#### UNITED STATES of America, Plaintiff-Appellee, v. Anthony KNIGHT, Willie J. Newton Jr., and Troy C. Williams, Defendants-Appellants.

Nos. 01-4219, 01-4264 and 01-4339.

United States Court of Appeals, Seventh Circuit.

Argued May 22, 2003.

Decided Aug. 18, 2003.

*700Carol L. Kraft (Argued), Office of the United States Attorney, Milwaukee, WI, for Plaintiff-Appellee.

Thomas G. Wilmouth, Milwaukee, WI, Paul Flynn (Argued), Federal Defender Program, Rockford, IL, for Defendant-Appellant Anthony Knight.

Michael J. Fitzgerald, Glynn, Fitzgerald & Albee, Milwaukee, WI, Paul Flynn (Argued), Federal Defender Program, Rockford, IL, for Defendant-Appellant Willie J. Newton, Jr.

Paul Flynn (Argued), Federal Defender Program, Rockford, IL, for Defendant-Appellant Troy C. Williams.

Before BAUER, KANNE, and ROVNER, Circuit Judges.

KANNE, Circuit Judge.

Defendants Anthony Knight and Troy Williams appeal their convictions for possession with intent to distribute more than five kilograms of cocaine. Knight, Williams, and defendant Willie J. Newton, Jr. appeal their convictions for conspiracy to distribute and to possess with intent to distribute more than five kilograms of cocaine. All three defendants argue that they are entitled to a new trial because the government improperly withheld material exculpatory evidence. They also contend that the district court violated *Apprendi v. New Jersey,*530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), by not requiring the jury to return defendant-specific findings of drug quantity for each offense (as opposed to the offense-specific findings *701that the jury returned on a special verdict form). Williams raises two additional challenges to his convictions and one to his sentence, arguing that the appointment of the prosecuting Special Assistant United States Attorney was improper and rendered his indictment invalid, that the prosecution improperly used its peremptory challenges to strike two jurors for racial reasons, and that *Apprendi*required the evidence of his prior convictions to be pleaded in the indictment and proven to the jury. We find all of the defendants’ challenges unavailing and affirm each of their convictions and sentences.

HISTORY

Between 1993 and 1999, the defendants collaborated in a complex scheme to traffic large quantities of cocaine from Los Ange-les, California, to Milwaukee, Wisconsin. Not surprisingly, their activities required the efforts of a number of associates, principally as couriers and dealers, many of whom would eventually testify against the defendants during their nearly three-week-long trial.

Knight was the organizer and leader of this criminal drug organization and Williams was his second in command. Newton and another codefendant, James Durant (who voluntarily dismissed the appeal of his conviction), were Knight’s middle-management lieutenants. They recruited and managed the organization’s couriers and dealers and performed other functions at Knight’s request.

In 1993, Newton and Durant recruited two female drug couriers, Margaret Hicks Frampton and Doris Outlaw, to begin transporting cocaine from Los Angeles to Milwaukee. The two women packed the drugs in their luggage, used public transportation to travel between the two cities, and then checked into local hotels to complete the delivery. In July 1995, while en route to Los Angeles, Frampton was arrested at a Phoenix, Arizona airport with over $100,000 in cash in her suitcase. She was charged with money laundering in an Arizona state court, which brought an end to her career as a courier. Outlaw, on the other hand, voluntarily quit her employment with Knight and Williams in 1997. Shortly thereafter, she was arrested in Arkansas with a carload of cocaine and marijuana (which she was transporting for someone else). Her arrest led to a federal conviction for drug trafficking.

With Frampton and Outlaw no longer at their disposal and with the risks inherent in the use of public transportation for their criminal purposes apparent, Knight and Williams bought a number of cars, which they registered in the name of their cocon-spirators or under fictitious names, and outfitted them with secret compartments to conceal cocaine.

Durant ran the secret-compartment-car operation. He began driving the cars himself before he recruited William Wirth to assist him and make additional trips for Knight. Wirth was paid between $5000 and $6000 per trip, and made a number of drug runs. Six of these trips were documented by various Milwaukee hotel records, which included information about the cars he drove — information that the investigation later matched to the coconspira-tors or aliases that the organization had employed to purchase and register the ears.

Knight promoted Wirth to run the secret-compartment-car operation after Durant was arrested in California while transporting thirty kilograms of cocaine in one of the cars. Believing that he was compromised by the arrest, Knight no longer trusted Durant and began to issue his orders directly to Wirth. Wirth, however, was arrested in February 1998, while *702attempting to transport six kilograms of cocaine in a van he was driving to Memphis, Tennessee, and began cooperating with federal authorities.

Despite these periodic courier arrests, Knight and Williams were still successful in obtaining large amounts of cocaine from their drug-shipping network. They employed a number of associates to distribute this supply, including Laura Collins, Carl McAfee, and Marcus Adams.

Collins introduced Knight and Williams to her boyfriend, McAfee, in the summer of 1994. McAfee thereafter began to purchase kilograms of cocaine from Knight. McAfee did one or two deals per month with Knight for a period of seven to eight months, purchasing between two and ten kilograms per deal — for a total of approximately thirty kilograms. McAfee was arrested in August 1995, while attempting to purchase four kilograms of cocaine from an undercover police officer in an unrelated transaction.

