
    UNITED STATES of America, Appellee-Cross-Appellant, v. CERTIFIED ENVIRONMENTAL SERVICES, INC., Nicole Copeland, Elisa Dunn, Defendants-Appellants-Cross-Appellees, Barbara Duchene, Thomas Juliano, Defendants, Sandy Allen, Frank Onoff, Defendants-Appellees.
    Docket Nos. 11-4872 LEAD, 11-4974 CON, 11-4969 XAP, 11-4875 CON, 11-4976 CON, 11-4972 XAP, 11-4877 CON, 11-4968 XAP.
    United States Court of Appeals, Second Circuit.
    Argued: June 14, 2013.
    Decided: May 28, 2014.
    
      Gabriel M. Nugent (Daniel J. French, on the brief) Hiscock & Barclay, LLP, Syracuse, NY, for Defendant-Appellant-Cross-Appellee Certified Environmental Services, Inc.
    Brian J. Fischer, Matthew D. Cipolla, Jenner & Block LLP, New York, NY (Carl N. We doff, Jenner & Block LLP, New York, NY; Donald T. Kinsella, Stockli, Greene, Slevin & Peters LLP, Albany, NY on the brief), for Defendanb-Appellant-Cross-Appellee Nicole Copeland.
    Dennis B. Schlenker, Esq., Albany, NY, for Defendant-Appellant-Cross-Appellee Elisa Dunn.
    Craig A. Benedict, Assistant United States Attorney (Rajit S. Dosanjh, Assistant United States Attorney, on the brief), for Richard S. Hartunian, United States Attorney for the Northern District of New York, Syracuse, NY, for Appellee-Cross-Appellant the United States of America.
    James R. McGraw, Esq., Syracuse, NY, for Defendant-Appellee Sandy Allen.
    Before: RAGGI and CARNEY, Circuit Judges, and RAKOFF, District Judge.
    
    
      
      . The Honorable Jed S. Rakoff, of the Southern District of New York, sitting by designation.
    
   RAKOFF, District Judge:

Certified Environmental Services, Inc. (“CES”); Nicole Copeland, former CES Technical Services Manager; and Elisa Dunn, former CES air monitor and field supervisor, appeal from their convictions of conspiracy, aiding and abetting violations of the Clean Air Act, mail fraud, and making false statements to federal officials. Seeking a new trial, these defendants contend that the district court improperly excluded evidence that they acted under a good-faith belief that they were complying with state law and that, in any event, their convictions and sentences were irreparably tainted by prosecutorial misconduct. The Government cross-appeals the sentences given to CES, Copeland, and Dunn, and appeals from the sentences given to Sandy Allen, a CES air monitor, and Frank Onoff, a supervisor at a contractor that performed improper asbestos abatement work. The Government argues that the district court erred in determining restitution, erred in calculating loss, misapplied the advisory sentencing guidelines, and imposed sentences that were substantively unreasonable.

For the reasons that follow, we vacate the convictions of CES, Copeland, and Dunn, and remand for a new trial. We also vacate the sentences of Allen and Onoff and remand for resentencing.

BACKGROUND

I. Regulatory Framework

Certain technical state and federal regulations governing the removal of asbestos underlie the charges in this case. Asbestos is severely toxic, and “medical science has not established any minimum level of exposure to asbestos fibers which is considered to be safe.” 20 U.S.C. § 3601(a)(3). Its complete removal is therefore required by both federal and state regulations.

A. Federal Regulations

Under the Clean Air Act, 42 U.S.C. §§ 7401-7515, the Environmental Protection Agency (“EPA”) is authorized to adopt what the agency has called “national emission standards for hazardous air pollutants,” including asbestos. See 40 C.F.R. pt. 61; 42 U.S.C. § 7412(c) & (d). The standards for asbestos are enforced in part by work-practice standards that govern covered renovation and demolition activities involving asbestos. See 40 C.F.R. § 61.145; see also 42 U.S.C. § 7412(h). As relevant here, these work-practice standards provide that, when removing regulated asbestos-containing material, the site owner or operator must wet the material to prevent it from escaping into the air and must ensure that the material remains adequately wetted until it is packed and sealed in leak-tight containers. See 40 C.F.R. §§ 61.145(c)(6)(i), 61.150. Asbestos-containing material is not adequately wetted “[i]f visible emissions are observed coming from [the] material.” Id. § 61.141. The owner or operator also must ensure that no visible emissions are discharged to the outside air and must deposit the material with an authorized disposal site as soon as practicable. Id. § 61.150(a)-(b). The Clean Air Act provides criminal penalties for any person who knowingly violates these work-practice standards. See 42 U.S.C. § 7413(c)(1).

Under the Toxic Substances Control Act (“TSCA”), 15 U.S.C. §§ 2601-2697, the EPA has promulgated additional regulations governing asbestos removal from elementary and secondary school facilities. See 40 C.F.R. pt. 763, subpt. E; see also 15 U.S.C. § 2643. As relevant here, these regulations require that, after any asbestos abatement project is completed, the school must confirm that the area is free of asbestos by, among other things, designating a person to “collect air samples using aggressive sampling.” 40 C.F.R. § 763.90(i)(2)(i). “[A]ggressive sampling” involves taking steps before and during sample collection to dislodge asbestos particles that may have settled on the surfaces in the work area. Beforehand, the “floors, ceiling and walls [must] be swept with the exhaust of a ... leaf blower,” and during collection, “[stationary fans” must be situated, one for each ten thousand cubic feet of worksite, with the “[f]an air ... directed toward the ceiling.” Id. pt. 763, subpt. E, App. A, III.B.7(d)(iii), (iv).

EPA regulations under the TSCA also contain provisions to avoid conflicts of interest. The regulations provide that “[s]ampling operations must be performed by qualified individuals completely independent of the abatement contractor.” Id. II.B.2, III.B.l. Similarly, “[a]ll sample preparation and analysis [must] be performed by a laboratory independent of the abatement contractor.” Id. II.E.l.

Asbestos abatement activities are also regulated by the Occupational Safety and Health Administration (“OSHA”) under the Occupational Safety and Health Act. See 29 C.F.R. § 1926.1101; 29 U.S.C. § 655. OSHA regulations impose numerous requirements on employers to ensure the wellbeing of employees who perform abatement work. See 29 U.S.C. § 654(a). For example, the regulations require employers to “provide or require the use of protective clothing, such as coveralls or similar whole-body clothing, head coverings, gloves, and foot coverings.” 29 C.F.R. § 1926.1101(i)(l). Employers must ensure that their employees enter and exit the work area through “[decontamination areas” designed to prevent asbestos from escaping into the surrounding environment. Id. § 1926.1101(j)(l)(i). Employers must also provide respirators to employees who work with certain categories of asbestos-containing materials. Id. § 1926.1101(h).

In addition, OSHA regulations require employers to “perform monitoring to determine accurately the airborne concentrations of asbestos to which employees may be exposed.” Id. § 1926.1101(f)(l)(i). Employees must wear air sampling devices to collect representative “breathing zone air samples,” id. § 1926.1101(f)(l)(ii), which are then subjected to laboratory analysis to determine each employee’s asbestos exposure. Individuals who perform this analysis must receive specialized training. See id. § 1926.1101, App. A.II.3.

B. State Regulations

Asbestos abatement activities in New York are also subject to state regulation under New York Industrial Code Rule 56 (the “Code Rule”), 12 N.Y.C.R.R. pt. 56 (1994), enforced by the New York State Department of Labor (“DOL”). The Code Rule at times mirrors federal requirements and at times is stricter. As relevant here, the Code Rule imposes requirements for preparing the work area, for performing abatement work, for cleaning up after the abatement work is complete, and for air monitoring. The Code Rule also contains certain standard variances and exceptions.

With respect to pre-abatement procedures, the Code Rule requires contractors to construct containment structures around the work area, known as “isolation barriers.” Id. § 56-8.1(j). These barriers consist of two layers of- plastic sheeting (referred to as “poly”), which must be placed over “all openings” in the work area, including windows, doors, skylights, corridors, and ducts (often referred to as “criticáis”). Id. In addition to the criticáis, contractors also must place two layers of poly over all surfaces in the work area, including floors, walls, and ceilings, exposing only the asbestos to be removed. Id. § 56-8.1(k)(5). All seams in the poly must be staggered from one another and sealed with tape. Id.

Like the OSHA regulations, the Code Rule also requires contractors to construct decontamination areas, which must be separated from the work area by “airlocks” to ensure that asbestos does not escape into the surrounding environment. Id. §§ 56-9.1-56-10.1. To the same end, the Code Rule also requires contractors to establish negative air pressure in the work area relative to the areas outside, “to ensure that contaminated air in the work area does not filter back to an uncontaminated area.” Id. § 56-6.1(c). Once the isolation barriers have been erected and negative pressure is established, the contractor must wait twelve hours before beginning abatement work to ensure that the barriers remain secure and intact. Id. § 56-11.1(b). The contractor then must maintain negative air pressure “continuously, 24 hours a day, from the start of the abatement work through the cleanup operations and clearance air monitoring.” Id. § 56-6.1(b).

With respect to the abatement itself, the Code Rule makes plain that “[n]o dry removal or disturbance of asbestos material shall be permitted.” Id. § 56.12.1(a). Rather, “[t]he asbestos material shall be wetted frequently,” id. § 56-12.1(b), and must be either bagged immediately once removed or dropped into a flexible catch basin, id. § 56-12.1(c). All abatement workers, including air monitors, must enter and exit the work area through the decontamination area, and must sign a log each time they do so. Id. § 56-4.1(a)-(b). Workers exiting the work area must decontaminate themselves, their equipment, and the bags containing asbestos waste before leaving. Id. § 56-5.1(a)-(f).

Once asbestos material has been removed from the work area, the Code Rule imposes detailed requirements for cleanup activities. First, the contractor must place all asbestos waste in proper containers. Id. § 56-15.2(a). Then the contractor must “wet-clean[ ]” the work area, id. § 56-15.2(b) — in other words, the contractor must “eliminat[e] asbestos contamination from surfaces, equipment or other objects by using cloths, mops, or other cleaning tools which have been dampened with amended water,” id. § 56-1.4(bz). After the first wet-cleaning, the contractor can remove the first layer of poly from the surfaces of the work area, leaving the criti-cáis in place. Id. § 56-15.2(c). The contractor must then observe a twelve-hour waiting period to allow agitated asbestos fibers to settle. After the waiting period, the contractor performs a second wet-cleaning, after which the second layer of poly can be removed from the surfaces in the work area. Id. § 56-15.2(d). After a second twelve-hour waiting period, the contractor performs a third wet-cleaning, after which all tools, equipment, and containers of asbestos waste are decontaminated and removed. Id. § 56-15.2(e)-(g). It is at this point that an air monitor like Defendant CES performs “[clearance air monitoring.” Id. § 56-15.2(h). Only after clearance air monitoring yields passing results can the contractor finally remove the criticáis and eliminate negative air pressure. Id. § 56-15.2(i).

