#### UNITED STATES, Appellee, v. Steven A. MILKIEWICZ, Defendant, Appellant.

No. 06-1192.

United States Court of Appeals, First Circuit.

Heard Sept. 11, 2006.

Decided Dec. 6, 2006.

*391Terrance J. McCarthy for appellant.

Paul G. Levenson, Assistant United States Attorney, with whom Michael J. Sullivan, United States Attorney, was on brief, for appellee.

Before TORRUELLA, LYNCH and LIPEZ, Circuit Judges.

LIPEZ, Circuit Judge.

This case requires us to consider two unsettled issues in First Circuit law: the proper use of the various evidentiary rules governing the introduction of document summaries at trial, and the applicability of the constitutional rule set out in *United States v. Booker,*543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), to orders of restitution. The appellant, Steven A. Mil-kiewicz, was convicted of defrauding the United States District Court for the District of Massachusetts (“USDC”) through a scheme in which he — collaborating with a court administrator — sold office supplies to the USDC at inflated prices and billed it for quantities of products in excess of what he delivered.1

Appellant claims that he is entitled to a new trial because the district court improperly allowed the jury to consider two sets of summary charts, one depicting the allegedly fraudulent sales transactions and the other showing discrepancies in his income tax reporting. He also claims the district court’s restitution order, which was based on its own factual findings, violated his Sixth Amendment rights under the principles set out in *Booker.*Finding neither evidentiary nor constitutional error, we affirm appellant’s conviction and sentence.

*392I.

A. Factual Background

We summarize the facts as the jury could have found them, drawing all inferences in the light most consistent with the jury’s verdict. *See United States v. Charles,*456 F.3d 249, 251 (1st Cir.2006). Between February 1997 and June 2002, appellant Milkiewicz and Timothy Schroeder, the Procurement Officer for the Clerk of the USDC, used various techniques to ensure that Milkiewicz would win the USDC’s purchasing contracts and have the ability to overcharge for the products provided.2 For example, to avoid the USDC requirement that procuring officials obtain at least three competitive bids for the purchase of goods or services over $2,500, appellant — with Schroeder’s complicity— sometimes submitted bids from each of his two separate companies. The third bid at times was forged, and at least once came from a sham entity created by Schroeder. By eliminating competition, appellant not only was assured that he would be given the business but also was able to charge more and thereby elicit fraudulently inflated profits.

On other occasions, appellant’s collaboration with Schroeder allowed him to charge the USDC for items he never delivered. This conduct occurred repeatedly with respect to purchases of large amounts of paper and toner cartridges used for photocopiers and computer printers. In one such transaction, appellant billed the USDC $21,570 ($35.95 per carton) for 600 cartons of copier paper but arranged to deliver only 400 cartons. The illicit gains from this purchase included not only the money he received for the undelivered paper ($7,190), but also a fraudulent mark-up of about $4,000 that he was able to obtain thanks in part to cooperation from his supplier, who regularly submitted inflated competitive bids at appellant’s request.3

The evidence also showed that, during the years at issue, appellant understated his taxable income and gave his tax preparer false information about his gross receipts and business expenses. The government used the evidence of his illicit transactions to prove that he had earned income in excess of what he reported and that he had spent less than he stated to purchase inventory from his suppliers.

In December 2004, Milkiewicz was charged in an indictment with one count of conspiracy to defraud the United States, in violation of 18 U.S.C. § 371; eight counts of presenting to the United States false claims for payment, in violation of 18 U.S.C. § 287;4 one count of bribery of a public official, in violation of 18 U.S.C. § 201; and five counts of filing false tax returns, in violation of 26 U.S.C. § 7206(1). At the conclusion of an eight-day trial, a jury convicted him on all counts except the bribery charge and one of the false tax return charges. He subsequently was sentenced to a 41-month term of imprisonment and ordered to pay restitution in the sum of $196,796.63, the latter a joint and several obligation with his co-defendant, Schroeder.5

*393B. The Disputed Summary Charts

The evidence introduced at trial included several thousand pages of financial records offered by the government to prove specific transactions consistent with a more general description of the scheme that Schroeder provided in his testimony. Among these documents were approximately 600 pages of USDC records, including vouchers and invoices that showed purchases from appellant’s two companies. Another substantial set of documents contained business records, including purchase orders and invoices, from more than twenty vendors whom appellant allegedly used as suppliers for the products he sold to the USDC. These suppliers were identified by IRS investigators who had examined appellant’s bank activity. The records were offered into evidence, by stipulation, through affidavits from the various keepers of records.

Toward the end of its case, the government called an IRS agent, Jonathan Wlo-dyka, to testify about a series of charts that summarized the information contained in these voluminous financial documents. Two sets of charts are at issue in this case — what we shall call the “Transactions Set” and the “Tax Set.” The Transactions Set summarizes data from the records that the government offered as evidence of the fraudulent transactions with the USDC. The Tax Set summarizes documents related to the tax charges.

The Transactions Set consists of three relevant charts: Exhibits 1, la and lb. Exhibit la summarizes data from the USDC records reflecting purchases from appellant. Exhibit lb summarizes data from the roughly 1,300 pages of authenticating affidavits and vendor business records depicting appellant’s purchases from suppliers. Also included in that batch of records were copies of checks from appellant to the vendors, which the government offered to supplement incomplete vendor records. The checks were used to prove appellant’s purchases when vendors could not produce invoices documenting those purchases.