After McAfee went to prison, he arranged to have Collins introduce Knight and Williams to Adams. Adams would go on to purchase large quantities of cocaine from Knight and Williams. At a price of $20,000 per kilogram, Adams estimated he purchased over sixty-seven kilograms of cocaine over the course of his relationship with the organization.

While McAfee and Adams had purchased- multiple kilogram quantities of cocaine from Knight and Williams, Collins had contented herself with acting as the intermediary between the sellers and buyers (often allowing them to use her home to complete the transaction) and had herself only purchased small, one-ounce quantities of cocaine. But in October 1996, Collins told Williams she desired a larger role in the distribution network and wanted to sell larger quantities. Williams agreed. The decision would prove fateful, however, causing the fall of Knight and Williams’ drug empire.

On October 22, 1996, Knight and Williams came to Collins’s house to discuss her intention to sell a kilogram of cocaine. They returned later that evening, bringing five kilograms with them, which they set on the living room floor. Collins had made arrangements to sell one kilogram to Orlando Williams (no relation to defendant Williams, but rather a friend of McAfee’s) for $22,500. Orlando arrived at the house shortly after Williams and Knight. Collins took a kilogram from the living room, left the house, and got into Orlando’s car with him to close the deal. She returned a few minutes later with a bundle of cash, which she placed on the dining room table near where Knight was sitting. Williams then left the house to go to the liquor store.

Within minutes, someone kicked in the door. Thinking it was the police, both Knight and Collins fled the house through the back door and into an alleyway. They heard gunshots. Knight stopped running, telling Collins that it wasn’t the police after all that had entered the house, but robbers. Collins continued on alone.

Collins’s neighbors heard the gunshots and, drawn to the scene after the shots had ceased, observed a heavyset black man (Knight fits this description) running in and out of the back door of Collins’s house, carrying items into the alley. They also saw a second, thinner black male arrive in a black Ford Bronco (the make and model of the car Knight was known to drive at the time) and walk up to Collins’s front porch.

When police officers arrived, they discovered evidence of a drug-fueled gunfight. They found $2200 in blood-spattered money and six kilograms of cocaine strewn about Collins’s front yard. Blood was smeared on the front porch, a knit hat with *703a bullet hole lay nearby, and a trail of blood led from the house to the still-breathing body of Frank McRae. When the police discovered him, McRae was holding a gun and a $10,600 bundle of blood-stained cash. He died before telling the officers what had happened. Inside Collins’s home, police retrieved spent cartridge casings from two different guns— .45 caliber casings fired from McRae’s gun and .40 caliber casings fired from an unidentified weapon. McRae’s unoccupied truck, doors open and keys still in the ignition, was parked nearby Collins’s home. Further down the street, police found Williams’s photo ID and keys to his car.

Police discovered five kilograms of cocaine and about $200 cash in Collins’s living room. In the alley behind the house they found several cardboard boxes full of cocaine. The first box contained thirteen kilograms; another, ten. An additional ten kilograms of cocaine were found scattered about the alley and against the foundation of an adjacent home. In total, police recovered forty-four kilograms of cocaine in and around Collins’s home that evening. The substantial amount of drugs seized prompted local police to contact federal authorities.

Within a few days, Collins surrendered and agreed to cooperate. She gave several statements describing her drug transaction with Orlando, the break in and gunfight, and her flight from the house. It wasn’t until her third statement, however, that Collins identified Knight and Williams as her suppliers. Collins was charged with a drug trafficking offense. She pleaded guilty and, in accordance with her plea agreement, testified against Orlando (who also was arrested and charged with trafficking). Federal warrants were issued for Knight and Williams.

Knight was arrested in August 1999, by California authorities at a stash house, which Durant had rented for him after the October 22 raid. Knight had attempted to purchase forty kilograms of cocaine from an informant who was working with local police. Police recovered drugs, guns, drug paraphernalia, and nearly a half million dollars in cash from the house. Five vehicles parked on the property had secret compartments. One, a Toyota Previa van purchased by Newton, contained sixty-three kilograms of cocaine. Two others held fifty-six kilograms between them in their compartments. Still another, a Toyota sedan that Wirth had been known to drive, had empty compartments, but eight kilograms of cocaine in a gym bag were found in its trunk. Keys to all five vehicles were found on the key ring in the truck that Knight was known to drive at the time. In total, 144 kilogram bricks of cocaine were recovered from the stash house and the various cars. Williams was arrested a year later.

On April 23, 2001, a federal grand jury returned a second superseding indictment against Knight, Williams, Newton, and Durant. The first count charged Knight and Williams with possession with intent to distribute five or more kilograms of cocaine in violation of 21 U.S.C. § 841(a)(1), arising from the events that transpired on October 22 at Collins’s home. The second count charged all four defendants with violating 21 U.S.C. §§ 841(a)(1) and 846 by conspiring to distribute and to possess with intent to distribute five or more kilograms of cocaine.