With respect to air monitoring, the Code Rule prescribes several different kinds of monitoring. For most abatement projects, the Code Rule requires “background” air sampling to determine asbestos concentrations both inside and outside before the project commences, as well as “[p]re-abatement” air sampling while the work area is being set up. See id. § 56-17.1 tbl. 1. For non-minor abatement projects, the Code Rule also requires air sampling during the course of the project. Id. Most important, the Cod Rule, with minor exceptions not here relevant, requires “clearance air monitoring” on all abatement projects. Id. Clearance air monitoring consists of “[t]he collection of a volume of air using aggressive sampling techniques,” which is then “analyzed to determine the airborne concentration of fibers upon conclusion of an asbestos abatement project.” Id. § 56-1.4(x).

Because clearance air monitoring serves to confirm that all prior abatement work has been successful and that the work area is safe, the Code Rule carefully restricts how it is conducted. To begin with, the Code Rule, with minor exceptions not here relevant, provides that “[a]ir sampling and analysis shall not be performed by any party involved with the asbestos project.” Id. § 56 — 17.4(a). In addition, the individual who conducts air sampling must have “been trained in the selected methodology of sampling and analysis of asbestos,” and must possess a state-issued technician’s certificate. Id. § 56-17.4(b). Clearance air sampling may not commence until “no visible pools of liquid or condensation remain,” at least twelve hours after the third wet cleaning. Id. § 56-17.2(a). At that point, the technician collects an air sample by using a pump to draw air through a filter cassette that captures airborne asbestos fibers. Id. § 56-17.5(a). The Code Rule specifies the rate at which air is drawn through the cassette by the pump, which the technician must calibrate before and after each use. Id. § 56-17.5(b).

The Code Rule also requires the use of “aggressive sampling techniques,” similar to those mandated under the EPA’s TSCA regulations, to dislodge asbestos fibers that have settled out of the air. Before sampling begins, “the exhaust of forced-air equipment shall be directed against all walls, ceilings, floors, ledges and other surfaces in the rooms” for a minimum of “five minutes per 1,000 square feet of floor.” Id. § 56-17.2(f)(l). During sampling, a minimum 20-inch diameter fan “shall be placed in the center of each room,” with one fan per ten thousand cubic feet of work area. Id. § 56 — 17.2(f)(2). The fans must be “operated on slow speed and pointed toward the ceiling.” Id. Clearance air monitoring results are considered satisfactory when every sample taken shows an airborne asbestos concentration of less than 0.01 fibers per cubic centimeter, or the background level measured before the project commenced, whichever is greater. Id. § 56-17.8(a).

While the foregoing regulations generally apply to all asbestos abatement projects in New York, New York law recognizes two types of exceptions from these general rules. First, before 2006, the DOL recognized certain “applicable variances,” which set forth standard ways in which the Code Rule’s requirements could be modified. Most important for present purposes, these applicable variances included AV-120, which applied to projects for “the abatement of asbestos floor covering and mastic.” AV-120, pmbl. As relevant here, AV-120 allows the abatement contractor not to fully cover the walls of the work area with poly. See id. § 6. But the contractor still must maintain “negative air [pressure] ... within the abatement work areas.” Id. § 7. And, except as otherwise provided, “[a]ll other applicable provisions” of the Code Rule, including those requiring aggressive sampling techniques, continue to apply. Id. § 17.

The Code Rule also contains a set of exceptions for so-called “[i]n-plant operations.” Code Rule § 56-3.1(a). These operations are defined narrowly to include (1) projects that involve small amounts of asbestos material and are performed by the employees of the facility in question rather than by an outside contractor, and (2) projects involving the removal of specified types of asbestos material. Id. These exceptional materials do not include the floor coverings and mastics whose removal is governed by AV-120. As relevant here, in-plant operations are exempt from the Code Rule’s general requirements to erect isolation barriers around the work area and to maintain negative air pressure, so long as “the project is performed in a manner which will not expose the public to fiber concentrations exceeding background levels or .01 fibers per cubic centimeter, whichever is greater.” Id. § 56 — 3.1(b)(4). The Code Rule repeatedly provides, however, that in-plant operations are not exempt from the Code Rule’s general air monitoring requirements, including those requiring aggressive sampling techniques. See id. § 56-3.1(b)(2), (f); id. § 56-I.4(as)(2).

II. Proceedings Below

On June 10, 2010, a federal grand jury in the Northern District of New York returned a fifteen-count superseding indictment against CES, Copeland, Dunn, and Allen, as well as co-defendants Barbara Duchene and Thomas Juliano. Count One charged all of the defendants with conspiring in violation of 18 U.S.C. § 371 to defraud the United States by impeding the regulatory functions of the EPA and OSHA and to violate the Clean Air Act, the TSCA, and the mail fraud statute, 18 U.S.C. § 1341. As overt acts, the indictment charged the defendants with performing unlawful and fraudulent air monitoring on dozens of asbestos abatement projects in and around Syracuse, New York. Counts Two through Seven charged CES and Copeland with aiding and abetting Clean Air Act violations related to six abatement projects, in violation of 42 U.S.C. § 7413(c)(1), (2) and 18 U.S.C. § 2. Allen, Dunn, and Juliano were also charged in three of the aiding and abetting counts. Counts Eight through Thirteen charged CES and various defendants with substantive acts of mail fraud for mailing false clearance air monitoring reports, logs, and invoices in connection with six abatement projects, in violation of 18 U.S.C. §§ 1341 and 2. Copeland was charged with five counts of mail fraud, Allen with two, and Dunn and Juliano with one each. Finally, Counts Fourteen and Fifteen charged CES and Dunn with making false written statements to the EPA and OSHA regarding Dunn’s visual inspection of two project work areas, in violation of 18 U.S.C. § 1001.

As for Onoff, the original indictment, filed on May 28, 2009, charged Onoff with conspiracy, two counts of aiding and abetting Clean Air Act violations, three counts of aiding and abetting mail fraud, and one count of making false statements. On November 12, 2009, before the superseding indictment was returned, Onoff pled guilty to the conspiracy count pursuant to a plea agreement, and the remaining charges against him were dismissed.

A four-week trial against CES, Copeland, Dunn, Allen, and Juliano commenced on September 13, 2010. With respect to the conspiracy count, the Government presented evidence that the defendants conspired to aid two asbestos abatement companies, AAPEX Environmental Services, Inc. (“AAPEX”) and Paragon Environmental Services, Inc. (“Paragon”), in performing numerous illegal asbestos removals. These abatement companies engaged in what is known as “rip-and-run” removals, in which asbestos is stripped and removed dry, often without the safeguards needed to ensure that the surrounding area is not contaminated. Because they are cheaper to perform than proper removals, rip-and-runs can be lucrative, but can only go undetected if the abatement contractor can obtain passing final clearance air monitoring results from a company like CES.

To show an unlawful agreement among the alleged conspirators, the Government presented testimony from the owner and employees of AAPEX, who testified that the company had performed “at least two hundred” rip-and-run projects and used CES to perform air monitoring for the “majority” of them. G.A. 454, 483. The witness explained that AAPEX “used CES because we knew that we would get our final airs passed regardless of the methods used to take the asbestos down.” G.A. 454. With respect to another contractor, Paragon Environmental Services, Inc., a CES air monitor testified that Copeland told her that CES “had a close [working] relationship with” Paragon, G.A. 717, and as a result, the monitor did not even need to enter Paragon’s work areas to collect air samples. The monitor testified that, accordingly, she would instead hand blank air filter cassettes to Onoff (a Paragon supervisor) or a subordinate, whom the monitor would then trust to run the samples while she waited outside.

The Government also presented testimony from CES air monitors about the company’s air monitoring practices. The monitors testified that, following instructions from Copeland, CES air monitors routinely (1) began clearance air sampling without observing the required waiting periods and despite the visible presence of asbestos contamination and condensation throughout the work area; (2) failed to use aggressive air sampling techniques as required by the TSCA and the Code Rule; (3) falsified entries in sampling logs to conceal shoddy monitoring; and (4) failed to wear protective equipment, to decontaminate themselves and their equipment when exiting work areas, and to sign in and out of work areas.

The Government also presented testimony from a former CES lab technician. He testified (1) that, at Duchene’s direction, CES lab technicians analyzed thousands of samples without having received required training; (2) that Copeland, who also had not received training, improperly directed technicians not to count certain asbestos fibers; and (3) that the lab’s logbook, used to maintain quality control, was habitually out of date because of the lab’s high workload.

With respect to the Clean Air Act charges, the Government presented evidence that CES, Copeland, Dunn, and Allen aided and abetted rip-and-run asbestos removals at six worksites. The Government presented testimony that CES monitors failed to conduct visual inspections, collected air samples despite visible asbestos debris, failed to use aggressive air sampling techniques, and certified clearance air monitoring samples that should not have passed. In one instance, an employee of an abatement contractor testified that Dunn, a CES air monitor and supervisor, had helped him to reclean a dusty work area, in violation of the Code Rule’s conflict of interest regulations.

With respect to the mail fraud charges, the Government presented evidence that CES, Copeland, Allen, and Dunn prepared and mailed air monitoring reports, invoices, and logs representing that CES had conducted air monitoring in accordance with legal, regulatory, and industry standards. In actuality, according to the Government’s evidence, CES had done no such thing.

Finally, with respect to the false statement charges, the Government presented evidence that Dunn completed two “Visual Inspection/Clearance Air Sampling” certifications in connection with a particular abatement project. In these certifications, Dunn stated that she had “visually inspected the basement work area and found [that] the abatement appears to meet the scope of work provided” and “no visible debris” or “dust” was “apparent.” G.A. 1078-79. An employee of the contractor, however, testified that Dunn had in fact helped him try to clean up visible debris. And an EPA agent testified that when confronted with photographs showing the condition of the work area, Dunn admitted that the area “should never have passed final air clearances.” G.A. 777.