Exhibit 1 juxtaposes the information in the la and lb charts, providing a comparison in chronological order between what appellant sold to the USDC and what he purchased from his vendors. The calculated differences are listed in columns labeled “Price Difference” and “Quantity Difference.” The “Price Difference” column shows the disparity between what appellant charged the USDC for specific items on particular dates and what he allegedly paid suppliers for those goods. The government presented evidence suggesting that, if Milkiewicz and Schroeder had not manipulated the competitive bid process, some of Milkiewicz’s suppliers would have sold their products directly to the government at prices far below what Milkiewicz charged. The “Quantity Difference” column contains figures showing an amount appellant billed to the USDC where records show no corresponding purchase from a vendor. In some instances, the chart showed that appellant purchased fewer goods than he sold to the USDC, and for which he received payment, and at other times it showed no purchase at all of items for which the USDC had paid. In the rows involving alleged non-deliveries, the spaces in columns labeled “Quantity Purchased” and “Price Paid Per Unit” are blank.6

*394The government asserts that the “obvious inference” to be drawn from the flow of money and product depicted in Exhibit 1 is that appellant realized illicit profits both by charging prices in excess of what would have been paid in a legitimate bid process and by charging for some goods that he never delivered — either providing a lesser quantity than ordered or by not delivering an order at all. In closing argument, the prosecutor urged the jury to infer just that, and he emphasized in particular that where the charts were blank— i.e., where there was no evidence that Mil-kiewicz purchased an item from suppliers — he never delivered the item to the USDC.

The Tax Set similarly consists of three charts: Exhibits 2, 2a and 2b. Exhibit 2a lists the checks the government viewed as evidence of the “gross receipts” of appellant’s office supply business in each of the years 1997 through 2001. Documents supporting the data were in evidence, including records of hundreds of payments from the USDC.7 Exhibit 2b summarizes the documentary evidence of appellant’s purchases from his suppliers, or, in tax terms, his “cost of goods sold.” Exhibit 2 compares the figures appellant reported on his tax returns in the categories of “gross income” and “cost of goods sold” with the data developed in the investigation, as summarized in Exhibits 2a and 2b. Exhibit 2 also calculates, for each of the five years, the additional tax due based on the information compiled in the chart.8

Appellant’s counsel initially objected only to admission of the charts as independent evidence, consenting to their use as demonstrative jury aids, or “chalks.” He later opposed the court’s decision to allow the jury to have the charts during their deliberations, arguing that the summaries impermissibly shifted the burden of proof to appellant. Counsel asserted that the blank spaces on Exhibit 1 — which indicated that the government had found no evidence that appellant purchased certain *395supplies for which he charged the government — “cannot help but lead jurors to say, Well, how come the defendant is not filling those gaps.” The court rejected this objection, concluding that a similar “argument could be made with respect to any piece of circumstantial evidence.” It agreed, however, to specifically instruct the jury that appellant had no burden to produce evidence that he had purchased such goods.9

On appeal, Milkiewicz no longer pursues the burden of proof issue, instead arguing that the jury should not have been given the charts because the Transactions Set contained errors and significant omissions, rendering the summaries unreliable, while the Tax Set was improperly admitted through Agent Wlodyka, who was not qualified as an expert. Appellant relatedly argues that the summaries should not have been admitted because their probative value was outweighed by the danger of unfair prejudice. *See*Fed.R.Evid. 403.10

II.

In deciding whether — and how — to admit the Transactions and Tax summaries offered by the government, the district judge carefully reviewed our precedent on summary evidence and, during a lengthy explanation from the bench, admitted that he was perplexed. As we shall discuss, the judge ultimately relied on Federal Rules of Evidence 611(a) and 703 because he understood our precedent to foreclose admission of the charts under Rule 1006, which explicitly addresses the use of summaries, *see infra*at note 11. Noting that “this is an area where it would be helpful for the Court to provide some clarification to district judges,” he urged the First Circuit to consider “a slightly different approach” than he believed our case law required. Having done our own review, we agree that our precedent is somewhat opaque — a reflection, we believe, of the intricacies of the law generally — and we further agree with the district court’s assessment of the correct approach to Rule 1006 summaries. Also, a proper understanding of the evi-dentiary rules applicable to summaries is important because the basis for admission can affect how a summary is used, including whether a jury may rely on it as primary evidence and whether it is allowed in the jury room during deliberations, see *infra*at note 14. We therefore digress from appellant’s particular concerns to clarify the landscape.

A. Document Summaries: Legal Principles

The Federal Rules of Evidence offer multiple options for an attorney who wishes to summarize complex evidence and bring it to the jury’s attention in the form of a chart. The various rules are not always mutually exclusive, and so it is unsurprising that confusion sometimes arises — as it did in this case — over the appropriate basis for admitting a particular summary. We previously attempted to respond to the ambiguities in our own law in *Air Safety, Inc. v. Roman Catholic**396*Archbishop of Boston,*94 F.3d 1 (1st Cir.1996), where we observed that, contrary to statements in prior cases, evidence underlying summaries admitted under Rule 1006 need not be admitted into evidence and that “[t]he requirement of prior admission actually applies to a different sort of summary.” *Id.*at 7 n. 14. We did not, however, identify the rule under which such other summaries could be introduced and, indeed, left ambiguous whether Rule 1006 was inapplicable if the underlying documents *were*in evidence.11 We now give more focused attention to each of the options and explicitly hold that summaries that are otherwise admissible under Rule 1006 are not rendered inadmissible because the underlying documents have been admitted, in whole or in part, into evidence.