The defendants’ trial began on July 23, 2001. The government called forty-four witnesses, including couriers Frampton, Outlaw, and Wirth; dealers McAfee, Adams, and Collins; and coconspirator and mid-level manager Durant. In addition, the government produced the testimony of *704the various state and federal authorities responsible for the numerous arrests and continuing investigation. To corroborate the witnesses’ testimony regarding the events related above, the government presented, among other things, the testimony of hotel managers and employees, who provided hotel records establishing short overlapping local hotel stays for Knight, Williams, Newton, Durant, and the various couriers; photographic evidence of the crime scene at Collins’s home on October 22; and motor vehicle records for the numerous secret-compartment cars used by the organization.

The jury was instructed on the offenses utilizing the Seventh Circuit pattern jury instructions. The jury verdict forms required the jurors to determine each defendant’s guilt on each count; a special verdict question for each count then requested the jury to determine, once guilt was established, whether the offense charged involved five or more kilograms of cocaine. The jury returned guilty verdicts for all three defendants on all counts charged (Knight and Williams for conspiracy and possession, Newton for conspiracy only) and determined that for each offense, the drug involved was cocaine and the amount met or exceeded five kilograms. Knight, Williams, and Newton were thereafter sentenced to the statutory maximum — life in prison.

ANALYSIS

Knight, Williams, and Newton all claim that the government improperly withheld materia] exculpatory evidence and that the government’s untimely disclosure prejudiced their right to a fair trial. They also all claim that *Apprendi*required the jury to return defendant-specific findings of drug quantity and type instead of the offense-specific findings that the jury returned in this case. In addition, Williams raises three independent issues to his conviction and sentence. We address each argument in turn.

A *Discovery Disputes*

Williams filed several pretrial discovery demands, requesting the government to search for a generalized and exhaustive list of material favorable to him. (Neither Knight nor Newton made similar requests.) The district court noted that the general principles outlined by the Supreme Court in *Brady v. Maryland,*373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), *Giglio v. United States,*405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), *United States v. Agurs,*427 U.S. 97, 96 S.Ct. 2392, .49 L.Ed.2d 342 (1976), and *Kyles v. Whitley,*514 U.S. 419, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995), obliged the government to turn over the materials that Williams had requested in his motion. Nonetheless, the district court denied Williams’s generalized request, noting its confidence that the government would voluntarily comply with its discovery obligations under this line of precedent.

To that end and in accordance with its open-file policy, the government provided the defendants approximately 4000 pages of discovery materials and made available for inspection and copying the numerous telephone tapes, logs, and records that had been collected during the course of the investigation. In addition, on July 19, 2001, four days before the start of trial, the prosecutor drafted a letter to the defendants, addressing the benefits promised to government witnesses Frampton, Outlaw, McAfee, and Adams in exchange for their testimony.

On the first day of trial, the government supplemented these discovery materials with an updated criminal history for each of its witnesses. Throughout the trial, as the government continued to receive addi*705tional investigatory materials regarding its arrangements with testifying witnesses, it in turn provided them to the defense. After the first full week of trial, the government disclosed the results of a ballistic analysis performed in August 1998 on shell casings recovered from the shootout at Collins’s home on October 22,1996. Those results indicated that some of the casings had been fired from a firearm that the Milwaukee police later recovered from Danny Patrick Jones, an individual unaffiliated with any of the defendants or witnesses. Aso, the government disclosed after the first week of trial that Milwaukee police had recovered a latent fingerprint from one cocaine package recovered from Collins’s home that did not match either Knight’s or Williams’s prints.

The defendants complained that this rolling disclosure of impeachment and physical evidence prejudiced the preparation of their defense. In repeated oral motions for mistrial and motions to exclude the testimony of witnesses, they argued that given the complexity of the case, the government’s untimely disclosures precluded them from making effective use of any of the material exculpatory evidence being continually disclosed. The district court denied these various motions.

In this appeal of those denials and of the later denial of the defendant’s motion for a new trial, the defendants contest the government’s handling of two categories of discovery materials. First and foremost, they claim that the government suppressed impeachment information regarding four of its key witnesses' — Durant, Wirth, Outlaw, and McAfee. Second, they challenge the late disclosure of the fingerprint and ballistic analyses.

To prove a *Brady*violation, the defendants must show that (1) the evidence at issue is favorable to them because it is either exculpatory or could be used for impeachment; (2) the evidence has been suppressed (i.e., the existence of the evidence was known, or reasonably should have been known, to the government, the evidence was not otherwise available to the defendant through the exercise of reasonable diligence, and the government either willfully or inadvertently withheld the evidence until it was too late for the defense to make use of it); and (3) the suppression of the evidence resulted in prejudice (i.e., there is a reasonable probability that had the evidence been disclosed, the outcome might have been different, such that confidence in the actual outcome is undermined). *United States v. O’Hara,*301 F.3d 563, 569 (7th Cir.2002); *United States v. Wilson,*237 F.3d 827, 832 (7th Cir.2001); *United States v, Morris,*80 F.3d 1151, 1169 (7th Cir.1996). The district court maintains broad discretion to determine *Brady*violations; we will review the exercise of that discretion for abuse only. *Wilson,*237 F.3d at 831-32; *United States v. Hartmann,*958 F.2d 774, 790 (7th Cir.1992).

