The defendant, Mohammad Abu-Taqa, was convicted of conspiracy to defraud the United States, in violation of 18 U.S.C. § 371, as well as the predicate acts of fraud amounting to identity theft, in violation of 18 U.S.C. § 1028, interstate transportation of stolen property, in violation of 18 U.S.C. § 2314, and passing a forged check, in violation of 18 U.S.C. § 514(a)(2). He was sentenced to serve 33 months in prison and make restitution in the amount of approximately $103,000. He now appeals his conviction, contending (1) that the indictment was flawed because the conspiracy count was duplicitous and the remaining counts failed to state an offense; (2) that the government withheld information concerning its agreement with his co-defendant, Mohamad Hassan, as well as details about Hassan’s prior criminal record; and (3) that he was denied the right to trial by an impartial jury. We find no merit to these issues and affirm.
FACTUAL AND PROCEDURAL BACKGROUND
At Abu-Taqa’s trial, the government established that he and Mohamad Hassan were involved in a fraudulent scheme that Abu-Taqa initiated by creating counterfeit money orders and checks on his personal computer. The two defendants used the fake money orders to buy airline tickets from various travel agencies and then exchanged them for tickets on other flights in order to avoid detection. Hassan often conducted these transactions alone because his English was better than Abu-Taqa’s and because he had more experience with the travel industry. Abu-Taqa and Hassan also used the counterfeit money orders to purchase valid traveler’s checks and cashed these checks at several different banks, using false identification.
Abu-Taqa and his co-defendant were arrested at the Owensboro (Kentucky) Airport in January 2001 and were originally scheduled to be tried on October 22, 2001, less than six weeks after the tragic events of September 11, 2001. Citing possible anti-Arab bias, Abu-Taqa, a Muslim originally from Jordan who is now a naturalized United States citizen, moved to continue the trial. The court granted this motion and rescheduled the trial for March 11, 2002. In the interim, Abu-Taqa submitted a proposed jury questionnaire designed to expose bias against Arabs and Muslims. With only minor changes, the district court allowed the questionnaire to be mailed to potential jurors.
On March 1, 2002, Hassan pleaded guilty after extensive plea negotiations with the government. As part of the plea agreement, the government agreed to drop an illegal immigration charge against Hassan, and Hassan agreed to testify as a government witness at Abu-Taqa’s trial. That trial began on March 12, lasted for a week, and resulted in the defendant’s conviction on four counts of the indictment— the conspiracy charge and the three individual predicate acts.
DISCUSSION
1. The Indictment
The defendant’s challenge to the first count of the indictment as duplicitous — because it charges that the defendant knowingly conspired to commit three separate violations of three different stat*465utes — is reviewed de novo, as a question of law. United States v. Campbell, 279 F.3d 392, 398 (6th Cir.2002). That review does not require detailed analysis, however, because “[i]t has been clear since Braverman v. United States, 317 U.S. 49, 54, 63 S.Ct. 99, 87 L.Ed. 23 ... that the allegation, in a single count of conspiracy, of an agreement to commit several crimes is not duplicitous, as conspiracy is itself the crime.” United States v. Dale, 178 F.3d 429, 431 (6th Cir.1999).
The rule against duplicity is designed to ensure that the jury’s verdict as to any specific charge is actually unanimous. In this case, Abu-Taqa could have — but did not — request a specific unanimity instruction, nor did he object to the general unanimity charge. Concerning the first count of the indictment, the district court instructed the jury that:
The indictment accuses the defendant of conspiring to commit several federal crimes. The government does not have to prove that the defendants agreed to commit all these crimes. But the government must prove an agreement to commit at least one of them for you to return a guilty verdict on the conspiracy charge.
This charge, taken from the Sixth Circuit District Judges Association Pattern Criminal Jury Instructions 3.02 (Sixth Circuit 1991), was sufficient to apprise the jury of its function with regard to the conspiracy charge in the first count of the indictment. In addition, the predicate acts contained in the conspiracy count were charged in individual counts of the indictment, and the defendant was found guilty on those counts also. There simply is no possibility under these circumstances that the jury was in any way confused or that its verdict was less than unanimous.
The defendant next contends that the three individual counts fail to charge cognizable federal offenses because they allege only that Abu-Taqa and Hassan aided and abetted one another in the violation of 18 U.S.C. §§ 1028, 2314, and 514(a)(2), respectively, but do not charge either defendant as a principal. Because this question was not raised as a challenge to the indictment prior to trial, it is reviewed at this juncture under the standard set out in United States v. Gatewood, 173 F.3d 983, 986 (6th Cir.1999):
Under Rule 12(b)(2) of the Federal Rules of Criminal Procedure ..., a defendant who contends that the indictment fails to establish jurisdiction or to charge an offense may raise that challenge at any time. See United States v. Hart, 640 F.2d 856, 857 (6th Cir.1981). But when an indictment is not challenged until appeal, as in this case, the indictment must be construed liberally in favor of its sufficiency. See United States v. Gibson, 513 F.2d 978, 979 (6th Cir.1975). “Furthermore, unless the defendant can show prejudice, a conviction will not be reversed where the indictment is challenged only after conviction unless the indictment cannot within reason be construed to charge a crime.” Hart, 640 F.2d at 857-58.
It is, of course, well-settled that an aider and abettor may be punished as a principal, given that the common law distinction between principals and accessories has been abolished. See United States v. Superior Growers Supply, Inc., 982 F.2d 173, 177-78 (6th Cir.1992); United States v. Maselli, 534 F.2d 1197, 1200 (6th Cir.1976) (explaining that “one who causes another to commit an unlawful act is as guilty of the substantive offense as the one who actually commits the act”). Of course, before a conviction for aiding and abetting can be upheld, a jury must find that all essential elements of the underlying crime were committed by someone. See United *466States v. Horton, 847 F.2d 813, 322 (6th Cir.1988). However, it is not necessary that the indictment name the principals who committed the offense because their names are not essential elements of the offense. See United States v. Harris, 523 F.2d 172, 174 (6th Cir.1975).