Rule 1006 allows “[t]he contents of voluminous writings ... which cannot conveniently be examined in court [to] be presented in the form of a chart, summary, or calculation.” Fed.R.Evid. 1006.12 It creates an exception to Rule 1002, which requires that originals be used to prove the content of writings, recordings and photographs. Evidence admitted under Rule 1006 must be otherwise admissible and remains subject to the usual objections under the rules of evidence and the Constitution. “Most notably, Rule 1006 evidence normally is objectionable if the voluminous source material on which it is based is inadmissible.” 31 Charles A. Wright *&*Victor J. Gold, *Federal Practice and Procedure*§ 8043, at 521-22 (2000). The proponent must show that the voluminous source materials are what the proponent claims them to be and that the summary accurately summarizes the source materials. *Id.*at 525.

Under Rule 1006, the underlying documents must be made available to the other parties, and “[t]he court may order that they be produced in court.” The discretion accorded the trial court to order production of the documents means that the evidence underlying Rule 1006 summaries need not be introduced into evidence, *see, e.g., United States v. Janati,*374 F.3d 263, 272-73 (4th Cir.2004); *Air Safety,*94 F.3d at 7 n. 14, but nothing in the rule forecloses a party from doing so. For example, we can imagine instances in which an attorney does not realize until well into a trial that a summary chart would be beneficial, and admissible as evidence under Rule 1006, because the documents already admitted were too voluminous to be conveniently examined by the jury.

Most often, however, we think it likely that an attorney would anticipate the benefits of summarizing voluminous writings and would take advantage of the opportunity offered by Rule 1006 to present only the summary at trial. Consequently, while in most cases a Rule 1006 chart will be the *only*evidence the fact finder will examine concerning a voluminous set of documents, *see Air Safety,*94 F.3d at 7 n. 14; *United**397*States v. Bakker,*925 F.2d 728, 736-37 (4th Cir.1991); *cf.*6 Jack B. Weinstein & Margaret A. Berger, *Weinstein’s Federal Evidence*§ 1006.04[1] (Joseph M. McLaughlin, ed., 2d ed.2000), in other instances the summary may be admitted *in addition to*the underlying documents to provide the jury with easier access to the relevant information. *See, e.g., United States v. Green,*428 F.3d 1131, 1134-35 (8th Cir.2005); *United States v. Petty,*132 F.3d 373, 379 (7th Cir.1997); *United States v. Stephens,*779 F.2d 232, 238-39 (5th Cir.1985); *United States v. Lemire,*720 F.2d 1327, 1347 (D.C.Cir.1983).

This latter practice has drawn criticism as inconsistent with the purpose of Rule 1006 to provide an exception to the “best evidence rule” because, “[i]f the underlying evidence is already admitted, there is no concern that a summary is used in lieu of the ‘best evidence.’ ” *See Federal Practice and Procedure*§ 8043, at 523-24 n. 8. We agree with the Fifth Circuit, however, that “[t]he fact that the underlying documents are already in evidence does not mean that they can be ‘conveniently examined in court.’ ” *Stephens,*779 F.2d at 239 (quoting *Lemire,*720 F.2d at 1347). Thus, in such instances, Rule 1006 still serves its purpose of allowing the jury to consider secondary evidence as a substitute for the originals.

A trial judge also may allow use of a chart or other summary tool under Fed.R.Evid. 611(a), which gives the trial court “control over the mode ... [of] presenting evidence.”13*See, e.g., United States v. Harms,*442 F.3d 367, 375 (5th Cir.2006); *Janati,*374 F.3d at 273; *United States v. Bray,*139 F.3d 1104, 1111 (6th Cir.1998). Such summaries most typically are used as “pedagogical devices” to “clarify and simplify complex testimony or other information and evidence or to assist counsel in the presentation of argument to the court or jury.” *Bray,*139 F.3d at 1111; *see also Janati,*374 F.3d at 273; 6 *Weinstein’s Federal Evidence*§ 1006.08[4]. A summary chart used as a pedagogical device must be linked to evidence previously admitted and usually is not itself admitted into evidence. *Janati,*374 F.3d at 273; *Bray,*139 F.3d at 1112; *Air Safety,*94 F.3d at 7 n. 14.14

The lines between these two types of summary documents are easily blurred. A summary that is admissible under Rule 1006—and is thus most appropriately introduced under that rule — could properly be offered under Rule 611(a) if the supporting material has been admitted into evidence. Likewise, a chart that originally was offered as a jury aid to assist with review of voluminous underlying documents already in *evidence*— and which accurately summarizes those documents — alternatively could be admitted under Rule 1006 if the court concluded that the supporting documents could not be examined conveniently in court. To complicate matters, a court also has discretion under Rule 703 to provide the jury in some circumstances with the “facts or data” underlying *398an expert’s opinion, and such material may be presented in the form of a summary chart. Fed.R.Evid. 703; *Janati,*374 F.3d at 273.