1. Impeachment Evidence

The defendants claim that the government suppressed impeachment evidence regarding four of the government’s key witnesses — Durant, Wirth, Outlaw, and McAfee. There is no dispute among the parties that evidence probative of the testifying witnesses’ credibility, including the potential for bias, is evidence favorable to the accused. *See Crivens v. Roth,*172 F.3d 991, 998 (7th Cir.1999). Instead the government and defendants contest whether this evidence was ever suppressed and, if it was, whether the defense was prejudiced as a result.

It was no surprise to the defense that many of the material witnesses the government produced to testify had been convicted of or faced pending drug-related *706charges and that the witnesses had offered the government their testimony in exchange for leniency on their own offenses. The defense received the criminal histories and information regarding the existence of these arrangements before trial. While it was far from ideal that additional impeachment evidence came to light and was disclosed to the defense only during the course of a fairly complex drug-conspiracy trial, the defense had an appropriate opportunity to incorporate that information into their cross-examination of each witness. Therefore, because the government in fact provided this material with enough time for the defense to make use of it, it was never suppressed. *Accord O’Hara,*301 F.3d at 569 (finding no suppression where evidence pertinent to the issue of the witness’s credibility was disclosed with “plenty of time ... to make use of the information”).

More importantly, even if the government’s rolling disclosures regarding impeachment evidence were incomplete in some respects or were delivered too late for the defense to make effective use of that particular information, the suppression of this additional evidence did not prejudice the defendants. Given the effective cross-examination conducted on each of these four witnesses, which extensively covered their motivation to trade their testimony against Knight, Williams, and Newton in exchange for the promise of lenient treatment by the government, it is unlikely that any of the additional ■ information about which the defense complains would have made a difference to the jury in their appraisal of the evidence. In as much as this evidence was cumulative on the issue of motivation and bias, its suppression does not raise a reasonable probability that the outcome would have been different, so as to undermine our confidence in the actual outcome. *Accord Pruitt v. McAdory,*337 F.3d 921 at 926 (7th Cir.2003); *Wilson,*237 F.3d at 832-33 (finding no *Brady*violation where informant-witness had already been so thoroughly impeached that any additional impeachment evidence disclosed wouldn’t have made any difference).

For example, the defendants complain that they didn’t receive codefendant Durant’s complete criminal history or notice that he had entered into an additional plea agreement for federal drug charges he was facing in the Western District of Tennessee until the first day of trial on July 23. Durant, however, didn’t begin testifying until August 1 and wasn’t cross-examined until August 2. And on cross-examination, Durant was questioned thoroughly about the plea agreements he had entered into with the government both on the charges he faced in the instant case and in Tennessee. In addition, he was questioned extensively about the fact that in exchange for his testimony and for pleading guilty to lesser-included offenses, he expected the sentences he faced on these charges to be reduced from a maximum of life in prison to a maximum of ten years. (Tr. at 1591-93,1606,1620-21.)

Similarly, the defendants complain that the government withheld, until the day Outlaw testified, a copy of her 1999 Arkansas plea agreement, which showed that the federal prosecutor in Arkansas agreed to recommend a 10% downward departure in return for her substantial assistance. They also complain that the criminal history the government provided for Outlaw was incomplete and inaccurate. Nonetheless, the district court reviewed the plea agreement and questioned Outlaw about it, concluding that its terms were sufficiently clear to permit the defendants to cross-examine her about it and her motivation for testifying in the instant case. (Tr. at 569-73.) On the resulting cross-examina*707tion, Outlaw was interrogated thoroughly regarding her criminal history (she conceded that she had prior convictions for prostitution, bookmaking, and drug possession) 1; her ability to recall the events at issue; inconsistent statements she had made to law enforcement officers; and the terms of her plea agreement, the fact that her sentence for her Arkansas trafficking conviction was reduced from ten to six years in accordance with that agreement, and her hopes for a further sentence reduction in exchange for her testimony against the defendants. (Tr. at 579-612, 614-17, 620-25.)

The defendants address their complaints about the disclosures made regarding witnesses Wirth and McAfee in similar fashion. For each, the defendants assert that the government withheld impeachment information — in Wirth’s case, grand-jury transcripts and information regarding his bond status; in McAfee’s, tapes and phone records of his prison calls to Collins and others — that would have enabled them to present a more effective defense. The defendants fail to demonstrate with particularity, however, that there was anything helpful about this information. And even assuming that it was favorable, they once again have not shown that it was withheld until they were unable to make effective use of it or that they were prejudiced as a result. Wirth’s grand-jury testimony was made available to the defense on the first day of trial, July 23, and he didn’t testify until August 2; the McAfee tapes were part of the evidence that the government had invited the defendants to inspect and copy before trial and therefore were previously available to the defense through a reasonable exercise of diligence, *see Morris,*80 F.3d at 1170. And both witnesses were thoroughly cross-examined regarding their relevant criminal histories, plea arrangements, and, in Wirth’s case, bond status and prior testimony, and, in McAf-ee’s, telephone conversations. (Tr. at 668-72, 677-89, 695-704, 1715-23, 173444, 1746-48.)

In sum, the defendants have failed to show that favorable impeachment evidence was suppressed and that its suppression prejudiced their defense.

