McLAUGHLIN, Circuit Judge:

This appeal primarily concerns the scope of cross-examination of a character witness and the submission of a written charge to the jury. Henry Fulton appeals from a judgment of conviction in the United States District Court for the Southern District of New York (Sotomayor, ■/.) of conspiracy to bribe Board of Education officials for work on a project receiving federal financial assistance in violation of 18 U.S.C. § 371, bribing Board of Education officials for work on a project receiving federal financial assistance in violation of 18 U.S.C. § 666(a)(2), and mail fraud in violation of 18 U.S.C. § 1341.

BACKGROUND

In January 1991, the New York City Board of Education (“BOE”) entered into a lease with Medgar Evers Enterprises, Inc. (“Medgar Evers”) to use as an intermediate school a building owned by Medgar Evers on Eastern Parkway in Brooklyn. The lease obligated Medgar Evers to renovate the building so that it could be certified for occupancy as a school. Medgar Evers was to submit its renovation bills, including any third-party invoices, to the BOE for reimbursement. The BOE had allocated $2.5 million for the renovation project, including approximately $250,000 for professional fees, such as architectural and engineering work.

The general contractor on the renovation project retained Nicholas Senesey as the project’s architect. Senesey, in turn, hired Carmine Russo as an “expediter” on the project; as an “expediter” Russo was to help Senesey get plan approvals and invoice payments from the BOE.

By January 1992, Senesey had submitted a bill for professional services of only $93,450, and other professional billing on the project remained low. Therefore, considerable funds budgeted for professional fees remained un-disbursed. In November 1992, Russo offered Sheldon Rosenblum, a BOE lawyer, and Joseph Tantillo, a BOE engineer, $5,000 each if they could arrange to pay phony *950 invoices for professional services that were never actually performed from the undis-bursed funds allocated to the renovation project. Unbeknownst to Russo, both Rosen-blum and Tantillo were working with the government on an investigation of corruption in the BOE.

In January 1993, with construction finally complete, the New York City Department of Buildings issued a temporary certificate of occupancy for the Eastern Parkway building. Thereafter, in late February 1993, Russo and Senesey met with Tantillo and Rosenblum to discuss collection of the undisbursed money the BOE had budgeted for professional fees on the project. Russo volunteered to ask the defendant, Henry Fulton, a long-time friend and professional engineer who had worked as deputy commissioner of the New York City Department of Transportation, to submit approximately $35,000 in phony engineering bills. Fulton agreed.

In April 1993, Russo provided Tantillo with details of how he proposed to defraud the BOE of the undisbursed funds. He planned to have Fulton submit two phony engineering bills, one for $25,000 and another for either $5,000 or $11,000.

In April 1993, in the course of a telephone conversation, Russo introduced Tantillo to Fulton. During that conversation, Fulton asked Tantillo how the work description, hours and billing rate should appear in the phony invoices Fulton was preparing. Two days later, during another meeting, Russo introduced Tantillo and Senesey to Fulton, who produced a signed, phony invoice in the amount of $23,475 for engineering services purportedly performed during the renovation on Eastern Parkway. In Fulton’s presence, Russo referred to the bribes that had been agreed upon.

At this meeting, Fulton outlined a “strategy” for the submission of phony bills to the BOE. He proposed several ways to “back into” the $175,000 of professional fees that were still “left on the table.” He suggested, for instance, inflating the hours spent on the project while charging a low hourly rate. In that vein, Fulton repeatedly rejected higher hourly rates proposed by Russo and Senesey, warning that those rates would raise “a red flag.” Fulton also described how to prepare and submit false diaries, calendars and other fabricated documents:

What I have done in the past on jobs like this is ... I used to get my old diaries that had nothin’ in 'em and get one for 1991 and 19 — and just put in there, that’s the job book for ... Bedford Avenue. The job ... and then I just ... every time I went and visited I put in there ... Five hours.... At the end of the year you come to — that’s not such a hard number to come to, 435 hours. And not only that, but I found in court, when you go with a diary in your hand, that stands up, that’s a real written record. Hey, I kept it, it was [a] ... job.