For the defendants’ part, they argued both that the Government’s evidence was unreliable and that, in any event, they had acted in the good-faith belief that their conduct was consistent with relevant legal requirements. The defendants attacked the credibility of all of the Government’s key witnesses, noting that many witnesses had motives to lie and were testifying about events that had allegedly occurred many years earlier. The defendants also noted that several witnesses left CES before any of the charged projects commenced. The defendants similarly attacked the accuracy and relevance of the Government’s documentary and photographic evidence. For example, the defendants noted that photographs of the work-sites were not contemporaneous with the events in issue and that debris could have been concealed from CES air monitors behind the containment barriers. Similarly, the defendants noted that the documents like sample logs and lab reports did not show whether proper air sampling or analysis techniques were used.

The defendants also presented their own evidence to rebut the Government’s case. For example, the defendants presented evidence that CES frequently gave failing grades to clearance air samples collected from AAPEX projects — including two of the projects alleged in the indictment. The defendants also maintained that they had little financial incentive to engage in the charged misconduct, as CES in fact was turning down work from other contractors during the relevant period. In addition, CES worked on more than a third of the charged projects under a lucrative long-term contract with Syracuse University, which would have been jeopardized by substandard work. Copeland and another CES supervisor, Dan Hoosock, also testified that Copeland actually reported AAPEX to the DOL in 2005, after AAPEX’s owner attempted to direct a CES air monitor to conduct air sampling improperly.

More broadly, Copeland and Hoosock testified that CES had conducted air sampling in accordance with a good-faith interpretation of the Code Rule, whereby aggressive sampling was not required unless the work area had containment barriers erected over all critical openings and all floors, walls, and ceilings. The defendants contended that any other interpretation would require agitating contaminated air in ways that would risk dispersing asbestos-containing material from work areas into the surrounding environment. The defendants also noted that under any reading of the Code Rule, aggressive sampling is not required in all cases, and presented evidence that there was long-running discussion within the industry about when aggressive sampling should be conducted.

On October 12, 2010, the jury found CES, Copeland, Dunn, and Allen guilty of all counts against them, and acquitted Juli-ano of all charges against him. On October 26, 2010, CES, Copeland, Dunn, and Allen moved for a judgment of acquittal or in the alternative for a new trial, which the district denied on December 3, 2010.

With respect to sentencing, on August 1, 2011, after holding an evidentiary hearing, the district court issued a Memorandum Decision and Order determining the total restitution owed to the victims and apportioning responsibility for that restitution among the defendants. On October 21, 2011, CES was sentenced principally to five years of probation, a fine of $20,000, and restitution of approximately $117,000. Copeland principally received five years of probation, twelve consecutive weekends of intermittent confinement, no fine, and approximately $23,000 in restitution. Dunn and Allen each principally received “time served (1 day),” representing the brief time each had spent being processed by the U.S. Marshals following their initial appearances, no fine, and approximately $6,000 in restitution. On November 8, 2011, Onoff was sentenced principally to “time served (1 day),” no fine, and approximately $4,000 in restitution.

These appeals and cross-appeal followed.

DISCUSSION

I. The Defendants ’ Appeal

In their appeal, CES, Copeland, and Dunn seek a new trial based upon (1) improper prosecutorial bolstering of Government witnesses based on those witnesses’ cooperation agreements; (2) the exclusion of evidence related to the defendants’ good faith; (3) the Government’s belated production of certain discovery material, allegedly in violation of Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963); and (4) improper remarks in the Government’s rebuttal summation. The Government concedes error in many of these instances, but argues that the errors were harmless. We first consider each category of alleged trial error separately, and then consider the cumulative prejudice caused by those errors that we find have been established.

A. Bolstering Based on Witness Agreements

Most of the Government’s witnesses were given either immunity or the possibility of reduced sentences conditioned on their cooperating with the Government by providing testimony. “Cooperation agreements ... demand careful treatment under principles governing attack on and rehabilitation of witnesses’ credibility.” United States v. Cosentino, 844 F.2d 30, 32 (2d Cir.1988). These principles are well established in this Circuit, and can be summarized in a few straightforward propositions.

First, the existence of a cooperation agreement is a “double-edged sword,” United States v. Arroyo-Angulo, 580 F.2d 1137, 1146 (2d Cir.1978), which can be wielded by the defense and the Government. On the one hand, a cooperation agreement can provide ammunition for the defense to impeach the credibility of a Government witness, both by specifying the benefits the cooperator has received or will receive if he testifies at the Government’s behest and also “by revealing the witnesses] criminal background” or other prior wrongdoing. Cosentino, 844 F.2d at 32. On the other hand, the Government can use cooperation agreements to rehabilitate witnesses whose credibility has been questioned. Id. at 33. That is because cooperation agreements generally contain so-called “truth-telling” provisions, which “set[ ] out promises to testify truthfully as well as penalties for failure to do so, such as prosecution for perjury and reinstatement of any charges dropped pursuant to the deal.” Id. at 32.0verall, “the entire cooperation agreement bolsters more than it impeaches.” Id. at 33 (quoting United States v. Edwards, 631 F.2d 1049, 1052 (2d Cir.1980)) (emphasis added).

Second, the Government may not introduce the bolstering aspects of a cooperation agreement unless and until the witness’s credibility has been questioned in ways that “open the door” to the admission of the agreement. This proposition stems from “well established rules of evidence” relating to relevance, hearsay, bias, completeness, and otherwise, that taken together, provide that “absent an attack on the veracity of a witness, no evidence to bolster his credibility is admissible.” Arroyo-Angulo, 580 F.2d at 1146 (citing McCormick on Evidence, § 49 at 102 (2d ed.1972); 3 Weinstein’s Evidence ¶ 607(08)). An attack opening the door to such rehabilitation may take different forms. “A witnesses] credibility is often tested by a sequence of attack on cross-examination followed by rehabilitation on redirect.” Cosentino, 844 F.2d at 33. An attack also “may come in a defendant’s opening statement. If the opening sufficiently implicates the credibility of a government witness, we have held that testimonial evidence of bolstering aspects of a cooperation agreement may be introduced for rehabilitative purposes during direct examination.” Id. But whatever form the attack takes, unless and until it occurs the Government may not rehabilitate a witness by introducing the bolstering aspects of an agreement, whether by introducing the truth-telling provisions in particular or the agreement as a whole.

Third, although the Government may not introduce the bolstering aspects of an agreement until after the witness’s credibility has been attacked, this restriction does not apply to an agreement’s impeaching aspects, which the Government is free to introduce even on the witness’s direct examination. We have recognized that “[i]t may sometimes be useful ... to develop impeaching matter in direct examination of a ‘friendly’ witness in order to deprive an adversary of the psychological advantage of revealing it to the jury for the first time during cross-examination.” Id. For this reason, the “impeaching aspects of cooperation agreements may be brought out in the government’s direct examination of a witness who testifies pursuant to such an agreement.” Id. As we have explained,

[e]ven in the absence of a prior attack on credibility, “the elicitation of the fact of the agreement and the witnesses] understanding of it, as a motivation for the witness to testify for the Government, should be permitted on direct examination in order to anticipate cross-examination by the defendant which might give the jury the unjustified impression that the Government was concealing this relevant fact.”

Id. (quoting Edwards, 631 F.2d at 1052).

Finally, while the Government may, after a witness’s credibility is attacked, rehabilitate the witness using a cooperation agreement, “it is well established that prosecutors may not [personally] ‘vouch for their witnesses’ truthfulness.’ ” United States v. Carr, 424 F.3d 213, 227 (2d Cir.2005) (quoting United States v. Modica, 663 F.2d 1173, 1179 (2d Cir.1981)).

In the case at bar, the Government violated these principles repeatedly, often in direct contravention of clear orders from the district court. During the Government’s opening statement, the prosecutor permissibly told the jury that it would call witnesses who “engaged in absolutely deplorable behavior. I am not going to shine it up at all. They were involved in a conspiracy. Their conduct was despicable. They are here under plea agreements. They pled guilty to felonies.” J.A. 170. But the prosecutor then went further, telling the jury, “Their obligation is to tell the truth.” Id. Defense counsel objected, and the district court sustained, telling the prosecutor, “Don’t get into any bolstering, Mr. Benedict, about your witnesses. Just tell who is going to testify. Don’t try to tell any bolstering about them. You understand that.” Id. The prosecutor replied, “Yes, Your Honor, I do.” Id.

But then he continued: “We will introduce their plea agreements, and you will see through their plea agreements what their obligations are, what benefits they get, and what happens if they don’t tell the truth.” Id. Defense counsel again objected, and the district court again sustained, stating, “You better stand away from that, Mr. Benedict. We are not going to have any bolstering of these witnesses before we even hear them. And you are not even supposed to do it afterwards. Let’s go.” J.A. 170-71.

But the prosecutor continued on the same topic yet again: ‘You are going to hear that the witnesses will be immuned [sic] ..., and they will tell you under what conditions they were given immunity.” Id. at 170. Defense counsel objected yet again, and the district court stated, “All right. That is the end of it. Do you want me to conclude your opening statement right now, Mr. Benedict?” Id. The district court explained, “Stay away from all of those witnesses. They will be on the stand. The jury can decide their credibility at that time, and we don’t need any more statements from you about their credibility or lack thereof. Do you understand?” Id. The prosecutor responded in the affirmative, and apologized to the judge and the jury.

The defendants did not attack the credibility of the Government’s witnesses in their opening statements. But after trial commenced, the Government introduced into evidence on the direct examination of nine of its witnesses the entirety of their largely — bolstering cooperation agreements, notwithstanding strenuous defense objections on all but two occasions. The Government even went so far as to ask one witness on direct examination about his “understanding of what happens to your immunity if you provide false information today.” G.A. 499.

Finally, in its opening summation, the prosecutor personally vouched for the truthfulness of these witnesses, stating that “the immunity agreements are very simple. We wanted to ensure that people taking the stand provided the truth.” J.A. 264. Defense counsel objected, and the district court sustained the objection.

On appeal, the Government now concedes that the prosecutor’s discussion of the bolstering aspects of the immunity agreements during the Government’s opening statement was improper. Similarly, the Government does not dispute that the introduction of the immunity agreements on direct examination of its witnesses, as well as some of the questions on direct examination relating to the agreements, were premature, though the Government notes that defense counsel sometimes failed to object. The Government also concedes that the prosecutor’s statement that “we wanted to ensure that people taking the stand provided the truth,” id. (emphasis added), constituted impermissible vouching.