2. Physical Evidence

Knight and Williams defended the possession charge on the grounds that they were not present at Collins’s home the night of October 22 when it was robbed. Given this, both sides agree that the results of the fingerprint and ballistic analy-ses, which point to the possibility of another actor’s involvement, were evidence favorable to their defense. The parties instead split over whether the evidence was withheld beyond a time when the defendants could make effective use of it or whether, if actually suppressed, the evidence was so favorable to the defense that there exists a reasonable probability that if disclosed, the outcome of the trial would have been different so as to undermine confidence in the actual verdict.

The results of the ballistic evidence, which showed that some of the casings recovered from the shootout at Collins’s home had been fired from a gun that Milwaukee police took from Danny Patrick Jones during an unrelated drug arrest one-and-a-half years after the incident, was only disclosed to the defense during the trial, nine days before the start of the defense’s case. The government in response claims it did not receive this Au*708gust 1998 report from the Milwaukee police department until after the trial had started and that it disclosed it at the earliest opportunity on the next trial day. Assuming *arguendo*that the government reasonably should have known about this evidence earlier and should have made efforts to retrieve it from the Milwaukee police department, *see United States v. Bhutani,*175 F.3d 572, 577 (7th Cir.1999) (observing that even if the prosecution has only consulted with a government agency on a case, the agency is considered part of the prosecution and information within the agency’s knowledge and control will be imputed to the prosecution), we nonetheless conclude that the defense had sufficient opportunity to make use of the evidence once it was disclosed.

The defendants do not effectively counter this point. They do not assert that they would have attempted to locate Jones had they had more time to review the report. And the record reveals that the defense made as effective use of this evidence as was likely possible under even the best of circumstances. The ballistics expert told the jury that Jones had been arrested for a drug-related offense, had been found in possession of a weapon that matched some- of the casings recovered from Collins’s home, and suggested, somewhat tenuously, that Jones may have been a participant in the drug and robbery activity that evening. In the defendants’ closing argument, counsel used this testimony to argue that the government had unreasonably focused its investigative efforts on the defendants, while ignoring the culpability of others such as Jones — who, in the words of defense counsel, was “the man whose gun was used to shoot Frank McRae.” (Tr. at 2206.) As this reference makes clear, the argument that it was Jones who was involved with the aborted drug deal at Collins’s house and not the defendants was emphasized in the defense’s case before the jury.

Likewise, the defense made effective use of the finger-print-analysis results despite the government’s late disclosure. Those results indicated that one of the packages of cocaine had been handled by someone whose fingerprints did not match those of Knight or Williams. This May 2001 Milwaukee police report was disclosed to the defense upon its receipt by federal prosecutors on July 31, 2001, eight days into the trial, eight days before the government rested its case, and nine days before the start of the defense. The defendants did not seek to call the fingerprint examiner as a witness to discuss the substance of his analysis that excluded Knight, Williams, McRae, Collins, and Orlando as the source of the print. Nor have they argued that they tried, but were unable to do so, because nine days was not enough time. In any event, even without calling the analyst as a witness, the defense in closing repeatedly called the jury’s attention to the fact that *none*of the packages retrieved from Collins’s home bore Knight’s *or*Williams’s fingerprints.

It was not surprising, however, that the jury did not accept as persuasive the defense’s theory of the case, supported by its use of the ballistic analysis and the absence of Knight’s and Williams’s fingerprints. There was substantial evidence showing that Knight and Williams delivered the cocaine to Collins’s home that evening, including, among other things, Collins’s testimony, her neighbor’s observation of a man meeting Knight’s description carrying objects out into the alley after the gunfire stopped, the recovery of forty-four kilograms of cocaine, much of it from that alley, the neighbor’s sighting of a car at the scene matching the description of Knight’s vehicle, the location of Williams’s identification and car keys, and *709Adams’s testimony that Knight had told him that Knight’s drugs had been the target of the robbery attempt at Collins’s home. The jury weighed this evidence and concluded that the testimony and circumstantial evidence impheating Knight and Williams was credible and proved, beyond a reasonable doubt, that they were in possession of the cocaine recovered from Collins’s home that night. The defendants have not shown how any additional use of the ballistics or fingerprint evidence beyond what they were able to place before the jury would have undermined confidence in that conclusion. They, therefore, have not established that this evidence was suppressed in that they could not make use of it, nor have they shown that, if suppressed, they were prejudiced by it.

Our opinion should not be read as a ringing endorsement of the government’s actions. We believe that the delay in delivering this material could have been avoided or, at the least, diminished. And we emphasize that we are aware of the probability that eve-of-trial disclosures or, as here, in-trial disclosures may prevent the defense from “diverting] appropriate resources from other initiatives and obligations that are or may seem more pressing” in order to “assimilate [this new] information into its case.” *Leka v. Portuondo,*257 F.3d 89, 101 (2d Cir.2001) (citation omitted). That possibility was raised by the late disclosures here. Nonetheless, the defendants have not established that the possibility for prejudice ripened into actual harm on account of their inability to make effective use of information that reasonably may have affected the trial’s outcome. That their counsel was able to incorporate these continuing disclosures into the defense of a complex drug-conspiracy case is certainly a testament to their mettle as trial counsel. Regardless, we must deny the defendants’ *Brady*claim because they have not made the requisite showings of suppression or prejudice.