Transcript of taped conversation. Fulton boasted that his techniques would not fail because he had successfully used them in the past.

In May 1993, Senesey provided the BOE with a fraudulent one-page invoice for $176,-000 for professional services purportedly performed on the renovation. The BOE advised Senesey that in order to receive payment of the invoice he would have to submit significant documentation to substantiate the fees represented by the invoice.

A few days later, Russo delivered to the BOE documentation to support Senesey’s invoice. These materials included Fulton’s handwritten summary invoices for $33,312 representing fees claimed for 674 hours of engineering work between June 1990, and June 1993 and weekly time sheets reflecting engineering work that Fulton did not do. The materials also included a diary prepared by Senesey of work purportedly done in connection with the Eastern Parkway renovation project. Various entries in the diary indicated that Fulton had provided engineering services in connection with the work.

In September 1993, a final certificate of occupancy was issued for the Eastern Parkway building. In October 1993, the BOE agreed to pay Senesey $150,000 for professional work allegedly done on the renovation. At a meeting to discuss the mechanics of paying the bribes still due Tantillo and Rosenblum, Fulton offered, in the event the *951 bribe was paid in cash, to carry the $9,000 to Tantillo and Rosenblum. Ultimately, however, Senesey and Russo concluded that Sene-sey would pay the bribe by a check for a phony accounting invoice.

On January 21, 1994, an FBI agent mailed to Senesey a phony Accounting Associates invoice in the amount of $9,500. On January 28, 1994, another FBI agent retrieved from the mail delivered to Accounting Associates a postmarked envelope containing a $9,500 check payable to Accounting Associates and drawn on Senesey’s bank account.

The government now had a completed crime, documented by videotapes and recordings of most of the meetings. The government charged Fulton with: (1) conspiracy to commit bribery and mail fraud, in violation of 18 U.S.C. § 371; (2) bribery, in violation of 18 U.S.C. § 666; and (3) mail fraud, in violation of 18 U.S.C. § 1341. Fulton was also charged with one conspiracy count and one bribery count in connection with an aborted asbestos removal scheme at the Julia Rich-man High School in Manhattan.

At trial in the United States District Court for the Southern District of New York, the defense called four character witnesses to testify as to Fulton’s honesty and integrity. Two of these witnesses were cross-examined, over repeated defense objections, using questions that the defense argues assumed Fulton’s guilt.

The first of these two witnesses, Pastor Joseph Funaro, was asked by Fulton’s own counsel on direct examination if Funaro was aware that Fulton had been charged with certain crimes. When Funaro answered yes, counsel asked whether “these charges of which you are aware [are] consistent or inconsistent with Mr. Fulton’s integrity and honesty as you know him?” Funaro answered that the charges were inconsistent with what he knew about Fulton’s character.

On cross-examination, the prosecution questioned Funaro about his knowledge of the charges against Fulton. Most of the questions began with the phrase “Did [Fulton] ever tell you that he ...,” including the following:

Q. With respect to this case, did Mr. Fulton ever tell you that he prepared any bills for work that he did not do?

Q. Did he ever tell you that at any of those meetings he suggested ways to inflate the bills by increasing the number of hours for a project?

Q. Did he ever tell you that during the course of those meetings with the Board officials, he suggested reducing the rate to charge and increasing the number of hours on a project?

Q. Did Mr. Fulton ever tell you that he offered to share the profits of an asbestos removal contract with a BOE official?

Q. Did he ever tell you that he agreed to pay $2,000 up front to a BOE lawyer in connection with an asbestos removal contract?

Q. Did he ever tell you about his offer to carry $9,000 as part of a bribe payment for an architect at the project at 402 Eastern Parkway, Brooklyn?

Funaro answered no to all these questions.

The defense’s last character witness, Gloria Waldron, also sang praises of Fulton’s honesty and trustworthiness. During cross-examination the prosecution asked Waldron questions concerning her familiarity with Fulton’s business, including the following:

Q. At any time has Mr. Fulton ever told you about whether or not he has met with BOE officials at a restaurant or other meeting place outside of the BOE?

