. Luis also submits that there is no evidence that he had any decision making authority beyond the ability to determine the time of the transaction.

In spite of Luis's argument that he was nothing more than Soto's "glorified mule," we cannot find that the district court clearly erred in finding that Luis played a leadership role in the offense. Although Luis argues that there is no evidence that he did or could have exercised control over his brother, an upward adjustment under section 3B1.1(c) does not require an explicit finding that the defendant exercised control, "so long as the criminal activity involves more than one participant and the defendant played a coordinating or organizing role." United States v. Bush, 79 F.3d 64, 67 (7th Cir. 1996) (internal quotation omitted); see also United States v. Billingsley, 115 F.3d 458, 465 (7th Cir. 1997). As we have stated, "the overall focus under sec. 3B1.1 is relative responsibility within a criminal organization." Bush, 79 F.3d at 67. It is evident from the record that Luis possessed sufficient responsibility to support a leadership role enhancement from the fact that he obtained the drugs, set up the time and place for the delivery, recruited his brother as an accomplice, and claimed rights to $17,000 out of $19,500 per kilogram of cocaine. Therefore, we uphold the district court's determination that Luis qualified for an upward enhancement under section 3B1.1(c).

Luis Carrera next contests the district court's refusal to award a two-level reduction under U.S.S.G. section 3E1.1. Section 3E1.1 provides that a defendant is entitled to a two-level reduction in base offense level if he clearly demonstrates acceptance of responsibility for his actions. See U.S. Sentencing Guidelines Manual sec. 3E1.1 (1998). Of course, a defendant is not entitled to an acceptance of responsibility reduction as a matter of right simply because he pleaded guilty. See United States v. Morris, 76 F.3d 171, 175-76 (7th Cir. 1996). In order to establish entitlement to this reduction, a defendant must show by a preponderance of the evidence that he: "(1) clearly recognized and accepted responsibility for his conduct; (2) timely notified authorities of his intention to enter a plea of guilty; and (3) truthfully admitted the conduct comprising the offense of conviction and admitted... the relevant conduct as it relates to the offense of conviction." United States v. Sierra, 188 F.3d 798, 804 (7th Cir. 1999). We will affirm the district court's findings so long as they are not clearly erroneous. See United States v. Galbraith, 200 F.3d 1006, 1015 (7th Cir. 2000).

Luis claims that the district court based its denial of the reduction on the fact that he did not plead guilty until the second day of trial, and he submits that the delayed plea was a result of the district court's erroneous refusal to postpone the trial to allow his new attorney to enter his appearance. According to Luis, if a continuance had been granted at the pre-trial hearing, or even if Ciardelli had been allowed to enter his appearance on the morning of the first day of trial, he would have pleaded guilty before the jury was empaneled and thus been entitled to the reduction.

As we explained in Part II.A.1 above, it was not improper for the district court to proceed to trial. Moreover, even if the district court had allowed Ciardelli to enter his appearance the morning that the trial began, a denial of the reduction would still have been justified. See Sierra, 188 F.3d at 805 (upholding a determination that the defendant did not accept responsibility because he pleaded guilty on the last business day before the trial). Second, although lack of timeliness was certainly one of the district court's reasons for denying the reduction, it is clear that the district court also found that Luis's admissions were not trustworthy. During sentencing, the district judge explained her rationale for denying the acceptance of responsibility reduction as follows:

[E]ven if I had permitted Mr. Ciardelli to disrupt the trial, send the jury back down to the jury room... I would not have viewed that as timely acceptance of responsibility, even under that scenario. So, in terms of timeliness, I think the record itself refutes entitlement to consideration for reduction for acceptance of responsibility. In terms of the contradictory statements Mr. Luis Carrera has made about his own conduct, I find that there is a lack of trustworthiness in his admissions, his limited admissions, and his changing admissions. So I find that the presentence report's omission of a reduction for accepting responsibility is a valid one, and I cannot find by a preponderance of the evidence that Mr. Luis Carrera accepted responsibility.

Tr. of Luis Carrera's Sentencing Hr'g. at 8.