*B. Drug Quantity*

Knight, Williams, and Newton next argue that the district court erroneously instructed the jury on the two counts of conviction. Reviewing the district court’s instruction, we “must determine from looking at the charges as a whole, whether the jury was misled in any way and whether it had understanding of the issues and its duty to determine those issues.” *United States v. Fawley,*137 F.3d 458, 467 (7th Cir.1998) (quotation omitted). “So long as the instructions treat the issues fairly and accurately, they will not be disturbed on appeal.” *United States v. Doerr,*886 F.2d 944, 960 (7th Cir.1989) (quotations omitted).

Here, the court gave the Seventh Circuit Pattern Instruction pertaining to 21 U.S.C. §§ 841(a)(1) and 846, together with a special verdict question for each count. (Tr. at 2287-95.) The special verdict question, to be answered only if the jury found at least one defendant guilty of the charge, asked the jury to determine if the offense involved five kilograms or more of cocaine. The special verdict question was prompted by the Supreme Court’s ruling in *Apprendi v. New Jersey,*530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000) and tracked the relevant language of 21 U.S.C. § 841(b)(1).

The defendants argue, as they did below, that the instructions were erroneous. They contend that *Apprendi*requires a defendant-specific finding regarding drug quantity and type rather than the offense-specific finding used by the district court. Accordingly, they argue that this Circuit’s pattern instruction is facially deficient and that the defect was not cured by the court’s special verdict question. They ar*710gue that the alternate jury instructions they proposed more closely approximated the *post-Apprendi*legal landscape and would have better informed the jury.

In *Apprendi,*the Supreme Court held 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, 120 S.Ct. 2348. Before *Apprendi,*courts treated the penalty provision of § 841(b), with its escalating drug-quantity triggers, as sentencing factors— to be determined by judges by a preponderance of the evidence at sentencing.

After *Apprendi,*drug type and quantity remain sentencing issues, but the burden of proof and fact finder have changed. *See Horton v. United States,*244 F.3d 546, 552 (7th Cir.2001). *Apprendi*means that the defendants may be subject to a statutorily enhanced sentence based on drug type and quantity, as provided in § 841(b), only if those facts are charged in the indictment and proven to a jury beyond a reasonable doubt. *United States v. Nance,*236 F.3d 820, 824-25 (7th Cir.2000).

The requisite content of a jury instruction in a multi-defendant case alleging drug conspiracy and possession post*Apprendi*is an issue of first impression in this circuit. It has, however, been addressed by other circuits. In *Derman v. United States,*298 F.3d 34, 42 (1st Cir.2002), the First Circuit found that *Apprendi*did not require defendant-specific findings of drug type and quantity to a conspiracy charge. The court relied upon *Edwards v. United States,*523 U.S. 511, 118 S.Ct. 1475, 140 L.Ed.2d 703 (1998), in which the Supreme Court held that “as long as (1) the jury finds beyond a reasonable doubt that a defendant participated in a conspiracy, and (2) the Court sentences him within the statutory maximum applicable to that conspiracy, the court may ‘determine both the amount and the kind of “controlled substances” for which [the] defendant should be held accountable — • and then ... impose a sentence that varies depending upon amount and kind.’ ” *Derman,*298 F.3d at 42 (quoting *Edwards,*523 U.S. at 513-14, 118 S.Ct. 1475).

We agree with the First Circuit that *Apprendi*did not overrule *Edwards*and that its holding does not require defendant-specific findings of drug type and quantity in drug-conspiracy cases. As that court observed,

> the two decisions are easily harmonized: in a drug conspiracy case, the jury should determine the existence *vel non*of the conspiracy as well as any acts about the conspiracy that will increase the possible penalty for the crime of conviction beyond the default statutory maximum; and the judge should determine, at sentencing, the particulars regarding the involvement of each participant in the conspiracy.

> This means that once the jury has determined that the conspiracy involved a type and quantity of drugs sufficient to justify a sentence above the default statutory maximum and has found a particular defendant guilty of participation in the conspiracy, the judge may lawfully determine the drug quantity attributable to that defendant and sentence him accordingly .... The rule, then, is that the government need only allege and prove to the jury the bare facts necessary to increase the statutory sentencing maximum for the conspiracy as a whole.

*Id.*at 42-43 (citations and footnote omitted); *see also United States v. Turner,*319 F.3d 716, 722-23 (5th Cir.2003) (following *Derman).*

*711German’s analysis remains sound despite the Supreme Court’s more recent decision in *Ring v. Arizona,*536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), which found that Arizona’s capital-punishment-sentencing scheme violated the defendant’s Sixth Amendment jury-trial right. *Id*at 602-09. Arizona’s scheme vested a single trial judge with the authority to increase a defendant’s sentence from life in prison to the death penalty by finding the presence of aggravating factors. Without the determination of those aggravating factors, the maximum sentence that could be imposed under a jury’s guilty verdict on a first-degree murder charge was life in prison. Consistent with *Ap-prendi,*the Supreme Court ruled that capital defendants, no less so than noncapital defendants, are entitled under the Sixth Amendment to a jury determination of any fact upon which the legislature increases their statutory maximum punishment. Since a defendant could face the death penalty only upon proof of the aggravating factors, they must be submitted to a jury and proved beyond a reasonable doubt. *Id.*at 609, 122 S.Ct. 2428.