In a case where voluminous underlying records are involved, the key difference between these various approaches appears to be the purpose for which the summaries are offered. Charts admitted under Rule 1006 are explicitly intended to reflect the contents of the documents they summarize and typically are substitutes in evidence for the voluminous originals. Consequently, they must fairly represent the underlying documents and be “ ‘accurate and nonprejudicial.’” *Bray,*139 F.3d at 1111 (quoting *Gomez v. Great Lakes Steel Div., Nat’l Steel Corp.,*803 F.2d 250, 257 (6th Cir.1986)); *see also Janati*374 F.3d at 272.15

By contrast, a pedagogical aid that is allowed under Rule 611(a) to illustrate or clarify a party’s position, or allowed under Rule 703 to assist expert testimony, may be less neutral in its presentation. Record support is necessary because such devices tend to be “more akin to argument than evidence,” 6 *Weinstein’s Federal Evidence*§ 1006.08[4]; *Bray,*139 F.3d at 1111, and “may reflect to some extent, through captions or other organizational devices or descriptions, the inferences and conclusions drawn from the underlying evidence by the summary’s proponent,” *Bray,*139 F.3d at 1111; *see also Janati*374 F.3d at 273. In some cases, however, such pedagogical devices may be sufficiently accurate and reliable that they, too, are admissible in evidence, even though they do not meet the specific requirements of Rule 1006. *Bray,*139 F.3d at 1112; 6 *Weinstein’s Federal Evidence*§ 1006.04[2].

B. Appellant’s Objections to the Summary Charts

Our review of the court’s decision to allow the jury to consider the summaries during its deliberations is highly deferential: “It is hard to imagine an issue on which a trial judge enjoys more discretion than as to whether summary exhibits will be helpful.” *Fraser v. Major League Soccer, L.L.C.,*284 F.3d 47, 67 (1st Cir.2002). The district court exercised that discretion here with meticulous care. It required the government to modify the summaries to eliminate unnecessary and potentially prejudicial information and labels,16 and it explicitly considered “the usefulness versus the potential misuse of summaries of this nature,” concluding that the jurors needed the charts to be able to sort through such “an extraordinarily complex document case.”

The court recognized the risk of prejudice inherent in such a compact presentation of the evidence, but concluded that the jurors “will clearly understand that those charts are based on assumptions and they’re only as valid as the underlying assumptions----” In addition, although the general principles we have outlined above would have permitted the court to admit most, if not all, of the charts into evidence under Rule 1006, the court chose not to do so because it read our precedents to foreclose admission of a summary chart *399when the underlying documents already were in evidence.17 The court instead allowed their use under Rules 611 and 703, but did not admit them into evidence. It gave a cautionary instruction that typically is used to ensure that jurors considering non-evidentiary summaries focus on the underlying documents rather than on the summaries:

> A witness for the government and a witness for the defendant testified about certain documents that purported to summarize various documents that have been admitted into evidence. Such summaries are not independent evidence of their subject matter and are only as valid and reliable as the underlying evidence they summarize. You are free to disregard them entirely. It is for you to decide whether they accurately, completely and objectively reflect the content of the underlying documents. Your evaluation of the summaries should be based on your consideration of all testimony you heard about who prepared the summaries, the manner in which they were prepared, and the reliability and completeness of the underlying documents.

Despite these precautions, appellant argues that the court abused its discretion in allowing the jury to consider the summaries. We find his claims of error meritless.

1. Flaws in the Data

Appellant initially complains about the records on which the summaries were based, describing the data as unreliable and “corrupted.” As noted earlier, much of the underlying financial information was presented via affidavits by stipulation, and appellant explicitly waived objection to the data’s admission. At trial, seven keepers of records testified about their companies’ business dealings with appellant and were cross-examined by defense counsel. Nonetheless, in his brief, appellant identifies errors or omissions contained in the affidavits and asserts that the summaries should have been excluded under Rule 403 because of inaccuracies in the underlying data.

To the extent that appellant is attempting to mount a challenge to the data on which the charts are based, it is much too late to do so. When a defendant affirmatively agrees to the government’s proposed use of evidence, there has been a waiver and the defendant is not entitled even to plain error review of a claim that the evidence was inadmissible. *United States v. Medina,*427 F.3d 88, 91-92 (1st Cir.2005); *United States v. Mitchell,*85 F.3d 800, 807 (1st Cir.1996).

Appellant fares no better to the extent his claim is based solely on the jury’s access to the summaries during deliberations. To be sure, the underlying records were imperfect,18 and, as a result, the summaries in all likelihood did not reflect every relevant transaction. But defense counsel explored the deficiencies during his cross-examinations of Agent Wlodyka and the record-keeping witnesses, and gaps or other imperfections in the underlying data do not necessarily undermine the value of the summary charts as pedagogical aids under Rule 611(a). In *United**400*States v. Nivica,*887 F.2d 1110, 1125-26 (1st Cir.1989), we noted that the government need not prove that it has uncovered all records relevant to a case and may summarize the data it has managed to collect through the exercise of “due diligence.” We continued:

> If defendants possessed exculpatory records not in the government’s files, they could have offered them at trial or prepared their own summary. By the same token, if there were gaps in the charts, the defense — knowledgeable as to [the business’s] operation — had every opportunity to exploit them. In the last analysis, completeness of the underlying records was for the jury.

*Id.*at 1126; *see also United States v. Sawyer, 85*F.3d 713, 740 (1st Cir.1996).