B. Exclusion of Evidence of Good Faith

We review a district court’s rulings on the admissibility of evidence for abuse of discretion. See Boyce v. Soundview Tech. Grp., Inc., 464 F.3d 376, 385 (2d Cir.2006). Here, the defendants challenge the district court’s exclusion of three pieces of evidence they claim supported their argument that they acted in the good-faith belief that they were conducting air monitoring in compliance with the Code Rule.

First, the district court excluded testimony from Daniel Hoosock, a CES air monitoring supervisor, regarding a conversation he had with an unknown DOL employee in 1994. Hoosock was prepared to testify that during this conversation, he asked the DOL for clarification regarding the circumstances under which air monitors were required to use aggressive sampling techniques. In particular, Hoosock supposedly asked whether air monitors must use aggressive sampling for projects where the work area was not fully enclosed under negative air pressure. Hoo-sock explained that he was concerned that in the absence of a negative pressure full enclosure, aggressive sampling ran the risk of spreading asbestos fibers out of the work area into the surrounding environment. The DOL employee purportedly advised Hoosock “[t]hat if the work did not require a negative pressure enclosure, ... aggressive clearance wouldn’t be required.” J.A. 248. Although Hoosock did not memorialize this conversation in writing, the defendants contend that it is corroborated by a CES document called the “Cheat Sheet,” according to which it was CES policy to use aggressive air sampling only for projects “with Full Containment.” J.A. 486.

Second, the district court excluded an email exchange between Hoosock and the DOL in 2006. The exchange began on August 17, 2006, approximately one year after government investigators began interviewing CES employees about the company’s air monitoring practices, when Hoo-sock sent an email to the DOL as follows:

I was wondering if you could provide some clarification regarding clearance air sampling requirement for asbestos abatement projects. Prior to the amending of the Code Rule 56 in 1994, the vast majority of abatement projects were completed under full negative pressure containments. When the Code Rule was amended in 1994, and in particular under the In-Plant and Emergency Operations guidelines ..., many projects were completed without the use of containments and/or negative pressure, often times with only barrier tape and signs demarcating the active work area. Some time shortly after the 1994 revisions, I spoke with someone at the Department regarding the proper procedures to be utilized for collecting clearance air samples.
The specific concern at the time was [that] the utilization of aggressive air sampling techniques, on projects completed without the presence of a negative pressure enclosure, could potentially/likely result in the spreading of asbestos fibers into areas outside of the regulatory work area....
As a result of my inquiry, I was advised at the time that the use of aggressive air sampling techniques would only be prudent and required when abatement efforts were completed within a negative pressure enclosure (full containment or tent enclosure). On projects where a negative pressure containment was not utilized, I was advised that the work area should be free of visible asbestos/debris, no visible pools of liquid or condensation should remain, and clearance air samples should be collected in the same manner as Background air samples....
While I believe it to be the case, I was wondering if you could clarify for me whether or not the interpretation I previously received is still valid.

J.A. 480-81. The next day, Christopher Alongé, DOL Senior Safety and Health Engineer, responded, stating in relevant part:

Yes, you are correct. For regulated abatement work areas that are not required to have a negative pressure containment enclosure of some kind, then aggressive methods are not required to be utilized. For example, all negative pressure tent enclosures would be subject to a[g]gressive methods, as well as any room, area, or space subject to negative pressure ventilation requirements during abatement. This clarification will be added to the first revision of the [Code Rule] guidance document....

J.A. 479.

Third, the district court excluded the Code Rule guidance document referenced at the close of the 2006 email exchange, which the DOL had published on January 30, 2009. The 2009 guidance document simply restated the above email exchange with nonsubstantive modifications as part of a list of “Frequently Asked Questions.” J.A. 484.

The Government defends these evidentiary rulings on the grounds that the proffered evidence was inadmissible hearsay and was irrelevant. But the statements were not hearsay since they were offered, not for their truth, but for their effect on defendants’ state of mind, which was very much in dispute. Hearsay, of course, is an out-of-court statement offered to prove the truth of the matter asserted. Fed.R.Evid. 801(c). An out-of-court statement offered for some other purpose, such as to show that a statement was made, United States v. Kohan, 806 F.2d 18, 22 (2d Cir.1986), to demonstrate the statement’s effect on the listener, United States v. Puzzo, 928 F.2d 1356, 1365 (2d Cir.1991), or to show the circumstances under which subsequent events occurred, United States v. Pedroza, 750 F.2d 187, 200 (2d Cir.1984), is not hearsay. In this case, the proffered evidence was not offered for its truth but to show that the statements occurred and that, given their effect on the defendants’ state of mind, they provided a good faith basis for the defendants’ actions. Indeed, the district court acknowledged as much. See J.A. 153 (noting that the evidence was not inadmissible hearsay to the extent “offered to prove the state of mind of the defendant”). But the district court also found that the proffered evidence was irrelevant because it was “too remote in time and in substance.” J.A. 251. Temporally, the district court noted that the 1994 conversation occurred five years before the charged conspiracy began in 1999, and “the 2006 e-mails occurred after the majority of the charged conduct in this case, and applied only to alleged conduct that occurred prior to the emails.” J.A. 153. And the 2009 guidance document was published after the last charged project had been completed. Moreover, the district court found that the proffered evidence concerned “[in-plant] operations,” an exceptional designation under the Code Rule that did not apply to any of the projects charged in the indictment. J.A. 251. The district court further explained that, according to Hoosock’s own proffered testimony, “aggressive air monitoring is required on all projects with negative and containment or enclosure. And that is the vast majority of the projects here.” Id.

In general, evidence is relevant if it has any tendency to make a material fact more or less probable than it would be otherwise. See Fed.R.Evid. 401. “[E]vidence need not be conclusive in order to be relevant. An incremental effect ... is sufficient.” Doe v. N.Y.C. Dep’t of Soc. Servs., 649 F.2d 134, 147 (2d Cir.1981). With respect to temporal relevance, we have held that “[a] suggestion that an item of evidence relates to a period that is too remote goes to both the item’s relevance and its weight.” Fitzgerald v. Henderson, 251 F.3d 345, 365 (2d Cir.2001). At the same time, our case law “recognizes the possibility that an expression of state of mind on one occasion may be relevant to state of mind at a later time where the statement reflects ‘a continuous mental process.’ ” United States v. Farhane, 634 F.3d 127, 172 (2d Cir.2011) (Raggi, /., concurring) (quoting United States v. Cardaseia, 951 F.2d 474, 488 (2d Cir.1991)).

While evidentiary rulings are reviewed for abuse of discretion, the question of the defendants’ intent and good faith was a contested issue in this case, and the definition of relevance under Fed. R.Evid. 401 is very broad. On review, we find that the district court abused its discretion in finding that the proffered evidence was temporally irrelevant. With respect to the 1994 conversation, while that evidence predated the charged conspiracy by five years, it concerned the nature of an ongoing regulatory requirement and, according to the defendants, informed the creation of a consistent company policy. In addition, while CES air monitors attended state-mandated refresher courses during the relevant period, no pertinent portion of the Code Rule changed between the 1994 conversation and the commencement of the charged conspiracy in 1999, nor did the DOL promulgate any updated guidance that would disabuse the defendants of the understanding purportedly conveyed to Hoosock. The 1994 conversation thus concerned “a pattern of activity that continued up to the time of the charged conduct.” United States v. Curley, 639 F.3d 50, 59 (2d Cir.2011). In these circumstances, we do not perceive how the passage of time rendered the 1994 conversation irrelevant.

As for the 2006 email exchange, it is true that that evidence post-dated all of the relevant projects charged in the indictment. But, again, the defendants presented evidence that CES conducted air monitoring pursuant to a longstanding interpretation of the Code Rule embodied in a standard company policy. The 2006 email exchange thus provides evidence of the content of a longstanding continuous mental process. Moreover, the DOL representative’s favorable response to Hoo-sock’s inquiry is consistent with Hoosock’s proffered testimony regarding the 1994 conversation, and therefore would tend to corroborate that testimony.

Furthermore, while the Government notes that the 2006 email exchange took place after Hoosock was aware of the Government’s investigation into CES, that fact at most raises questions about Hoosock’s credibility. But again, the email exchange was not offered for the truth of the matters asserted therein by Hoosock or the DOL representative. And the most probative part of the exchange is not Hoosock’s initial inquiry, but DOL’s response thereto.

Finally, because the 2009 guidance document memorialized the 2006 email exchange, it served to corroborate that evidence, and therefore was admissible for the same reasons.

As for the district judge’s finding that the DOL guidance only concerned “[in-plant] operations,” J.A. 251, this finding invaded the province of the jury. While Hoosock’s email in 2006 mentions that particular exception under the Code Rule, the guidance he sought was arguably broader. In the email Hoosock states his understanding that aggressive air sampling techniques are required “when abatement efforts [a]re completed within a negative pressure enclosure (full containment or tent enclosure),” but not “where a negative pressure containment [i]s not utilized.” J.A. 480. The DOL representative responds, “Yes, you are correct.” J.A. 479. At the very least, this guidance reasonably can be read to allow air monitors to forgo aggressive monitoring where a negative pressure enclosure is not employed, regardless of whether or not the project falls within the in-plant operations exception. While this may not be the only way, or even the best way, to read the guidance, the defendants were entitled to present their reading to the jury.

Similarly unpersuasive is the district court’s conclusion that the guidance was inapposite because a full negative pressure enclosure was required on “the vast majority of the projects here.” J.A. 251. Regardless of when negative pressure enclosures were in fact required under the Code Rule, Copeland and Hoosock testified that they believed in good faith that enclosures sufficient to trigger aggressive sampling were not required under AV-120, and the evidence showed that many of the charged projects were in fact conducted without any kind of negative pressure enclosure. The defendants contended that to have conducted aggressive sampling in such circumstances would have implicated the concerns Hoosock voiced about “spreading of asbestos fibers into areas outside of the regulatory work area,” J.A. 481, concerns the DOL had recognized as legitimate.