Although Luis acknowledges that the district court did find his admissions to be untrustworthy, he claims that we should remand for resentencing because it is not clear whether the district court would have denied the acceptance of responsibility reduction based solely on its finding that Luis was not completely truthful. We disagree. Even if the district court incorrectly determined that Luis's acceptance of responsibility was untimely, its finding that Luis was not completely honest in his admissions is an appropriate independent justification for denying the reduction. See United States v. Kamoga, 177 F.3d 617, 622 (7th Cir. 1999), cert. denied, 528 U.S. 942, 120 S. Ct. 355, 145 L. Ed. 2d 277 (1999) (holding that a defendant is not entitled to an acceptance of responsibility reduction if he fails to provide a "truthful and complete" admission); see also United States v. Purchess, 107 F.3d 1261, 1269 (7th Cir. 1997) (affirming sentence where district court's "denial of the acceptance of responsibility reduction [was] well grounded in a permissible factor"). Therefore, we uphold the district court's finding that Luis was not entitled to a two-level reduction for acceptance of responsibility.

David contends that the district court erred in admitting into evidence the contents of his wallet at the time of his arrest, thereby allowing the government to unfairly argue on rebuttal that David must be a drug dealer because he had unexplained wealth. At trial, David's attorney objected to the admission of the contents of the wallet, but did not object to the government's statements during rebuttal which referred to those contents. Therefore, our review of the district court's evidentiary rulings is for abuse of discretion, see United States v. Gibson, 170 F.3d 673, 680 (7th Cir. 1999), but our review of the government's comments during rebuttal is for plain error only, see United States v. Anderson, 61 F.3d 1290, 1299 (7th Cir. 1995).

Over David's objection, the contents of his wallet at the time of his arrest--which included $928 in cash as well as receipts for purchases totaling approximately $2500--were admitted into evidence during the government's direct examination of one of the arresting officers, Investigator Woytko. Both Investigator Woytko and David testified briefly as to the amount of cash found in David's wallet at the time of arrest, but neither witness discussed the receipts. Then, during rebuttal, the prosecutor made the following statement:

And again, this money... this $928 that the defendant has in his pocket when he's arrested. Not bad for a guy who is unemployed, who's been unemployed for quite some time. In addition, if you look at those receipts that were found in there, you will find another 25-2600 dollars' worth of receipts in expenditures that the defendant did within the two weeks preceding that drug deal. Not bad for a guy who is unemployed, has no money.

Tr. of Trial of David Carrera at 294. David argues that the admission of the wallet's contents--which led to thestatement about unexplained wealth in rebuttal--was erroneous because the evidence was irrelevant and confusing.

We disagree with David's contention that the contents of his wallet were irrelevant to the jury's determination of his guilt. "Expensive trips, gambling, and other instances of free spending and high living may be pertinent in crimesinvolving a motive of enrichment." United States v. Kwitek, 467 F.2d 1222, 1225 (7th Cir. 1972). Similarly, evidence of unexplained wealth is admissible in drug cases as long as: (1) the evidence presented creates an inference that the defendant was involved in drug trafficking; (2) the unexplained wealth was acquired during the period in which the drug crime allegedly occurred; and (3) the government presents other evidence to support the charge, including evidence that the income was not obtained through legitimate means. See United States v. Penny, 60 F.3d 1257, 1263 (7th Cir. 1995).

David contends that the government failed to show any evidence that the money was not obtained through legitimate means. He claims that, although the government argued in rebuttal that David was unemployed at the time of the drug deal, no evidence was presented to that effect. According to David, the government based its claim that he was unemployed at the time of the drug transaction on a "misunderstanding" of his trial testimony. On direct examination, David was asked whether he was working on the day of his arrest and he replied no. When asked why, he stated, "cause I was off--I was off because the doctor told me to be off because I had a... I was sick, really." Then, on cross, the following exchange took place:

Q: Mr. Carrera, when you were arrested you had a lot of money on you, didn't you?

A: I don't know. Like how much you say is a lot of money?

Q: Like $928.28, you consider that a lot of money?

A: Yeah, it's quite--it's some, yes.

Q: You were not working at the time you were arrested, were you?

A: That's correct.

If David's first answer was the only evidence that he was unemployed at the time of his arrest, he might have a stronger claim. Given the second exchange however, we can not say that the district court abused its discretion in finding that the government had presented at least some evidence that the unexplained wealth was not derived from legitimate means.

We also reject David's claim that it was improper for the government to argue in closing that David had unexplained wealth because $900 in cash and receipts for a few luxury items do not suggest "wealth." How much money is "wealth" is an issue that the jury is well-equipped to evaluate. Moreover, even if the government's claim that David was unemployed at the time of the transaction was incorrect, the government's statements did not "infect the trial with unfairness to such a degree as to make the resulting conviction a denial of due process." United States v. McClinton, 135 F.3d 1178, 1188 (7th Cir. 1998) (internal quotation omitted). So long as "the jury has evidence in its possession and is equipped to ascertain whether the government's characterization is accurate, a statement characterizing that evidence is not improper." United States v. Velez, 46 F.3d 688, 692 (7th Cir. 1995).