Here, too, appellant had ample opportunity to expose his concerns to the jury, and the court’s instruction that the jury should base its evaluation of the summaries on “the reliability and completeness of the underlying documents” underscored the jury’s prerogative to make its own assessment of both the supporting material and the summaries. Moreover, the court’s instruction on the burden of proof, *see supra*note 9, met appellant’s concern that the format of the summaries would lead the jury to infer guilt solely from the gaps in the information provided.19

Appellant’s shifting grounds of argument about the jury’s access to the summaries, *see supra*at 9-10, undoubtedly entitles him only to plain error review on this issue. Even were it a matter of discretion, however, we think it beyond debate that the court properly could find that the jury’s need for the summaries was substantial. In addition, the court’s efforts to excise prejudicial content — imposing the neutrality requirements of Rule 1006, though he ultimately found the summaries inadmissible under that rule — did much to diminish any harmful impact on appellant. Given the court’s care both in crafting the versions given to the jury and in guiding the jury’s use of them, we conclude that appellant was adequately protected from unfair prejudice.

2. Agent Wlodyka and the Tax Exhibits

The district court admitted the tax return exhibits pursuant to Rule 703, which addresses the admissibility of “facts or data” that form the basis for an expert’s opinion. When such information is “otherwise inadmissible,” it may not be

> disclosed to the jury by the proponent of the opinion or inference unless the court determines that [the] probative value in assisting the jury to evaluate the expert’s opinion substantially outweighs [its] prejudicial effect.

Fed.R.Evid. 703. The court explained that it utilized Rule 703 for these summaries because the re-calculation of appellant’s tax obligation that appeared in Exhibit 2 involved a “kind of expert interpretation” and, as a result, that chart was “not, strictly speaking, a summary of documents.”

Appellant asserts on appeal that Agent Wlodyka lacked the necessary qualifications as an expert to present the informa*401tion contained in the Tax Set and that, consequently, the district court should have excluded the charts under the standards governing admissibility of expert evidence that were outlined by the Supreme Court in *Daubert v. Merrell Dow Pharm., Inc.,*509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), and *Kumho Tire Co. v. Carmichael,*526 U.S. 137, 119 S.Ct. 1167, 143 L.Ed.2d 238 (1999). As this argument was not raised in the district court, it warrants only plain error review. *United States v. Torres-Rosario,*447 F.3d 61, 67-68 (1st Cir.2006). At any level of scrutiny, however, the claim fails.

The only arguably “expert” evidence in the Tax Set is Exhibit 2’s calculation of the new amount of tax owed for the years 1997 to 2001, based on the income and expense totals summarized in the two related exhibits. Wlodyka was not asked how he computed the amount of tax due; it appeared to be understood that he simply applied the standard tax tables to the new income totals.20 Even on appeal, appellant’s complaint does not appear to be about those calculations; it is that the court “allow[ed] the jury to consider the summary charts which had been prepared by one who[] does not qualify as an expert.”

If appellant means by that complaint that Wlodyka did not have the expertise to summarize the financial information contained in the charts, his argument is hopeless. The invoices, checks, and other documents were routine financial records, and creating summaries of the data took patience but not expertise. Moreover, even if he is challenging the agent’s credentials to do the tax computations, that challenge would fail. An IRS agent is qualified to express an opinion on the tax consequences of a transaction, *United States v. Mikutowicz,*365 F.3d 65, 72 (1st Cir.2004), particularly where, as here, the computation required no subjective judgment. *See United States v. Serafino,*281 F.3d 327, 330 (1st Cir.2002) (noting that an IRS agent presumably is qualified to testify as an expert regarding the amount of an outstanding tax liability). The district court thus fully met any gate-keeping responsibility to ensure the reliability and pertinence of expert testimony. *See Kumho Tire Co.,*526 U.S. at 141, 119 S.Ct. 1167; *Daubert,*509 U.S. at 597, 113 S.Ct. 2786. There was no error — plain or otherwise — in the court’s decision to allow the jury to consider the tax exhibits.

In sum, we find no error in the court’s handling of the summary exhibits and consequently no basis for disturbing the jury’s verdict.

III.

The district court found that the losses attributable to appellant’s crimes in-*402eluded $139,912.07 in payments made by the USDC for goods that were never delivered and $56,884.56 in excess payments that resulted from bid-rigging.21 Pursuant to the Mandatory Victims Restitution Act (“MVRA”), 18 U.S.C. § 3663A, the court consequently imposed restitution on appellant, jointly and severally with Schroeder, in the total amount of $196,796.63.22 Appellant argues that the court’s reliance on its own fact-finding for the restitution amount violated his Sixth Amendment rights under *United States v. Booker,*543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).

We begin by noting that the government urges us either to deem this claim waived, foreclosing any appellate consideration, or to review it only for plain error, in which case it would be governed by *United States v. Burnette,*423 F.3d 22 (1st Cir.2005). We held there that a restitution order based on judicial fact-finding was not plain error. *Id.*at 25. While we agree that appellant is entitled to no more than plain error consideration, we have chosen to fully address *Booker’s*impact on restitution here because the issue is appearing with increasing frequency in our cases. Moreover, at least nine other circuits already have held that judicial fact-finding on restitution is permissible under *Booker, see infra*at 30, and we see no reason to delay our agreement with their conclusion.