C. Brady Claim

Under Brady and its progeny, “the Government has a constitutional duty to disclose favorable evidence to the accused where such evidence is ‘material’ either to guilt or to punishment.” United States v. Coppa, 267 F.3d 132, 139 (2d Cir.2001). “Favorable evidence includes not only evidence that tends to exculpate the accused, but also evidence that is useful to impeach the credibility of a government witness.” Id. “[E]vidence is ‘material’ within the meaning of Brady when there is a reasonable probability that, had the evidence been disclosed, the result of the proceeding would have been different,” such that the failure to disclose “ ‘undermine[s] confidence in the verdict.’ ” Cone v. Bell, 556 U.S. 449, 469-70, 129 S.Ct. 1769, 173 L.Ed.2d 701 (2009) (quoting Kyles v. Whitley, 514 U.S. 419, 435, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995)). Thus, “[t]here are three components of a true Brady violation: (1) The evidence at issue must be favorable to the accused, either because it is exculpatory or because it is impeaching; (2) that evidence must have been suppressed by the [Government], either willfully or inadvertently; and (3) prejudice must have ensued.” United States v. Jackson, 345 F.3d 59, 71 (2d Cir.2003) (quoting Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)).

“Although the government’s obligations under Brady may be thought of as a constitutional duty arising before or during the trial of a defendant, the scope of the government’s constitutional duty ... is ultimately defined retrospectively, by reference to the likely effect that the suppression of particular evidence had on the outcome of the trial.” Coppa, 267 F.3d at 140. As a result, “strictly speaking, there is never a real ‘Brady violation’ unless the [Government’s] nondisclosure was so serious that there is a reasonable probability that the suppressed evidence would have produced a different verdict.” Strickler, 527 U.S. at 281, 119 S.Ct. 1936. This aspect of Brady affects not only what the Government is obligated to disclose, but when it is required to do so. Temporally, “the timing of a disclosure required by Brady is ... dependent upon the anticipated remedy for a violation of the obligation to disclose: the prosecutor must disclose ... exculpatory and impeachment information no later than the point at which a reasonable probability will exist that the outcome would have been different if an earlier disclosure had been made.” Coppa, 267 F.3d at 142.

Here, the defendants claim that the Government violated its Brady obligations by failing in a timely manner to turn over certain handwritten interview notes taken by EPA Agent Michael Dwyer. During pretrial discovery, the Government turned over typewritten summaries of investigative interviews Agent Dwyer conducted, but no handwritten notes. During the Government’s case-in-chief, Agent Dwyer testified about interviews he conducted with three CES air monitors — Dunn, Juli-ano, and Michael Pettit. As relevant here, Dwyer testified that Juliano and Pettit told him that they had never used aggressive air sampling techniques while employed at CES. Dwyer also testified that Dunn had initially stated that she had “primarily not” used aggressive sampling techniques, J.A. 177, but in a later interview stated that she “always utilized aggressive air monitoring techniques when required.” G.A. 408.

Several days after Dwyer testified, the Government called an investigator with the New York State Department of Environmental Conservation, James Masuicca, who was present with Dwyer at the interviews of Dunn and Juliano. Masuicca testified that Dwyer had taken handwritten notes during the interviews, and that Ma-suicca had reviewed those notes before testifying. Having previously been unaware of Dwyer’s notes, defense counsel requested that they be produced. After a colloquy, the Government agreed to turn the notes over, explaining that it had not realized that Masuicca had reviewed the notes before testifying. Based on this belated disclosure, defense counsel moved to strike Dwyer’s testimony and dismiss the indictment. The district court denied that motion, but gave the defendants time to review the notes and leave to recall Dwyer if they so desired.

It transpired that Dwyer’s notes of the interview with Juliano contained an unexplained reference to the CES “Cheat Sheet,” which is not mentioned in Dwyer’s typewritten interview reports. As noted above, the Cheat Sheet indicates that it was CES policy to use aggressive sampling techniques for all projects “with Full Containment.” The defendants maintain that Juliano’s reference to the Cheat Sheet supported their theory that the defendants operated under a good-faith belief that, under the Code Rule, air monitors were not required to use aggressive sampling techniques in the absence of a full enclosure with negative air pressure. Defense counsel cross-examined Masuicca about Dwyer’s notes and the reference to the Cheat Sheet, but elected not to recall Dwyer. Nevertheless, the defendants contend that the Government’s belated disclosure of the notes prevented them from effectively using the notes to undermine Dwyer’s testimony.

The Government argues that Dwyer’s handwritten notes were not material under Brady and that the timing of their disclosure did not prevent their effective use at trial. We agree. To begin with, Dwyer’s notes were at best marginally helpful to the defense. There was no dispute at trial that the Cheat Sheet existed or that it had been referenced in investigative interviews. Indeed, defense counsel cross-examined Pettit about statements he made regarding the Cheat Sheet during his interview with Dwyer. Moreover, the reference to the Cheat Sheet was not inconsistent with Dwyer’s testimony that Juliano had admitted that he had never used aggressive sampling techniques while employed at CES. The Cheat Sheet concerned CES’s written policy with regard to air sampling; Dwyer testified as to what Juliano stated he actually did, which may or may not have complied with company policy or with the Code Rule and other applicable regulations. And to the extent defense counsel believed that Dwyer’s notes truly contradicted Dwyer’s testimony, the district court afforded the defense the opportunity to recall Dwyer to try to impeach him. Whatever effect an earlier disclosure of the notes would have had on the trial, it falls far short of “‘under-minting] confidence in the verdict.’ ” Cone, 556 U.S. at 470, 129 S.Ct. 1769 (quoting Kyles, 514 U.S. at 435, 115 S.Ct. 1555).

This is not to suggest, however, that the prosecutors did nothing wrong in failing to disclose Dwyer’s handwritten notes along with the typewritten summaries. To begin with, we see no reason — and the Government offers none — why the prosecutors here could not and should-not have “acted in favor of disclosing the Brady material earlier.” United States v. Rittweger, 524 F.3d 171, 182 (2d Cir.2008).

Moreover, Brady is not the only source of the Government’s disclosure obligations. Federal Rule of Criminal Procedure 16(a)(1)(B) provides that, “[u]pon a defendant’s request, the government must disclose to the defendant ... (ii) the portion of any written record containing the substance of any relevant oral statement made before or after arrest if the defendant made the statement in response to interrogation by a person the defendant knew was a government agent.” Fed.R.Crim.P. 16(a)(1)(B) (emphasis added). By its plain terms, this rule encompasses both typewritten summaries and contemporaneous handwritten notes. The prosecutors violated their obligations under this rule in this case.

Moreover, the Government’s failure to disclose Dwyer’s interview notes raises a further concern under 18 U.S.C. § 3500. Insofar as Dwyer testified as a witness to various air monitors’ statements, his interview notes can be viewed as a witness’s prior “statement” relating to the subject matter of his testimony, which statement the Government was obliged to disclose pursuant to § 8500.

Nonetheless, for the reasons already explained, the district court’s ruling here reduced any prejudice to a minimum. Accordingly, while “we are disappointed by the government’s failure to disclose [Dwyer’s handwritten notes] in a more timely fashion,” Rittweger, 524 F.3d at 183, that failure does not support the defendants’ request for a new trial in this case.

D. The Government’s Rebuttal Summation

As already noted in connection with the Government’s opening statement and opening summation, “[i]t is well established that prosecutors may not ‘vouch for their witnesses’ truthfulness.’ ” Carr, 424 F.3d at 227 (quoting Modica, 663 F.2d at (1179)). A prosecutor also may not “express his or her personal belief or opinion as to the truth or falsity of any testimony or evidence or guilt of the defendant.” Modica, 663 F.2d at 1178 (quoting ABA Standards for Criminal Justice, Standard 3 — 5.8(b) (1980)). These proscriptions are central to the fair administration of justice, as comments that “convey the impression that evidence not presented to the jury, but known to the prosecutor, supports the charges against the defendant ... jeopardize the defendant’s right to be tried solely on the basis of the evidence presented to the jury.” United States v. Young, 470 U.S. 1, 18, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985). Moreover, “the prosecutor’s opinion carries with it the imprimatur of the Government and may induce the jury to trust the Government’s judgment rather than its own view of the evidence.” Id. at 18-19, 105 S.Ct. 1038. As we have explained,

The prosecutor is cloaked with the authority of the United States Government; he stands before the jury as the community’s representative. His remarks are those, not simply of an advocate, but rather of a federal official duty-bound to see that justice is done. The jury knows that he has prepared and presented the case and that he has complete access to the facts uncovered in the government’s investigation. Thus, when the prosecutor conveys to the jurors his personal view that a witness spoke the truth, it may be difficult for them to ignore his views, however biased and baseless they may in fact be. Personal expressions of opinion are especially improper if phrased to leave the impression that the prosecutor’s opinion is based on matters in the investigative file and not in the trial evidence.

Modica, 663 F.2d at 1178-79 (2d Cir.1981) (internal citation omitted).

Despite these clear proscriptions, the prosecutor here, as the Government now concedes, made repeated improper comments in his rebuttal summation. Such improprieties, arising when defense counsel no longer has an opportunity to reply, are particularly egregious.

First, the prosecutor began his rebuttal summation by stating:

[L]adies and gentleman, apparently we have made a terrible mistake. Apparently we have misunderstood the evidence. The agents who have worked as you have heard for thirteen years in this field don’t know how to investigate a case. Don’t know how to find out if asbestos debris and other materials were left behind or if illegal activities occurred. How did this happen? How was it that we came to this situation where Department of Justice people, Assistant U.S. Attorneys from this town and this community—

J.A. 277. Defense counsel objected, and the district court sustained, stating, “Come on, Mr. Benedict. Just argue the case.” Id. The Government now concedes that the prosecutor’s reference to the local community constituted impermissible vouching insofar as it impermissibly injected the prosecution team’s own beliefs into the case.

Second, after noting that the punishment AAPEX and its owner received was outside the record of this case, the prosecutor then explained to the jury:

There are all sets of circumstances that you don’t know anything about that we can’t go into, that we can’t explain to you. It is just a fact. [EPA Agent] Derx has been prosecuting cases for thirteen years and is a recognized expert in the field. I assure you, he has more to do than he knows what to do with.

Id. The Government now concedes that this comment too, which referenced facts not in evidence, was improper.

Finally, the prosecutor made reference to the effects the verdict would have:

[D]id they act over the course of nine years with sympathy for their victims? Did they in any way show a dedication to complying with a law that protects the public from a known carcinogen? Did they in any meaningful way instruct their employees to follow the rules? ... [Copeland] instructed everybody to violate the law. She gathered them. She marshalled them. She still works for CES. CES is still in business. Your verdict is going to have consequences, ladies and gentlemen.