David next argues that his conviction must be reversed because the district court committed plain error by instructing the jury that the government was not required to prove that the defendant knew either the exact nature or quantity of the controlled substance involved in the offense. He argues that the Supreme Court's recent decision inApprendi v. New Jersey, 530 U.S. 466, 490, 120 S. Ct. 2348, 147 L. Ed. 2d 435 (2000), requires the government to submit to the jury the question of whether David knew that the substance involved in the offense was cocaine. David did not challenge the jury instructions below, therefore our review is for plain error. See United States v. Jones, 245 F.3d 645, 648 (7th Cir. 2001).

David's argument that Apprendi required the government to prove beyond a reasonable doubt that he knew the quantity and type of controlled substance involved in the conspiracy falls short. A defendant may be convicted of a violation of 21 U.S.C. sec. 846 without knowing the exact type of drug involved. See United States v. Sheppard, 219 F.3d 766, 770 (8th Cir. 2000), cert. denied, 121 S. Ct. 1208, 149 L. Ed. 2d 121 (2001); United States v. Osmani, 20 F.3d 266, 268 & n.5 (7th Cir. 1994). The government need only prove that the defendant was aware that some controlled substance was involved. See United States v. Fragoso, 978 F.2d 896, 902 (5th Cir. 1992). Apprendi does not change this rule. Apprendi requires that "[o]ther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury and proved beyond a reasonable doubt." 530 U.S. at 490. With respect to sec. 846, the defendant's knowledge of the quantity and type of controlled substance is not a fact that may be used to increase the penalty beyond the statutory maximum--only the actual quantity and type of controlled substance may increase the statutory maximum. Here, the jury was required to find beyond a reasonable doubt that David conspired to commit an offense involving a controlled substance. Moreover, although the jury was not required to find the quantity of cocaine involved, David's sentence of 78 months was well within the statutory maximum of 20 years provided by 21 U.S.C. sec. 841(b)(1)(C). See Jones, 245 F.3d at 649. (explaining that, for offenses involving cocaine, sec. 841(b)(1)(C) determines the statutory maximum if no drug amount is charged in the indictment and submitted to the jury). Therefore, there is no Apprendi error. See Talbott v. Indiana, 226 F.3d 866, 869 (7th Cir. 2000) ("[W]hen a drug dealer is sentenced to less than 20 years imprisonment--the limit under 21 U.S.C. sec. 841(b) (1)(C)--... Apprendi is irrelevant.").

David Carrera next challenges the specificity of the district court's findings underlying its decision to apply a two-level obstruction of justice enhancement for perjury. Perjury is an appropriate basis for an obstruction enhancement under U.S.S.G. section 3C1.1; however, "not every instance of false testimony under oath warrants the enhancement." United States v. Gage, 183 F.3d 711, 715 (7th Cir. 1999). Instead, the enhancement is limited to situations in which "a defendant 'gives false testimony concerning a material matter with the willful intent to provide false testimony, rather than as a result of confusion, mistake, or faulty memory.'" United States v. Turner, 203 F.3d 1010, 1020 (7th Cir. 2000) (quoting United States v. Dunnigan, 507 U.S. 87, 94, 113 S. Ct. 1111, 122 L. Ed. 2d 445 (1993)). Standing alone, the fact that a defendant denied his guilt at trial and then was found guilty is not enough to merit a section 3C1.1 enhancement. See United States v. Webster, 125 F.3d 1024, 1037 (7th Cir. 1997). To properly support an enhancement for obstruction of justice, the district court must make independent findings as to all of the elements of perjury: falsity, willfulness, and materiality. See Turner, 203 F.3d at 1020. We review de novo whether the district court made the appropriate findings to support an obstruction of justice enhancement. See Gage, 183 F.3d at 715. The district court's underlying findings of fact are reviewed for clear error. See id.

David claims that his case should be remanded for resentencing because the district court failed to make sufficient findings to support the imposed enhancement for obstruction of justice. At David's sentencing hearing, the district court explained:

Well, I do find by a preponderance of the evidence that the defendant, David Carrera, testified untruthfully at his trials. And I base this on the total record before me during those two trials. Mr. Carrera's own prior post-arrest statements, which were inherently more reliable than his trial testimony where he basically denied the matters he affirmed during his post-arrest statement. So I find that he was untruthful by a preponderance of the evidence.