In the well known trio of cases culminating with *Booker,*the Supreme Court established that the Due Process Clause of the Fifth Amendment and the jury trial guarantees of the Sixth Amendment require a jury to find beyond a reasonable doubt any fact that increases the maximum penalty for a crime, other than the fact of a prior conviction. *See Booker,*543 U.S. at 244, 125 S.Ct. 738; *Blakely v. Washington,*542 U.S. 296, 303-04, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004); *Apprendi v. New Jersey,*530 U.S. 466, 490, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000).23 In *Blakely,*the Court reviewed the Washington state sentencing guidelines and, relying on the Sixth Amendment, stated that “[w]hen a judge inflicts punishment that the jury’s verdict alone does not allow, the jury has not found all the facts ‘which the law makes essential to the punishment,’ ... and the judge exceeds his proper authority.” 542 U.S. at 304, 124 S.Ct. 2531 (internal citation omitted).

The Court in *Booker*extended this approach to the federal Sentencing Guidelines, stating that a defendant’s Sixth Amendment right “is implicated whenever a judge seeks to impose a sentence that is not solely based on ‘facts reflected in the jury verdict or admitted by the defendant.’” 543 U.S. at 232, 125 S.Ct. 738 (quoting *Blakely,*542 U.S. at 303, 124 S.Ct. *4032531). The Court also reiterated the basic principle: “[a]ny fact (other than a prior conviction) which is necessary to support a sentence exceeding the maximum authorized by the facts established by a plea of guilty or a jury verdict must be admitted by the defendant or proved to a jury beyond a reasonable doubt.” 543 U.S. at 244, 125 S.Ct. 738.

The question before us is whether this Sixth Amendment right to have certain facts found by a jury beyond a reasonable doubt requires that the jury, rather than the judge, calculate the loss underlying a restitution order.24 A literal application of the Supreme Court’s language might suggest the answer would be an affirmative. If “the question is whether the verdict *‘alone*’ allows the judge to impose restitution with no additional finding of fact[,][o]bviously, it doesn’t.” *United States v. Leahy,*438 F.3d 328, 342 (3d Cir.2006) (en banc) (emphasis in original) (McKee, J., concurring in part and dissenting in part). The statutory procedure for fixing a restitution amount calls for fact-gathering by the probation officer after conviction, 18 U.S.C. § 3664(a),25 with any disputes to be “resolved by the court by the preponderance of the evidence,” *id.*at § 3664(e). The court is then directed to order restitution “in the full amount of each victim’s losses as determined by the court.” *Id.*at 3664(f)(1)(A). Thus, it can reasonably be argued that the “maximum” amount of restitution based solely on the fact of conviction is zero dollars. Because any increase in that amount depends upon additional facts, one could argue — as did the dissenters in the Third Circuit’s en banc decision on this issue — that *Booker*requires such findings to be made by a jury. *Leahy,*438 F.3d at 344 & n. 15 (McKee, J., concurring in part and dissenting in part) (concluding that a scheme allowing judge-made findings on restitution runs “afoul of the Sixth Amendment” because “[rjestitution in any amount greater than zero clearly increases the punishment that could otherwise be imposed”).

While we understand the logic behind this approach, we think it ignores important considerations and, like all of the other circuits to consider this question, we conclude that *Booker*and its antecedents do not bar judges from finding the facts necessary to impose a restitution order. *See United States v. Williams,*445 F.3d 1302, 1310-11 (11th Cir.2006); *United States v. Reifler,*446 F.3d 65, 118-20 (2d *404Cir.2006); *Leahy,*438 F.3d at 337-38; *United States v. Miller,*419 F.3d 791, 792-93 (8th Cir.2005); *United States v. Sosebee,*419 F.3d 451, 454, 461 (6th Cir.2005); *United States v. Garza,*429 F.3d 165, 170 (5th Cir.2005) *(per curiam); United States v. Bussell,*414 F.3d 1048, 1060 (9th Cir.2005); *United States v. George,*403 F.3d 470, 473 (7th Cir.2005); *United States v. Wooten,*377 F.3d 1134, 1144-45 (10th Cir.2004).

The statutory restitution scheme is materially different from the sentencing regimens at issue in *Blakely*and *Booker.*Under the latter, a judge determines the appropriate penalty from within a specified range, based on a variety of facts and factors that are not necessarily predetermined by the jury’s finding of guilt. For restitution, however, the jury’s finding of guilt leads to only one outcome; in *every*case in which such punishment is imposed, “the jury’s verdict automatically triggers restitution in the ‘full amount of each victim’s losses,’ ” *Leahy,*438 F.3d at 338 n. 11. Post-conviction judicial fact-finding to determine that amount “by no means im-postes] a punishment beyond that authorized by jury-found or admitted facts,” or “beyond the ‘statutory maximum’ as that term has evolved in the Supreme Court’s Sixth Amendment jurisprudence.” *Id.*at 336-37 (noting that the “relevant ‘statutory maximum’ for *Apprendi*purposes is the maximum sentence a judge may impose based solely on facts reflected in the jury verdict or admitted by the defendant”); *see also Reifler,*446 F.3d at 119. As the Third Circuit majority in *Leahy*stated in its response to the dissenters:

> [T]here is no restitution range ... that starts at zero and ends at “the full amount of each victim’s losses”; rather, the single restitution amount triggered by the conviction under the MVRA, or permitted under the VWPA, is the full amount of loss.