J.A. 281. Defense counsel then objected, and the district court overruled the objection. Id. The Government concedes that the “consequences” comment was improper in that it urged the jury to reach a decision based on impermissible considerations — viz., protecting the public and deterring future lawbreaking. While the criminal justice system as a whole strives to achieve such protection and deterrence, the jury role in that process is specifically and singularly focused, not on the possible “consequences” of a verdict, but on whether the government has sustained its burden to prove guilt beyond a reasonable doubt.

In light of these concessions, we need not address the additional remarks on rebuttal summation that the defendants challenge. The conceded errors are sufficient to establish that the Government’s rebuttal summation included repeated improprieties that “diverged] the jury from consideration of the evidence.” United States v. Terry, 702 F.2d 299, 313 (2d Cir.1983).

F. Cumulative Prejudice

We now turn to the cumulative prejudice caused by the foregoing errors and improprieties. These various errors carry different prejudice standards. When reviewing claims of prosecutorial misconduct based on inappropriate remarks in the Government’s opening statement or summations, we will reverse if the misconduct caused “substantial prejudice by so infecting the trial with unfairness as to make the resulting conviction a denial of due process.” United States v. Elias, 285 F.3d 183, 190 (2d Cir.2002) (internal quotation marks omitted); see also United States v. Helmsley, 941 F.2d 71, 96 (2d Cir.1991). “In assessing whether prosecutorial misconduct caused ‘substantial prejudice,’ this Court has adopted a three-part test,” which considers “the severity of the misconduct, the measures adopted to cure the misconduct, and the certainty of conviction absent the misconduct.” Elias, 285 F.3d at 190.

With respect to erroneous evidentiary rulings improperly admitting or excluding evidence, we ordinarily will reverse only where the improper admission or exclusion “affect[ed] substantial rights” and therefore was not harmless. See United States v. Miller, 626 F.3d 682, 688 (2d Cir.2010) (quoting Fed.R.Crim.P. 52(a)). Where the appellant fails to preserve an evidentiary challenge by lodging a timely objection, we review for plain error. See United States v. Gaind, 31 F.3d 73, 76 (2d Cir.1994). Under that standard, we consider whether there was “(1) ‘error,’ (2) that is ‘plain,’ and (3) that ‘affect[s] substantial rights.’ ” Johnson v. United States, 520 U.S. 461, 466-67, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997) (quoting United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)) (alteration in the original). If these conditions are met, we may then exercise “discretion to notice a forfeited error, but only if (4) the error ‘seriously affects the fairness, integrity, or public reputation of judicial proceedings.’” Id. (quoting Olano, 507 U.S. at 732, 113 S.Ct. 1770).

With these standards in mind, we would hesitate to vacate and remand this case for a new trial based on any one of the errors discussed above in isolation, or perhaps even any one category of those errors. But considering the record as a whole, we are compelled to conclude a new trial is warranted.

To begin with, evidentiary errors and prosecutorial misconducted infected every stage of the trial below. In the Government’s opening statement, the prosecutor made repeated improper comments; on direct examination of numerous key government witnesses, improper evidence was introduced and improper questions were asked; during the defense case, evidence supporting one of the defendants’ principal trial defenses was improperly excluded; during the Government’s initial summation, the prosecutor made yet another improper comment; and during the Government’s rebuttal summation, the prosecutor made still more improper comments. Impropriety permeated the proceedings here.

Moreover, the improprieties were not insubstantial. The prosecutor’s comments in the Government’s opening statement repeatedly bolstered the credibility of key government witnesses, in direct contravention of repeated admonitions from the district court. Although defense counsel at times failed to object, plainly improper bolstering continued through the Government’s case-in-chief and into the Government’s summation. We will not lightly overlook such repeated violations of clearly announced rules. See United States v. Borello, 766 F.2d 46, 58 (2d Cir.1985) (“For us to disapprove of the present procedure permitting the bolstering of the witness’s testimony and then to declare it harmless error would make our remarks in the previous cases purely ‘ceremonial.’ ”).

The improperly excluded evidence of good faith was also significant. In its absence, the jury was left without vital context and corroboration for the defendants’ defense of good faith and lack of criminal intent. As already noted, while the intent element differed among the various charges — -for example, only the mail fraud charge required a specific intent to defraud — the complex regulatory background against which the defendants conducted their activities made their professions of good faith relevant, directly or indirectly, to every question of knowledge and intent in dispute in the case. Furthermore, the defendants’ protestations of good faith bore directly on assessment of their credibility, and the improper exclusion of corroboration of their good faith undermined the fairness of that evaluation. As the Tenth Circuit stated in similar circumstances, with the aid of such corroboration “[a] jury would be more inclined to give weight and consideration to statements and conversations upon which a conclusion was based than to a mere statement by the accused of his conclusion, unsupported by such statements.” Miller v. United States, 120 F.2d 968, 970-71 (10th Cir.1941).

The comments in the Government’s rebuttal summation were troubling as well. We recognize that summations, and particularly rebuttal summations, are not fully constructed in advance. See Donnelly v. DeChristoforo, 416 U.S. 637, 646-47, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974). But the improvisatory nature of a rebuttal summation is no license for improper vouching, referencing facts not in the record, or appealing to extraneous “consequences” of a verdict.

We further find that the curative measures employed by the district court were insufficient to overcome the prejudicial effect of these significant errors. To be sure, the district court sustained defense objections to the prosecutor’s improper remarks in the Government’s opening, while making clear that credibility determinations were for the jury alone to make. But improper bolstering continued into later stages of the trial without similarly “emphatic” curative steps. United States v. Friedman, 909 F.2d 705, 710 (2d Cir.1990). As for the three concededly improper comments in the Government’s rebuttal summation, the district court sustained two objections, but overruled the objection to the prosecutor’s impermissible reference to the “consequences” of the jury’s verdict. And the jury instructions included only standard charges on the nature of evidence, the testimony of government witnesses, and the burdens of proof, with no special curative charges.

As for the alleged certainty of conviction absent the errors, the Government’s case was quite strong but not overwhelming. The Government’s evidence, while extensive, contained no “smoking gun,” and relied heavily upon testimony from witnesses taking the stand pursuant to immunity and cooperation agreements. Copeland and Hoosock also testified for the defense and denied any wrongdoing, requiring the jury to judge their credibility and weigh it against the credibility of the Government’s witnesses. Furthermore, while the defendants attempted to present their good-faith defense to the jury, the presentation was substantially undercut by the district court’s evidentiary rulings, which prevented the defendants from providing important context and corroboration. See Miller, 120 F.2d at 970-71.

Under the circumstances, we are compelled to conclude that the totality of the Government’s misconduct in this case, combined with the district court’s erroneous exclusion of evidence favorable to the defense, denied the defendants their right to a fair trial. Accordingly, the judgments of conviction as to CES, Copeland, and Dunn are vacated, and a new trial is ordered.

II. The Government’s Appeal

Because we vacate the convictions of CES, Copeland, and Dunn, we need not consider the Government’s cross-appeal of those defendants’ sentences. But we must address the Government’s appeal with respect to the sentences of Allen and Onoff. Though convicted at trial, Allen has not challenged his conviction on appeal, and Onoff was convicted pursuant to a guilty plea. The Government challenges four aspects of Allen and On offs sentences — the amount of restitution awarded; the loss calculated for purposes of the advisory sentencing guidelines; the use of the fraud guideline, U.S.S.G. § 2B1.1, rather than the hazardous substances guideline, U.S.S.G. § 2Q1.2; and the substantive reasonableness of the sentences. To place these issues in context, we first describe the sentencing proceedings below in greater detail.

After trial, the Government argued that, for purposes of calculating restitution and the applicable guidelines ranges, the losses caused by the defendants’ criminal activity generally fell into three categories: (1) the costs of cleaning up the contamination caused by AAPEX and Paragon’s rip-and-run projects; (2) payments to CES for fraudulent air monitoring services on abatement projects conducted at Syracuse University by contractor Environmental Protection Services, Inc., which performed the underlying abatement work properly; and (3) payments made by victims to AA-PEX and Paragon for rip-and-run projects facilitated by CES’s fraudulent air monitoring. For defendant Onoff — who, unlike the other individual defendants, was not a CES employee but a supervisor at Paragon — the Government advocated a narrower set of losses, calculated as the cleanup costs and contract amounts paid in connection with three Paragon abatement projects.

The Probation Office adopted this categorization of losses in the defendants’ initial Presentence Reports (“PSRs”). For Allen, the Probation Office initially calculated the losses as totaling approximately $439,000 for category one, $141,000 for category two, and $210,000 for category three. In all, this amounted to approximately $790,000 in losses, resulting in a 14-level increase to his base offense level. See U.S.S.G. § 2Bl.l(b)(l)(H). For Onoff, the Probation Office calculated his losses as totaling approximately $228,000, resulting in a 12-level increase. Id. The Allen’s guidelines imprisonment range was calculated as 121 to 151 months; Onoffs was 51 to 63 months. These calculations were based on the fraud guideline, U.S.S.G. § 2B1.1, rather than the hazardous substances guideline, U.S.S.G. § 2Q1.2, because, given the large loss amounts, the fraud guideline produced the higher total offense level. See U.S.S.G. § 3D1.3(a).

The defendants objected to the initial loss calculations. After holding a hearing, the district court issued an order setting each defendant’s restitution liability. As relevant here, the district court concluded that, with respect to the losses in category one (cleanup costs), the Government was “precluded” from claiming losses greater than $87,345, which was the amount of restitution the Government had previously agreed to collect from AAPEX and Paragon in plea agreements with those defendants. Special App. 15. Similarly, with respect to the losses in category two (payments to CES for fraudulent services), the district court determined that these losses should only include payments for fraudulent final clearance air monitoring services and should not include payments for other air monitoring services, such as background monitoring prior to abatement. In the district court’s view, payments made to CES for services other than final clearance air monitoring were “not related to the offense conduct,” id. at 11, and therefore the district court limited the losses in category two to approximately $25,000, id. at 12.

In total, the district court ordered restitution of approximately $117,000. The district court held CES responsible for this entire amount, but reduced the joint and several liability of the individual defendants based upon each defendant’s role in the charged scheme and financial circumstances. As relevant here, the court apportioned five percent of the total restitution liability to Allen and thirty percent of the Paragon-specific restitution liability to Onoff.