Q. Have you had any discussions with Mr. Fulton regarding anything to do with a project at Julia Richman High School? Q. Has Mr. Fulton ever told you whether or not he has engaged in discussions concerning billing regarding a project at 402 Eastern Parkway?

Q. At any time, Ms. Waldron, has Mr. Fulton shown you any videotapes in connection with this case?

Q. At any time has Mr. Fulton provided you with any audiotape recordings of conversations in connection with this case?

Waldron answered no to all these questions.

After Waldron’s testimony, the court had second thoughts and reversed its earlier deci *952 sion overruling defense counsel’s objections to the prosecution’s cross-examination of Fu-naro. While noting that the defense may have “opened the door” to such cross-examination by asking Funaro if he was aware that Fulton had been charged with certain crimes and if those charges were consistent with Fulton’s character, the court nevertheless struck the questions and the answers from the record. The court, however, found the cross-examination of Waldron appropriate because those questions were intended “to elicit how much, if anything, she knew about this situation from the defendant” and they “did not assume any facts going to the question of guilt ...”

At the close of trial, the district court furnished a written copy of its charge for the jury to take with it during deliberations. The defense objected to giving the jury written instructions, arguing that it gave an intellectual edge to jurors with higher reading comprehension. The court disagreed and gave the written charge to the jury with a cautionary instruction to consider the charge as a whole and to send out written questions to the court if necessary.

The jury convicted Fulton of all charges relating to the 402 Eastern Parkway project, but acquitted him of the asbestos removal scheme charges. The court sentenced Fulton to twenty-one months in prison.

Fulton now appeals his conviction and sentence on several grounds.

DISCUSSION

Fulton raises several issues on appeal only two of which warrant discussion — (a) whether Fulton was deprived of a fair trial when the prosecution cross-examined Fulton’s character witnesses allegedly using guilt-assuming hypotheticals and (b) whether the district court erred by submitting a written copy of the charge to the jury. The remaining issues are resolved by a summary order filed herewith. See United States v. Russo, 96-1394.

A. Cross-Examination of Character Witnesses

The Federal Rules of Evidence allow a defendant to put his good character in issue as part of his defense to criminal charges. Fed.R.Evid. 404(a)(1). Once a defendant offers character testimony, the prosecution is afforded substantial latitude to rebut such evidence. See United States v. McGuire, 744 F.2d 1197, 1204 (6th Cir.1984). There are however restraints on how far the government may go on cross-examination in posing guilt-assuming hypotheticals to a character witness. See United States v. Oshatz, 912 F.2d 534 (2d Cir.1990); see also United States v. Velasquez, 980 F.2d 1275 (9th Cir.1992); United States v. Krapp, 815 F.2d 1183 (8th Cir.1987); United States v. Page, 808 F.2d 723 (10th Cir.1987); McGuire, 744 F.2d at 1197.

We have held that the prosecution may not cross-examine a defendant’s character witness by asking the witness whether his or her opinion of the defendant would change if the defendant were guilty of the charges against him. Oshatz, 912 F.2d at 539. The prosecution also may not ask a defendant’s character witness whether the witness is aware that the defendant is guilty. Krapp, 815 F.2d at 1186. The reasoning behind these limitations is that guilt-assuming hypo-theticals, such as “would your opinion of the defendant change if he were guilty” or “are you aware that the defendant is guilty of the crimes charged,” trench too deeply into the presumption of innocence. See Oshatz, 912 F.2d at 539. We have acknowledged that:

to some extent a guilt-assuming hypothetical question might be probative of the credibility of testimony given by a non-expert character witness. Steadfast adherence to a favorable opinion by a witness asked to assume the defendant’s guilt might provide some basis for concluding that the witness is simply supporting the defendant, rather than providing credible testimony about his character. But we share the view of [an earlier Second Circuit panel] that such cross-examination is nevertheless to be prohibited because it creates too great a risk of impairing the presumption of innocence. Moreover, ... the jury might infer from the judge’s permission to ask a guilt-based hypothetical *953 question that the prosecutor has evidence of guilt beyond the evidence in the record.