Tr. of David Carrera's Sentencing Hr'g. at 11. David argues that the district court's findings were insufficient because they did not refer to any specific answer that was false and that neither the above explanation nor the PSR adequately found the elements of perjury necessary to support the enhancement.

We disagree. David's contention that the district court utterly failed to identify the source of the perjured testimony is belied by the record. Although the district court did not identify exact statements that were perjurious, the dis trict court did specifically point to testimony that conflicted with the agents' account of David's post-arrest statements-- his denial of the fact that he knew his brother was a drug dealer and that he was going along to help count the money--as the source of its belief that David testified untruthfully. Nor are we convinced by David's argument that the district court's findings of the elements of perjury were insufficient.

In United States v. Dunnigan, 507 U.S. 87, 113 S. Ct. 1111, 122 L. Ed. 2d 445 (1993), the Supreme Court stated that "it is preferable for a district court to address each element of the alleged perjury in a separate and clear finding," but also noted that a section 3C1.1 enhancement that did not specifically address each element could be upheld on the condition that "the [district] court makes a finding of an obstruction of, or impediment to, justice that encompasses all of the factual predicates for a finding of perjury." Id. at 95. David is correct that the district court in his case did not take the preferred route and indicate its findings with respect to each element of perjury. We believe, however, that the district court's findings did encompass falsity, willfulness, and materiality.

It is clear that the district court found that David's testimony at trial contradicted the arresting officers' account of his earlier post-arrest statements, and that the officers' account was inherently more reliable. In United States v. Turner, we upheld the district court's application of a section 3C1.1 enhancement based on its finding that the defendant's "testimony was so diametrically opposed to that of the other witnesses that one version had to be a lie." 203 F.3d at 1020. Like the defendant in Turner, David's trial testimony was irreconcilable with the testimony of other witnesses. Nor has David ever claimed that the inconsistent testimony was the result of confusion, mistake, or faulty memory. Moreover, there can be no doubt that the district court considered David's knowledge of his brother's drug dealing activities to be material.

Therefore, although it is close, we find that the district court's findings do encompass all of the required elements of perjury. Because we do not believe that the district court "mechanically appl[ied] the enhancement merely because the accused took the stand and was found guilty," see United States v. Brimley, 148 F.3d 819, 824 (7th Cir. 1998) (internal quotation omitted), we uphold the district court's application of a two-level enhancement for obstruction of justice.

Both David and Luis Carrera rely on Apprendi v. New Jersey, 530 U.S. 466, 120 S. Ct. 2348, 147 L. Ed. 2d 434 (2000), to support their argument that they are entitled to resentencing--or at least a one-year reduction in their terms of supervised release--because the district court imposed four years of supervised release on each defendant under the erroneous belief that four years was the proper mandatory minimum term. Neither defendant objected to the length of supervised release imposed at sentencing; therefore, our review is for plain error. See United States v. Robinson, 250 F.3d 527, 529 (7th Cir. 2001).

Both defendants received terms of supervised release within the maximum term authorized by 21 U.S.C. sec. 841(b) (1)(C), which applies to defendants who are found guilty of a drug offense involving any quantity of a Schedule II controlled substance. See United States v. Shorty, 159 F.3d 312, 315 & n.6 (7th Cir. 1999), cert. denied, 526 U.S. 1147, 119 S. Ct. 2024, 143 L. Ed. 2d 1035 (1999) (finding that sec. 841(b) (1)(C) establishes a minimum of three years of supervised release and a maximum of life). Nonetheless, defendants challenge the imposed term of four years of supervised release, arguing that the district court erred in sentencing them under sec. 841(b)(1)(B), which applies to quantities of cocaine exceeding 500 grams. Section 841(b)(1)(B) provides for "a term of supervised release of at least 4 years." According to the Carreras, the district court's finding that the offenses involved over 500 grams of cocaine violated the rule announced by the Supreme Court in Apprendi because it resulted in a mandatory minimum term of supervised release. Even if we were not proceeding under a plain error standard, this claim fails. We have made it quite clear that Apprendi does not "govern[ ] proof of events that determine the minimum lawful sentence." United States v. Hill, 252 F.3d 919, 921 (7th Cir. 2001); see also United States v. Rodgers, 245 F.3d 961, 966-68 (7th Cir. 2001) ("Indeed, since Apprendi was decided, we have specifically rejected the notion that a factual determination which has the effect of triggering a mandatory minimum sentence constitutes an element of the offense that must be submitted to the jury."). We therefore reject the defendants' challenge to the imposed terms of supervised release.

For the foregoing reasons, we AFFIRM the convictions and sentences of Luis and David Carrera.