After the restitution order, the Probation Office, in line with the district court’s order, issued amendments to each defendant’s PSR, recalculating each defendant’s guideline range by substituting the defendant’s apportioned restitution amount for the previously calculated loss amount. As a result, Allen’s range became 33 to 41 months, and Onoff s range became 12 to 18 months.

On October 21, 2011, the district court sentenced the various CES defendants. At each sentencing, the district court adopted the factual statements in the PSRs, as well as their guidelines calculations. Both in its sentencing submissions and at each sentencing hearing, the Government objected to the guidelines calculation in the PSRs, arguing that restitution and loss are distinct, and that if the amounts set in the restitution order were used as loss amounts, then the defendants’ guidelines ranges should be determined by the hazardous substances guideline rather than the fraud guideline. At the sentenc-ings of CES, Copeland, and Dunn, the district court “so noted” the Government’s objections. G.A. 937, 952, 979. When the Government again raised the same objection at Allen’s sentencing, however, the court stated, after a colloquy, that, “[n]ow that you have brought that up for the first time as far as I am aware, I will take care of that.” G.A. 1000. The court explained that it would “add to the record for all of the other sentencings that I will also accept and take into account the factors and advisory guidelines under [the hazardous substances guideline].” G.A. 1002. The court explained that “[t]his is an acceptable, flexible approach by the Second Circuit, especially at arriving at a more appropriate sentence outside of the guidelines.” Id. The district court later made a similar statement at Onoff s sentencing on November 21, 2011.

Ultimately, the court imposed below-guidelines sentences on all five defendants. As relevant here, Allen, and Onoff each received incarcerative sentences of “time served (1 day),” representing the brief time each spent being processed by the U.S. Marshals following their initial appearances. Allen and Onoff received no fines. G.A. 303, 09. Each defendant was ordered to pay restitution as calculated in the court’s prior order.

A. Restitution Order

We turn first to the district court’s restitution order, which we review for for abuse of discretion. See United States v. Luden, 347 F.3d 45, 52 (2d Cir.2003). “To identify such abuse, we must conclude that a challenged ruling rests on an error of law, a clearly erroneous finding of fact, or otherwise cannot be located within the range of permissible decisions.” United States v. Pearson, 570 F.3d 480, 486 (2d Cir.2009) (quoting United States v. Boccagna, 450 F.3d 107, 113 (2d Cir.2006)).

By statute, district courts “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). Where more than one defendant contributes to a given victim’s loss, however, courts “may apportion liability among the defendants to reflect the level of contribution to the victim’s loss and economic circumstances of each defendant.” Id. § 3664(h). In ordering restitution, “a district court must consider that the purpose of restitution is essentially compensatory: to restore a victim, to the extent money can do so, to the position he occupied before sustaining injury.” United States v. Gonzalez, 647 F.3d 41, 66 (2d Cir.2011) (quoting Boccagna, 450 F.3d at 115) (internal quotation marks omitted).

Here, the Government first argues that the district court erred in relying on the plea agreements with AAPEX and Paragon to determine the restitution necessary to cover cleanup costs. The defendants respond that, because the guidelines provide that “stipulations shall ... not contain misleading facts,” U.S.S.G. § 6B1.4(a), the stipulations constituted presumptively reasonable factual representations by the Government as to the relevant loss amounts. The defendants contend that these representations constitute adequate evidence supporting the district court’s findings.

But as the Government points out, the court below did not treat the stipulations here merely as persuasive evidence of the relevant loss amounts. The only basis the district court provided for its finding as to the losses for cleanup costs was the legal conclusion that the Government was “precluded” from seeking more in restitution from these defendants than it had previously sought from AAPEX and Paragon. Special App. 15. Although the reasoning behind this legal conclusion is not entirely clear from the record, it appears that the district court was adopting the defendants’ argument, pressed below but now abandoned on appeal, that the Government should be “estopped” from seeking restitution in excess of the earlier stipulations. G.A. 251-52. The district court thus apparently relied on the doctrine of nonmutual collateral estoppel, in which “one party is barred from relitigating an issue decided in a previous proceeding, where the parties were not the same in the prior proceeding.” United States v. Ustica, 847 F.2d 42, 49 n. 14 (2d Cir.1988).

The district court’s apparent reliance on this doctrine in setting restitution in this case was erroneous. To begin with, the Supreme Court has held that nonmutual collateral estoppel is generally unavailable against the Government, see United States v. Mendoza, 464 U.S. 154, 159-64, 104 S.Ct. 568, 78 L.Ed.2d 379 (1984), and has long rejected application of nonmutual collateral estoppel against the Government in criminal trials, see Standefer v. United States, 447 U.S. 10, 21-25, 100 S.Ct. 1999, 64 L.Ed.2d 689 (1980). Several of our sister circuits have rejected the application of nonmutual collateral estoppel in criminal sentencing. See United States v. Pierce, 409 F.3d 228, 233-34 (4th Cir.2005); United States v. Montes, 976 F.2d 235, 239 (5th Cir.1992); United States v. Elfand, 1 Fed.Appx. 650, 652-53 (9th Cir.2001) (per cu-riam). And we have been wary of giving preclusive effect to factual findings made in a criminal sentencing even when the parties to the subsequent proceeding are the same, holding that “precluding relitigation on the basis of [sentencing] findings should be presumed improper.” United States v. U.S. Currency in the Amount of $119,984, 304 F.3d 165, 172 (2d Cir.2002) (quoting SEC v. Monarch Funding Corp., 192 F.3d 295, 306 (2d Cir.1999)) (alteration in the original). In light of this substantial authority, we hold that principles of non-mutual collateral estoppel do not prohibit the Government from relitigating a factual issue in one criminal sentencing that has been decided in a prior sentencing of another defendant.

This does not mean, of course, that a Governmental factual representation in one part of a case is not relevant to factual determinations in other parts of the case. Indeed, a decision in the Seventh Circuit suggests that where a district court accepts inconsistent factual representations from the Government, and fails to provide an explanation, the unexplained discrepancy may indicate a clear error. See United States v. Barnes, 602 F.3d 790, 797 (7th Cir.2010) (holding that, where a district court without explanation rejected a stipulated drug quantity for one co-conspirator that it had accepted for other co-conspirators based on the same factual record, “such a discrepancy in factual findings is clearly erroneous”).

But the decision below cannot be justified as an attempt to avoid problematic inconsistent factual findings. Apart from the fact that the district court did not frame its decision in those terms, the district court was simply mistaken in finding that the plea agreements with AAPEX and Paragon had “accepted $87,345.00 as being the amount of loss these victims suffered.” Special App. 11. In fact, the record shows that the losses stipulated in the plea agreements and the losses caused by the defendants here were different. AAPEX was charged with two counts: conspiracy to violate the Clean Air and Clean Water Acts, and mail fraud against its insurance carrier. While AAPEX pled guilty to both of these crimes, the stipulated restitution on which the district court relied pertained only to the mail fraud offense and was to be paid to AAPEX’s insurer, Team Transportation Trust. The AAPEX plea agreement says nothing about the losses for cleanup costs suffered by the property owners who were the victims of the defendants’ crimes here.

As for the Paragon plea agreement, Paragon pled guilty to conspiring to violate the Clean Air Act in connection with three rip-and-run abatement projects. The stipulated restitution amount, however, pertained to only one of those projects. Nothing in the agreement suggests that the amount on which the district court relied represented the total loss for cleanup costs suffered by all of the property owners for Paragon projects.

Beyond the finding as to category one (cleanup costs), the Government also challenges the district court’s decision to exclude from its restitution award certain costs in category two (payments to CES for fraudulent services) — costs not associated with final clearance air sampling. The district court gave three reasons for finding these costs to be unrelated to the offense conduct, but each is unpersuasive.

First, the district court found that non-air sampling services, such as bulk asbestos sampling and analysis — that is, testing of solid materials for asbestos content— “did not pertain to the crimes charged.” Special App. 11. But the indictment charged that the defendants falsely represented to CES’s clients that CES would perform all of its work in compliance with the law, not just air monitoring. And at trial, the Government presented evidence that CES’s laboratory violated applicable regulations when analyzing all kinds of samples, not just final clearance air samples. Elsewhere in its restitution order, the district court acknowledged and accepted this evidence. See id. at 9 n. 2.

Second, the district court noted that air monitoring services other than final clearance air sampling, such as background sampling and pre-abatement sampling, “are required prior to any asbestos abatement work,” and are “generally done without entering the contained abatement work area and therefore would not be affected by improper asbestos abatement.” Id. at 11-12. But for all of the projects in category two, it was undisputed that the underlying abatement work had been conducted properly and that the defendants’ wrongdoing consisted of fraudulently certifying the propriety of its own services. Contrary to the district court’s apparent assumption in this instance, the defendants’ crimes were broader than merely aiding and abetting unlawful abatement work. As the district court noted, even where “the actual asbestos abatement was done properly,” the “sampling and laboratory analysis done by CES were not done properly.” Id. at 9 n. 2.

Third, the district court found that “the government failed to establish any wrongdoing pertaining to the sampling and analysis of background air sampling, pre-abatement air sampling, and environmental air sampling.” Id. at 12. But again, the district court itself found that, beyond air sampling, the “laboratory analysis done by CES w[as] not done properly.” Id. at 9 n. 2.

In light of these legal errors and conflicting factual findings, we conclude that the district court clearly erred in setting the amount of restitution.

B. Procedural and Substantive Reasonableness

In addition to the restitution order, the Government also challenges the procedural and substantive propriety of the defendants’ sentences. We review a district court’s sentence for procedural and substantive reasonableness, a standard “akin to review for abuse of discretion.” United States v. Cavera, 550 F.3d 180, 188 (2d Cir.2008) (en banc) (quoting United States v. Fernandez, 443 F.3d 19, 27 (2d Cir.2006)). With respect to procedural reasonableness, a district court commits procedural error when, among other things, it “makes a mistake in its Guidelines calculation.” Id. at 190. We review district court’s factual findings informing its guidelines calculation for clear error, and its conclusions of law de novo. See United States v. Uddin, 551 F.3d 176, 180 (2d Cir.2009). With respect to substantive reasonableness, a sentence is substantively unreasonable only in the “exceptional case[ ] where the trial court’s decision ‘cannot be located within the range of permissible decisions.’ ” Cavera, 550 F.3d at 189 (quoting United States v. Rigas, 490 F.3d 208, 238 (2d Cir.2007)).