> ... [W]hen the court determines the amount of loss, it is merely giving definite shape to the restitution penalty born out of the conviction.

438 F.3d at 337-38 (footnote omitted).

Hence, we agree with the other courts that have concluded that the *Booker-Blakely*principles have “no application” to orders of restitution. *Reifler,*446 F.3d at 118; *see also, e.g., Williams,*445 F.3d at 1311; *Sosebee,*419 F.3d at 454; *Wooten,*377 F.3d at 1144 n. 1.

IV.

We hold that the district court appropriately exercised its discretion in allowing the jury to consider the government’s summary charts during its deliberations under Rules of Evidence 611(a) and 703, but we clarify that the prior introduction of the underlying documents would not have barred the court from admitting the summaries into evidence under Rule 1006. We further hold that the court’s restitution order did not violate appellant’s Sixth Amendment jury trial right. Judicial fact-finding on the amount of loss is permissible under *Booker*because it does not increase the “maximum” punishment beyond that authorized by jury-found facts.

*For the foregoing reasons, we affirm both the judgment of conviction and the sentence imposed.*

*So ordered.*

1

. Following the government’s practice, we shall use the term "USDC” to refer to the United States District Court for the District of Massachusetts as a governmental purchaser of goods and services, reserving the term "court” or "the district court” to refer to the district court judge who handled the trial level proceedings in this case.

2

. Schroeder pled guilty and testified at Mil-kiewicz’s trial pursuant to an agreement with the government.

3

. The government presented evidence showing that the competitor, Richard Kelly of New England Office Supply ("NEOS”), submitted what he knew would be losing bids to the USDC, but did so because he also knew that, if Milkiewicz won the contract, NEOS would be the actual supplier.

4

. These counts alleged eight specific episodes of over-charging or under-delivering, including the one described above.

5

. The sentence also included a term of supervised release and a special assessment of $1,300.

6

. For example, the chart lists two court invoices dated October 9, 2001. The first listing shows that Milkiewicz billed the USDC for 400 cartons of paper, at $36.95 per carton, for a total price of $14,780. This is matched up with a vendor invoice, dated October 17, for 300 cartons of paper, at $23.50 per carton, totaling $7,050. The "Price Difference” *394column contains the figure "$4,035,” reflecting the mark-up of $13.45 on the 300 cartons. The "Quantity Difference Column” contains the figure "$3,695,” reflecting the $36.95 payment for 100 undelivered cartons.

The second listing for October 9 is for 60 cartons of color paper, at $45 per carton. It is matched with an invoice, also dated October 17, showing the purchase of 60 cartons at $32.50 per carton. The figure $750 appears in the "Price Difference” column (($45-$32.50) x 60), and the "Quantity Difference” column is blank.

The listing for October 5, 1999, depicts a complete non-delivery. Milkiewicz billed the USDC $8,760 for 240 cartons of paper, but there is no corresponding purchase identified. The columns showing "Quantity Purchased” and "Price Paid Per Unit” were blank, and the "Quantity Difference” was listed as the full $8,760.

7

. Many of the documents underlying the Tax Set — such as the USDC records — were the same as those used to generate the Transactions charts.

8

. Exhibit 2 is set up with five vertical boxes representing each year from 1997 to 2001 and a column on the left side listing various components of appellant’s income and expenses, including "Taxable Interest,” "Business Income/Loss,” "Other Income,” and "Credits.” The "Business Income” listing is subdivided into separate lines for appellant's and his wife's income. His business income is further subdivided into "Gross Income,” "COGS” ("cost of goods sold”) and other expenses. Each of the boxes containing data for a particular year is divided into two columns, one titled “Per Return” and one titled "Per Investigation.” For 1998, for example, the chart shows gross business income for appellant of $167,385 in the “Per Return” column and "$188,929” in the "Per Investigation” column. The corresponding amounts for "COGS” were $136,000 "Per Return” and $58,647.05 "Per Investigation.” Each annual column also included entries for the tax reported "Per Return” and the total tax owed "Per Investigation.”

9

. After generally advising the jury that the burden is on the government to prove guilt beyond a reasonable doubt and that no presumption of guilt can be drawn from a defendant’s failure to call witnesses or produce any evidence, the court added:

> In particular, I instruct you that Mr. Mil-kiewicz has no burden to produce evidence that he purchased goods that the government contends he did not deliver to the Clerk’s Office. The burden of proof on this issue, as is the case with all issues, remains with the government.

10

. Rule 403 provides for the exclusion of evidence if "its probative value is substantially outweighed by the danger of unfair prejudice. ...”

11

. The district court had the impression that Rule 1006 did not apply in such a case:

> I understand, based on my reading of the First Circuit's opinion in *Air Safety ...*that the distinction turns on whether the actual documents are admitted into evidence.... I understand the Court to say ... that where the underlying documents are themselves admitted into evidence, the use of a summary is not justified by Rule 1006.

12

. The rule states in full:

> The contents of voluminous writings, recordings, or photographs which cannot conveniently be examined in court may be presented in the form of a chart, summary, or calculation. The originals, or duplicates, shall be made available for examination or copying, or both, by other parties at [a] reasonable time and place. The court may order that they be produced in court.