*Ring,*however, is under *Derman’s*analysis as reconcilable with *Edwards*as is *Apprendi.*Once the jury determines the existence of the conspiracy, the defendants’ participation in it, and assigns a type and quantity attributable to the conspiracy as a whole, it has established the statutory maximum sentence that any one participant in that conspiracy may receive. *Derman,*298 F.3d at 42. Once that maximum sentence has been established (ceiling), the judge may determine the drug quantity attributable to each defendant (floor) and sentence him accordingly. *Id.*at 42-43. The sentencing judge’s findings do not, because they cannot, have the effect of increasing an individual defendant’s exposure beyond the statutory maximum justified by the jury’s guilty verdict. This arrangement, therefore, does not compare with Arizona’s capital-sentencing scheme, which allowed a judge’s subsequent finding of aggravating factors to raise the ceiling of maximum punishment authorized by the jury’s verdict. *See Ring,*536 U.S. at 603, 122 S.Ct. 2428.

Furthermore, a review of our own case law, though not directly own point, leads us to the same conclusion that the First Circuit reached in *Derman.*In *United States v. Trennell,*for example, we implicitly approved a jury instruction and special verdict form substantially similar to the one at issue here. 290 F.3d 881, 889 (7th Cir.2002). In *Trennell,*we addressed an *Apprendi*challenge where drug quantity was not pleaded in the indictment but was submitted to the jury with instructions and special verdict questions that asked the jury to find the total amount of the drugs distributed in the conspiracy. *Id.*at 888-89. Rejecting the defendant’s claim that the jury instructions created a variance from the indictment and that the failure to allege the drug quantity in the indictment created constitutional error, we found that the special verdict form properly instructed the jury to return a drug-quantity finding attributable to the conspiracy. *Id.*at 889.

And in *United States v. Patterson,*when reviewing under the plain-error standard the post *-Apprendi*sentence of a defendant whose drug quantity had not been submitted to the jury, we observed that for purposes of determining whether the error was harmless “[f]ocus on [the amount possessed by] the conspiracy is the right perspective.” 241 F.3d 912, 914 (7th Cir.2001) (per curiam). This was so “because each of the defendants ... was convicted of conspiring with the others to distribute drugs, and as a member of the conspiracy each is accountable for the acts of all other *712conspirators within the scope of that agreement.” *Id.*at 914.

In sum, then, we find that the district court’s instructions were legally proper and adequately advised the jury about the applicable law. Under those instructions and making use of the special verdict form, the jury determined whether each defendant was guilty of participating in the conspiracy and then determined that the conspiracy involved a type and quantity of drugs sufficient to trigger the statutory maximum of life in prison. Once the defendant’s participation in the drug conspiracy was proven, the judge at sentencing appropriately determined the drug quantity attributable to that particular defendant and sentenced him accordingly. *Derman,*298 F.3d at 42-43.

The defense was therefore not entitled to its proposed instructions, which were not then, nor are they now, accurate statements of the law. *See Fawley,*137 F.3d at 468-69. The defense’s proposed instructions were based on a broad interpretation of the Ninth Circuit’s holding in *United States v. Nordby,*225 F.3d 1053 (9th Cir.2000), a case for which we reserve comment save to note, as did the First Circuit in *Derman,*that *Nordby*was limited by the Ninth Circuit’s subsequent decision in *United States v. Buckland*and modified further by its decision in *United States v. Patterson*to be consistent with the reasoning we adopt today. *Derman,*298 F.3d at 43 (citing *Buckland,*289 F.3d 558, 567-68 (9th Cir.2002) (en banc), and *Patterson,*292 F.3d 615, 623 (9th Cir.2002)).

Finally, the record in this case contains overwhelming evidence demonstrating that each of these three defendants is personally responsible for, and could easily foresee that the conspiracy involved, five or more kilograms of cocaine. *Accord Patterson,*241 F.3d at 914. At Collins’s house alone, police recovered forty-four kilograms of cocaine. Couriers Frampton, Outlaw, and others supervised by Newton made numerous trips back and forth from California to Milwaukee bringing with them multiple kilograms of cocaine. Wirth made dozens of trips in secret-compartment cars that could hold dozens of kilograms of cocaine. Williams picked up each load. McAfee and Adams bought cocaine from Knight and Williams on multiple occasions in quantities up to twenty kilograms. And 144 kilograms of cocaine were recovered from Knight’s California stash house, some of it already loaded into cars in preparation of the next drug run. Moreover, the evidence establishes that these defendants were the core members of this conspiracy and not fringe members; the full weight of drugs involved were thus foreseeable and attributable to each. Therefore, even if there was error in not attributing a defendant-specific finding on the charges in this case, any error would have been harmless given the evidence. *Neder v. United States,*527 U.S. 1, 10-11, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (holding that erroneous jury instruction that omitted an element of the offense is subject to harmless-error analysis); *Nance,*236 F.3d at 825 (observing that to satisfy harmless-error analysis the court must ask whether it is “clear beyond a reasonable doubt that a rational jury would have found the defendant guilty absent the error.” (quotation omitted)).