It follows that the indictment need not identify with particularity who among a number of defendants acted as a principal and who acted as accessories. In a case similar to Abu-Taqa’s, for example, we noted:
The government pleaded the count in terms of accessorial principles, perhaps because it was difficult to tell — as between [the two defendants] — who was the principal and who the accessory. It is axiomatic, however, that the government may always prove the defendant is guilty as a principal, even where the indictment charges only that he acted as an accessory.
United States v. Mullins, 22 F.3d 1365, 1368 (6th Cir.1994). Here, the jury was instructed to find the defendant guilty as an aider and abettor only if all the elements of each crime had been proven beyond a reasonable doubt and the evidence established that the defendant did something to assist, with the intent that the offense be committed. Under all the circumstances, we cannot conclude that the indictment in this case was deficient in any manner.
2. Hassan’s Plea Agreement and Prior Record
The defendant alleges that the government violated the rule in Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), when it failed to reveal a “secret agreement” with co-defendant Hassan to file a § 5K1.1 motion permitting a downward departure in his sentence based on assistance provided to the prosecution and did not disclose to defense counsel the full extent of Hassan’s criminal history. Armed with this information, the argument goes, Abu-Taqa would have been better able to impeach Hassan’s testimony as a government witness at the trial. We conclude that the record fails to establish that Hassan had a secret agreement or that Abu-Taqa had less than full information about his co-defendant’s background.
What the record does reveal is that during plea negotiations with Hassan, the government initially proposed a plea agreement in which it retained the discretion to make a § 5K1.1 motion. However, the government withdrew the proposal when Hassan failed a polygraph examination, raising doubts about his ability to testify truthfully and, therefore, his usefulness as a government witness. When a new agreement was finally reached, it included a provision that the government would “not make a motion pursuant to § 5K1.1 of the Sentencing Guidelines for a downward departure based on any assistance or cooperation provided by the Defendant.” Nevertheless, at Hassan’s sentencing hearing following his testimony at Abu-Taqa’s trial, the government did in fact make a § 5K1.1 motion for a two-level downward departure in Hassan’s offense level, based on the prosecution’s conclusion that Hassan had testified truthfully at Abu-Taqa’s trial and merited a sentence of proportionally less time than Abu-Taqa.
The government’s decision to make or withhold a § 5K1.1 recommendation is largely discretionary. Because there was no legal impediment to the government’s decision to change its position with regard to such a motion in Hassan’s case, a “secret agreement,” even if one had existed, would have had virtually no impeachment value. The most that would have been revealed was that the government was amenable to a § 5K1.1 departure if it *467turned out that Hassan testified truthfully, in the government’s estimation, at Abu-Taqa’s trial.
The matter of Hassan’s prior criminal history requires even less by way of comment. The record before us on appeal fails to disclose what information defense counsel did or did not have, but it is clear from the defendant’s motion to sever his trial from Hassan’s that defense counsel knew that the co-defendant had a criminal record.
3. Jury Selection
The defendant’s Sixth Amendment challenge to the impartiality of the jury that heard his case was directed at two specific members of the panel, Jurors 17 and 109. The complaint regarding Juror 17 is easily resolved. Although counsel for both parties appear to be oblivious to this fact on appeal, the court has been able to determine, through a great deal of effort, that prospective Juror 17 was not seated on the jury in this case. He was, in fact, struck by the government peremptorily, as the district court’s jury panel and jury attendance records show.
Juror 109 did sit on Abu-Taqa’s panel. He had indicated on the jury questionnaire that was sent out in advance of trial that he did not know whether he could render impartial judgment in a case involving an Arab or a Muslim. At voir dire, however, when asked about his response, he answered that after seeing the defendant and hearing the indictment read, he had concluded that he could put aside his reaction to the events of September 11th and base his verdict on the evidence. He was nevertheless challenged for cause by the defense and, at this point, was further questioned by the district judge about his ability to be fair. Juror 109 responded, ‘Tes, sir, I would have to be [fair]. Someone’s freedom is at stake here and so I would have to put [my feelings about September 11] aside.” Having satisfied himself that Juror 109 could render an impartial verdict, the district judge denied the defendant’s motion to strike him for cause.
A district court traditionally has broad discretion in the conduct of voir dire, which we review to ensure that jury selection in any given case comports with the “essential demands of fairness,” as required by the Sixth Amendment. Dennis v. Mitchell, 354 F.3d 511, 524 (6th Cir.2003) (quoting Morgan v. Illinois, 504 U.S. 719, 730, 112 S.Ct. 2222, 119 L.Ed.2d 492 (1992)). When, as in this case, the district court has denied a defendant’s motion to strike a prospective juror for cause and the defendant has exercised all of his peremptory challenges, the defendant may obtain a new trial only if an impaneled juror’s honest responses to questions during voir dire would have given rise to a valid challenge for cause. See McDonough Power Equip., Inc. v. Greenwood, 464 U.S. 548, 556, 104 S.Ct. 845, 78 L.Ed.2d 663 (1984). We find no abuse of discretion in the district judge’s determination, following his examination of Juror 109, that there was no valid basis to excuse him for cause. In the absence of a peremptory challenge, this juror was properly seated on the defendant’s jury panel.
CONCLUSION
For the reasons set out above, we AFFIRM the judgment of the district court.