13

. Rule 611(a) provides:

> *Control by Court.*The court shall exercise reasonable control over the mode and order of interrogating witnesses and presenting evidence so as to (1) make the interrogation and presentation effective for the ascertainment of the truth, (2) avoid needless consumption of time, and (3) protect witnesses from harassment or undue embarrassment.

14

. Courts usually do not allow such charts to go to the jury room absent consent of the parties. *See Harms,*442 F.3d at 375; *see also*31 *Federal Practice and Procedure*§ 8043, at 524 n. 9 (''[C]ourts often do not permit demonstrative evidence in the jury room.”); 6 *Weinstein’s Federal Evidence*§ 1006.08[4] (“While a court retains discretion to permit the jury to take such aids into their deliberation, most courts do not allow it.”).

15

. The records summarized must, of course, otherwise be admissible. *See, e.g., Janati,*374 F.3d at 273; *United States v. Jamieson,*427 F.3d 394, 409 (6th Cir.2005).

16

. For example, it required that the comparison columns in Exhibit 1 be re-labeled with less judgmental headings: "Profit by Margin" became "Price Difference” and "Profit by Shortage” became "Quantity Difference.” We note that, in requiring these refinements to make the Transactions Set more neutral, the district court undoubtedly was viewing them as Rule 1006 summaries, even though it ultimately felt compelled to rely upon Rule 611(a) in allowing them to be introduced.

17

. Toward the end of his lengthy explanation for allowing the jury to use the summaries, the court stated:

> I'm going to follow what I think is the First Circuit guidance on this.... So, I'm not admitting them pursuant to Rule 1006, although I think if it were up to me, I would.

18

. For example, at least three of the company representatives testified that their records dating to the relevant period were incomplete or unavailable.

19

. Appellant offers an undeveloped claim that Agent Wlodyka lacked the expertise to justify the assumptions built into the Transactions summaries about non-delivery of items to the USDC. The links between products ordered and products delivered arose logically, however, from the stipulated evidence. As the district court observed, the charts suggest correlations "based on temporal proximity, quantity, [and] product identification,” and "[t]hose assumptions are plain for the jurors." Moreover, the court explicitly told Wlodyka not to express opinions about the significance of the data on Exhibit 1. Following that admonition, Wlodyka explained the charts but did not comment on them.

20

. One portion of testimony reflecting this assumption unfolded as follows, with the questioning conducted by the prosecutor:

> Q. And, so, have you done the same thing on each tax year on your right-hand column where you’ve calculated-the numbers in bold are the numbers you stuck in from Exhibits 2a and 2b?

> A. Yes.

> Q. And you’ve gone through and made a calculation?

> A. Yes.

> Q. And then when you got a total for 1998, how much [tax due] was reported on the tax return that was filed?

> A. $22,668.

> Q. And how much did you calculate as total tax based on plugging in the numbers for 2a and 2b?

> A. $55,194.41.

> Q. And then did you do a subtraction to ... find the difference between those two numbers?

> A. Yes.

Wlodyka confirmed that the same calculation was done for each of the five years reported on the chart.

21

. The record does not indicate whether the government sought to collect the unpaid taxes reflected in Exhibit 2 outside of the restitution order.

22

. The restitution provisions of the MVRA and the Victim and Witness Protection Act (“VWPA”), 18 U.S.C. § 3663, are both enforced by means of 18 U.S.C. § 3664, which states in relevant part:

> In each order of restitution, the court shall order restitution to each victim in the full amount of each victim's losses as determined by the court and without consideration of the economic circumstances of the defendant.

18 U.S.C. § 3664(f)(1)(A). The later-passed MVRA supplemented the VWPA by, *inter alia,*making restitution mandatory for certain types of offenses.

23

.The Court first articulated the principle in *Jones v. United States,*526 U.S. 227, 243 n. 6, 119 S.Ct. 1215, 143 L.Ed.2d 311 (1999), where it stated: “[A]ny fact (other than prior conviction) that increases the maximum penalty for a crime must be charged in an indictment, submitted to a jury, and proven beyond a reasonable doubt.”

24

. Although restitution is “criminal” in many senses, *see United States v. Rostoff,*164 F.3d 63, 71 (1st Cir.1999) ("The nature of restitution is penal and not compensatory.”); *United States v. Savoie,*985 F.2d 612, 619 (1st Cir.1993) (noting that restitution imposed under the VWPA "is not a civil affair; it is a criminal penalty meant to have deterrent and rehabilitative effects”), we note that some courts have concluded that restitution is not the sort of “punishment” to which the Sixth Amendment applies. *See, e.g., United States v. Visinaiz,*428 F.3d 1300, 1316 (10th Cir.2005); *United States v. Carruth,*418 F.3d 900, 904 (8th Cir.2005); *United States v. George,*403 F.3d 470, 473 (7th Cir.2005). Such a view would, of course, render the *Booker*line of cases inapplicable to restitution. We do not choose to evaluate that alternate rationale here. Instead, for the reasons stated herein, we conclude that the reasoning of *Booker*does not require a jury to find the facts underlying a restitution order.

25

. Section 3664(a) states in relevant part:

> For orders of restitution under this title, the court shall order the probation officer to obtain and include in its presentence report, or in a separate report ... information sufficient for the court to exercise its discretion in fashioning a restitution order. The report shall include, to the extent practicable, a complete accounting of the losses to each victim, any restitution owed pursuant to a plea agreement, and information relating to the economic circumstances of each defendant.