Id. In this case, we find that the prosecution’s cross-examinations of Pastor Funaro and Gloria Waldron did not violate the rule against using guilt-assuming hypotheticals.

As to Pastor Funaro, we find that the government’s cross-examination of him was permissible because defense counsel “opened the door” to the issue of whether Funaro knew about the charges against Fulton and specifically what he knew about those charges. Departing from traditional direct examination of a character witness, defense counsel asked Funaro whether he was “aware of the fact that Mr. Fulton ha[d] been charged with certain crimes.” After an affirmative response, defense counsel asked Fu-naro whether “those charges of which [Funa-ro is] aware [are] consistent or inconsistent with Mr. Fulton’s integrity and honesty as [Funaro] know[s] him.” Because defense counsel “opened the door” by asking Funaro whether, in his opinion, Fulton’s character is consistent with the charges against Fulton, the government was allowed to determine how familiar Funaro was with the charges against Fulton. There was, therefore, no need for the court to have stricken the testimony it believed to be improper.

We express no opinion on whether the government’s cross-examination of Funaro would have been proper if defense counsel had not “opened the door.” To avoid this result in the future, we suggest that defense counsel adhere to a more traditional form of direct examination of a character witness, (e.g., “What is your opinion of the defendant’s honesty?” or ‘What is the defendant’s reputation for honesty?”). See Fed.R.Evid. 405(a). Likewise, we suggest that the government be more scrupulous in adhering not only to the letter of United States v. Oshatz, but also to its spirit.

As to Ms. Waldron’s testimony, we find that the prosecution’s cross-examination of her did not include questions that assumed guilt. Waldron’s cross-examination consisted solely of questions regarding whether Fulton had told her about legal aspects of his business. The questions all concerned activities that are perfectly legal, such as “has Mr. Fulton ever told you whether or not he has visited with BOE officials at an Accounting Associates Office,” and “has Mr. Fulton ever told you whether or not he has engaged in discussions concerning billing regarding a project at 402 Eastern Parkway.” This fine of questioning was appropriate, considering that Waldron testified that she had known Fulton for twenty-five years, had worked for him as an apprentice, had subsequently worked on design projects for him and had maintained a personal and professional relationship with him. The government’s questions were probative of how well Waldron knew Fulton and how familiar she was with the current state of his business.

B. Written Jury Instructions

Appellant faults the district court for providing the jury with a written copy of the court’s instructions. We disagree.

While some circuits disfavor this practice, all agree that the practice is properly committed to the trial court’s discretion. See United States v. Oreira, 29 F.3d 185, 191 (5th Cir.1994); United States v. Parent, 954 F.2d 23, 24 n. 1 (1st Cir.1992); United States v. Henry, 878 F.2d 937, 940 (6th Cir.1989); United States v. Schilleci, 545 F.2d 519, 525 (5th Cir.1977). We have expressly approved the submission of a written charge in the context of a long and complicated trial. United States v. Delano, 55 F.3d 720, 732 (2d Cir.1995).

We reaffirm the rule that the decision whether to submit written instructions to the jury properly lies within the discretion of the trial court. The submission of written instructions to a jury is often advisable. We believe the fear expressed by some courts that “the practice is conducive to dissection of the charge by the jury and overemphasis of isolated parts rather than consideration of the charge as a whole,” Schilleci, 545 F.2d at 526, is outweighed by the benefits of submitting a written charge to the jury. Written charges will usually enhance a jury’s understanding of the elements of the crime charged and the burdens of the prosecution. Additionally, such a practice is substantially more efficient,- because jurors can refer to a *954 copy of the charge when questions arise rather than coming back into court and having the court simply reread the instructions. Moreover, the District Judge carefully minimized the risk of any misuse of the written charge in the jury room by cautioning the jurors to consider the charge as a whole and to seek clarification if necessary.

The district court here acted well within its discretion and followed a practice we fully support.

CONCLUSION

We have considered all of Fulton’s additional arguments and find them to be without merit. The judgment of the district court is affirmed.