We turn first to the Government’s procedural challenges, starting with the challenge to the district court’s loss calculation for purposes of the fraud guideline, U.S.S.G. § 2B1.1. As noted, the district court used the amounts calculated in its restitution order as the relevant loss amounts. For the reasons already explained, the restitution calculations rested on reversible legal and factual errors. Those errors carried forward into the loss calculations.

In addition, even if the restitution calculations had been accurate, the district court erred in mechanically using each defendant’s restitution liability under 18 U.S.C. § 3664 as the relevant loss amount under U.S.S.G. § 2B1.1. Though restitution and loss involve closely related calculations, which ultimately produce the same figure in many cases, the inquiries are not identical. Restitution serves a compensatory function, Gonzalez, 647 F.3d at 66, and “focuses on the victim and the harm proximately caused by the defendant’s conduct.” United States v. Gossi, 608 F.3d 574, 580 (9th Cir.2010) (emphasis omitted). Loss under the fraud guideline, by contrast, focuses on the defendant, and seeks, however imperfectly, to measure the seriousness of his or her criminal conduct. See United States v. Byors, 586 F.3d 222, 225 (2d Cir.2009). Because “[a] defendant’s culpability will not always equal the victim’s injury,” United States v. Catherine, 55 F.3d 1462, 1465 (2d Cir.1995), “an amount-of-loss calculation for purposes of sentencing does not always equal such a calculation for restitution,” United States v. Germosen, 139 F.3d 120, 130 (2d Cir.1998).

These different purposes are reflected in the relevant statutory and guidelines provisions. Congress has authorized restitution for “the full amount of each victim’s loss,” 18 U.S.C. § 3664(f)(1)(A), which we have held encompasses only the “actual loss,” United States v. Marino, 654 F.3d 310, 320 (2d Cir.2011) (quoting Germosen, 139 F.3d at 130), that was “directly caused by the conduct composing the offense of conviction,” id. (quoting United States v. Silkowski, 32 F.3d 682, 689 (2d Cir.1994)). Loss for purposes of the fraud guideline, by contrast, is defined as “the greater of actual loss or intended loss.” U.S.S.G. § 2B1.1 cmt. 3(A). Actual loss, in turn, is defined as “the reasonably foreseeable pecuniary harm that resulted from the offense,” while intended loss is “the pecuniary harm that was intended to result from the offense.” Id. § 2B1.1, cmt. 3(A)(i), (ii). The term “offense” in these provisions includes all of the defendant’s offense conduct, as well as “all reasonably foreseeable acts and omissions of others in furtherance of [any] jointly undertaken criminal activity.” U.S.S.G. § lB1.3(a)(l)(B).

Furthermore, of particular relevance here, district courts may apportion the full amount of restitution among multiple defendants “to reflect the level of contribution to the victim’s loss and economic circumstances of each defendant.” 18 U.S.C. § 3664(h). Consideration of a defendant’s “economic circumstances,” however, is not permitted with respect to the guideline calculation. See U.S.S.G. § 5H1.10 (providing that “socio-economic status” is “not relevant in the determination of a sentence” as calculated under the guidelines).

Notwithstanding these distinctions between restitution and loss, the defendants argue that we may affirm the district court’s loss calculations on the ground that each defendant’s restitution liability naturally reflects the district court’s assessment of the losses that each defendant intended or could reasonably foresee. We decline to reframe the district court’s findings in this way. While the district court’s apportionment of restitution in part reflected each defendant’s role in the scheme alleged, which also may affect what losses each defendant could foresee, the apportionment also reflected economic considerations that have no place in calculating loss. See Special App. 14 (discussing Allen’s financial circumstances); id. 15 (discussing Onoffs financial circumstances). Although a sentencing court need not perform any “robotic incantations” to fulfill its obligations under the guidelines, United States v. Crosby, 397 F.3d 103, 113 (2d Cir.2005), and “need only make a reasonable estimate of the loss,” U.S.S.G. § 2B1.1, cmt. 3(C), we cannot presume that each defendant’s restitution and loss amounts are the same absent some indication that the district court made such a determination under the proper standards.

The Government also challenges the district court’s reliance on the fraud guideline rather than the hazardous substances guideline. The district court, following the approach taken in the PSRs, grouped the counts against each defendant under U.S.S.G. § 3D1.2(c). For counts grouped under that guideline, U.S.S.G. § 3D1.3(a) provides that “the offense level applicable to a Group is the offense level ... for the most serious of the counts comprising the Group, i.e., the highest offense level of the counts in the Group.” Under the loss amounts calculated by the district court, the fraud guideline produced an offense level of 20 for Allen and 13 for Onoff, while, according to the Government, the hazardous substances guideline produced an offense level of 22 for Allen and 21 for Onoff. Nevertheless, the district court applied the fraud guideline, though it stated, both at Allen and Onoffs sentencings and in the respective statements of reasons, that it would also consider the hazardous substances guideline.

The defendants contend that this approach to the guidelines calculation is permissible under this Court’s decision in United States v. Dhafir, 577 F.3d 411 (2d Cir.2009). In that case, we considered whether to calculate a defendant’s guidelines range under U.S.S.G. § 2Sl.l(a)(l), which sets the offense level for a money laundering offense based on the level of the underlying offense from which the laundered funds were derived, where that level can be determined; or under § 2Sl.l(a)(2), which in other circumstances sets the offense level based on the loss table in the fraud guideline. See Dhafir, 577 F.3d at 414. We found that certain “factual ambiguities” rendered it difficult to determine whether (a)(1) or (a)(2) applied. Id. at 415. To begin with, it was unclear from the record “whether [the] defendant used the proceeds of his fraud crimes to engage in promotional money laundering.” Id. In addition, if the laundered funds in fact represented proceeds from another offense, applying subsection (a)(2) would have produced the “odd” and “illogical result” that the defendant “would receive a lower sentence if the laundered money was ‘criminally-derived’ than if it was ‘legally obtained.’ ” Id. (quoting district court opinion).

Given these unusual circumstances, we held that the district court was “not bound in ambiguous circumstances ... to choose one Guidelines range in particular,” but was “free to take the more flexible — and often more, direct — approach of arriving at a more appropriate sentence outside the Guidelines.” Id. Under such an approach, “the judge could simply look at all of the facts, take both suggestions into account, consider the § 3553(a) factors, and come up with a ‘hybrid’ approach if he so chose.” Id. We noted that this possible tack aligned with prior cases stating that omission of the guidelines calculation may be justified in some instances “to avoid the need to resolve all of the factual issues necessary to make precise determinations of some complicated matters.” Id. (quoting Crosby, 397 F.3d at 112); see also Cavera, 550 F.3d at 190 (reaffirming Crosby in this regard); id. at 200 n. 4 (Raggi, /., concurring) (same).

But the flexible approach we endorsed in Dhafir is unsuited to this case. By the time it calculated the defendants’ guidelines ranges, the district court had resolved (albeit erroneously) all of the necessary factual issues. Nor did the application of the grouping rules under § 3D1.3(a) or the hazardous substances guideline present any unique or novel conceptual issues. Dhafir, Crosby, and Cavera lay out a limited exception to the general rule that “a district court should begin all sentencing proceedings by correctly calculating the applicable Guidelines range.” Gall v. United States, 552 U.S. 38, 49, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). In appropriate cases, that exception can conserve judicial resources and avoid turning a difficult guidelines calculation into an end unto itself, divorced from the considerations Congress has directed must ultimately determine an appropriate criminal sentence. See Cavera, 550 F.3d at 188-89;18 U.S.C. § 3553(a). That limited exception, however, is not a license for district courts to avoid calculating the proper guidelines range when the facts have been determined and the law is clear.

In short, the factual and procedural errors detailed above require us to vacate the sentences of defendants Allen and Onoff and remand for resentencing. Accordingly, we need not, and do not, consider whether their sentences were substantively unreasonable.

CONCLUSION

For the foregoing reasons, the judgments of conviction as to CES, Copeland, and Dunn, and the sentences of Allen and Onoff are VACATED. The case is REMANDED for a new trial as to CES, Copeland, and Dunn and for resentencing as to Allen and Onoff. 
      
      . When the Code Rule was repromulgated in 2006, these variances were incorporated into the Code Rule itself. See 28 N.Y. Reg. 8 (Jan. 11, 2006).
     
      
      . On April 6, 2010, the district court granted Duchene’s motion to sever her trial. On March 7, 2011, the charges against Duchene were dismissed after she pled guilty to state-law charges arising from the same conduct.
     
      
      . While the "intent” element of the various charges differed depending on the charge, the complex regulatory background made defendant’s protestations of good faith and lack of criminal intent directly or indirectly relevant to the jury’s evaluation of each of the charges.
     
      
      . For the first two witnesses, defense counsel did not object to the admission of the witness's cooperation agreement. Beginning with the third immunized witness, however, defense counsel began objecting to the admission of the agreements, but each time those objections were overruled. The district court explained that “since these exhibits had come in with earlier witnesses” without objection, "there was no reason why the jury should be deprived of these exhibits with later witnesses.” G.A. 832. Since the Government now concedes that its introduction of the agreements on direct examination was improper, we need not address whether the defense’s failure to object to the introduction of the agreements with the first two witnesses (which the defendants claim was motivated by the different stance the defense was taking as to their credibility compared with that of the later witnesses) amounted to a waiver or forfeiture.
     
      
      . The prosecutor’s improper remarks on rebuttal summation are canvassed separately, infra.
      
     
      
      . In United States v. Koskerides, 877 F.2d 1129 (2d Cir.1989), we held that the Government had fully complied with Rule 16 "by providing [the defendant] with the typewritten memoranda of interviews prepared from the agent’s handwritten notes.” Id. at 1133. That case, however, applied an earlier version of the rule, which required the Government to disclose only "the substance of any oral statement” that was made by the defendant during interrogation and that the Government intended to offer at trial. Id. (quoting the then-operable language of the rule). Rule 16 was amended in 1991 to add the language referencing "any written record,” broadening the Government’s disclosure obligations and superseding Koskerides in this respect. See Fed. R. Crim P. 16, Advisory Comm. Notes (1991 Amendments).
     
      
      . The defendants urge us to affirm the district court’s finding as to the losses for cleanup costs on alternative grounds independent of the plea agreements with AAPEX and Paragon. We decline to do so, as the factual issues the defendants raise are appropriately addressed by the district court in the first instance.
     