*C. Williams’s Individual Challenges*

The remaining three challenges raised solely by Williams are meritless, and we may dispose of them with minimal discussion. First, Williams argues that the district court should have dismissed his indictment. He argues that because the State of Wisconsin continued to pay the salary of the Assistant District Attorney Karine O’Byrne during her service as a *713Special Assistant U.S. Attorney (SAUSA), her appointment violated 28 U.S.C. § 548, which provides that the Attorney General of the United States shall fix the annual salaries of SAUSAs. He further argues that since her appointment was not valid, SAUSA O’Byrne was not an “attorney! ] for the government,” and her appearance before his indicting grand jury violated Federal Rule of Criminal Procedure 6(d). Notwithstanding the potential for error in this arrangement, any such error is harmless. The purpose of Rule 6(d) is “to protect the innocent from being indicted.” *United States v. Fountain,*840 F.2d 509, 515 (7th Cir.1988). Because Williams was found guilty at trial, he is “not a member of the class of beneficiaries of the rule” and is not entitled to invoke it to reverse his conviction. *Id. Accord United States v. Mechanik,*475 U.S. 66, 67, 71-72, 106 S.Ct. 938, 89 L.Ed.2d 50 (1986) (explaining that “the petit jury’s verdict of guilty beyond a reasonable doubt demonstrates *a fortiori*that there was probable cause to charge the defendants with the offenses for which they were convicted”); *United States v. Rosario,*234 F.3d 347, 352 (7th Cir.2000) (conviction at trial “indicates a proper grand jury proceeding would have still yielded an indictment”).

Second, Williams argues that his conviction must be reversed because the government violated *Batson v. Kentucky,*476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), by striking two jurors for racial reasons. Under *Batson,*after the defendant makes a *prima facie*showing that a prosecutor exercised a peremptory strike based on race, the burden shifts to the prosecutor to provide a race-neutral explanation for the strike. *Mahaffey v. Page,*162 F.3d 481, 482-83 (7th Cir.1998). If an explanation is provided, the ultimate burden rests upon the defendant to prove that the explanation was offered as mere pretext for racial discrimination. *Id.*at 483.

The district court found that the government’s proffer of reasons for striking these two jurors — the first juror for the observation that her difficulty in understanding the prosecutor’s voir dire questions made it likely that she would have difficulty understanding the wealth of information to be presented during the three-week trial; the second juror for his at best inattentiveness during voir dire and at worst excessive fatigue from working two jobs — was legitimate and not pre-textual. We review the district court’s findings for clear error, *United States v. James,*113 F.3d 721, 728 (7th Cir.1997), keeping in mind the fact that the district court is in the best position to determine whether a reason given for a strike is mere pretext and reversing only if “the reason given is completely outlandish or there is other evidence which demonstrates its falsity.” *Tinner v. United Ins. Co.,*308 F.3d 697, 703 (7th Cir.2002) (quotation omitted).

Williams cannot satisfy either test. It is not completely outrageous that the government would be interested in striking jurors who it felt either could not grasp the complexities of its trial evidence or were too tired to pay attention. And Williams has presented no independent evidence demonstrating that these reasons were false: for example, he identifies no non-African-American jurors who were similarly situated (i.e., noncomprehending or inattentive and sleeping) but who were allowed to remain. *See Coulter v. Gilmore,*155 F.3d 912, 921 (7th Cir.1998) (treatment of similarly situated jurors relevant to determine discriminatory intent). His *Batson*challenge thus fails.

Finally, Williams contends that his sentence offends *Apprendi*because evidence of his prior convictions, which *714Williams argues increased his sentence beyond the statutory maximum, were not proven to the jury- But *Apprendi*expressly reserved prior convictions from the scope of its holding. 530 U.S. at 490, 120 S.Ct. 2348. And as discussed above, based on the jury’s finding of drug type and quantity, the statutory maximum that Williams faced on both charges was life in prison. The sentence he received did not exceed the statutory maximum; it was the statutory maximum. Thus, *Apprendi*does not apply. The prior drug convictions may have increased his statutory *minimum*sentence for these offenses, but this is not prohibited by *Apprendi.*We have recognized that the Supreme Court in *Apprendi*expressly declined to overrule *McMillan v. Pennsylvania,*477 U.S. 79, 106 S.Ct. 2411, 91 L.Ed.2d 67 (1986), which upheld a statutory minimum prison term that was based solely on the sentencing judge’s preponderance-of-the-evidence findings. *United States v. Rodgers,*245 F.3d 961, 966 (7th Cir.2001); *see also Harris v. United States,*536 U.S. 545, 564-65, 122 S.Ct. 2406, 153 L.Ed.2d 524 (2002); *Nance,*236 F.3d at 825. In any event, the life sentence that Williams received was not dependant upon his prior conviction information, but rather the applicable guideline range, properly determined by the sentencing court to fall at the statutory maximum.

CONCLUSION

For the foregoing reasons, we Affirm the convictions of Knight, Williams, and Newton and we Affirm Williams’s sentence.

1

. We merely note that the defense was successful in putting this prior-conviction information before the jury. We express no opinion on whether its admission was proper under federal evidentiary rules.