                              In the

    United States Court of Appeals
                For the Seventh Circuit
                    ____________________
No. 18-1320
UNITED STATES OF AMERICA,
                                                  Plaintiff-Appellee,
                                v.

VAHAN KELERCHIAN,
                                              Defendant-Appellant.
                    ____________________

        Appeal from the United States District Court for the
         Northern District of Indiana, Hammond Division.
        No. 2:13-CR-66 — Joseph S. Van Bokkelen, Judge.
                    ____________________

     ARGUED APRIL 2, 2019 — DECIDED AUGUST 22, 2019
                ____________________

   Before HAMILTON, BARRETT, and SCUDDER, Circuit Judges.
    HAMILTON, Circuit Judge. Federal law imposes tight re-
strictions on private possession of machineguns and laser
gunsights but allows law enforcement agencies to purchase
and use both machineguns and laser sights. This appeal con-
cerns criminal conspiracies among a firearms dealer and law
enforcement oﬃcers to fool manufacturers into thinking they
were selling to local police forces when the machineguns and
laser sights were instead going into private hands.
2                                                   No. 18-1320

    Defendant-appellant Vahan Kelerchian was a licensed
firearms dealer. His co-conspirators were Joseph Kumstar, the
Deputy Chief of the Lake County Sheriﬀ’s Department in In-
diana, and Ronald Slusser, a patrolman who was the armorer
for the department’s SWAT team. The trio defrauded firearms
manufacturer Heckler & Koch and the laser sight producer
Insight Technologies into selling them machineguns and laser
sights restricted by law for law enforcement and military use.
After many fraudulent transactions, the three were indicted
on several charges. Kumstar and Slusser pleaded guilty.
Kelerchian went to trial and was convicted on four counts of
conspiracy and four counts of making false writings. On ap-
peal, Kelerchian raises numerous issues, but we aﬃrm his
convictions on all counts. In Parts I and II, we provide the fac-
tual and procedural background for Kelerchian’s arguments.
In Part III, we analyze his numerous challenges to his convic-
tions.
I. Factual Background
    A. Machineguns and Laser Sights
    Since enactment of the National Firearms Act of 1934, cod-
ified in the Internal Revenue Code as 26 U.S.C. § 5801 et seq.
(“the 1934 Act”), federal law has forbidden the importation of
machineguns, but with several exceptions. Two are relevant
here. First, machineguns may be imported for use by state or
federal departments or agencies, and second, machineguns
may be imported “solely for use as a sample by a registered
importer or registered dealer.” 26 U.S.C. § 5844; see also 27
C.F.R. § 479.112. The conspirators here submitted fake docu-
ments to Heckler & Koch to take advantage of these two ex-
ceptions.
No. 18-1320                                                     3

    The Gun Control Act of 1968, as amended and codified as
part of the criminal code in 18 U.S.C. § 921 et seq. (“the 1968
Act”), imposed additional restrictions on a much broader cat-
egory of firearms, as well as new recordkeeping laws. The
1968 Act, as amended, prohibits the transfer or possession of
machineguns made after 1986, except by a federal, state, or
local agency. 18 U.S.C. § 922(o). Both the 1968 and 1934 Acts
require importers and dealers of firearms to keep records re-
lated to their transactions. 18 U.S.C. § 923(g); 26 U.S.C. § 5843.
Both Acts make it a crime to make false statements with re-
spect to these records. 18 U.S.C. § 924(a)(1)(A); 26 U.S.C.
§ 5861(l). The Bureau of Alcohol, Tobacco, Firearms and Ex-
plosives (“ATF”) administers the recordkeeping requirements
and the exceptions.
    Laser sights, on the other hand, are regulated by the Food
and Drug Administration (“FDA”) as part of its regulation of
radiation-emitting devices. See 21 U.S.C. § 360ii. The power-
ful lasers on gunsights can cause eye damage, so federal law
ordinarily requires them to be equipped with visible or audi-
ble warnings before and during use, as well as protective co-
vers and key controls. 21 C.F.R. § 1040.10(f). They also must
have labels warning of the risk of eye damage. 21 C.F.R.
§ 1040.10(g)(2)(iii).
    The FDA may, however, grant exemptions or variances
from these requirements, such as for police departments that
might need to be able to use silent laser sights. 21 U.S.C.
§ 360oo(b); 21 C.F.R. § 1010.4(a). The FDA also requires accu-
rate records for laser sales. Laser manufacturers must collect
and preserve information that will enable the tracing of lasers
sold to distributors or to dealers. 21 C.F.R. § 1002.30(b)(1); see
also 21 U.S.C. § 360nn(f). Dealers and distributors must
4                                                  No. 18-1320

“obtain such information as is necessary to identify and locate
first purchasers” of lasers and forward this information “im-
mediately to the appropriate manufacturer.” 21 C.F.R.
§ 1002.40(a), (c).
    B. The Conspiracies
    Vahan Kelerchian was a licensed firearms dealer who ran
a business in Pennsylvania called Armament Services Interna-
tional, Inc., known as ASI. He met Lake County Sheriﬀ patrol-
man Ronald Slusser at a Kentucky machinegun show some
time in the early 2000s. A few years later at the same show,
Slusser introduced Kelerchian to his supervisor, Joseph Kum-
star, the Deputy Chief of the Lake County Sheriﬀ’s Depart-
ment. According to Slusser, he and Kelerchian stayed in touch
and did business together for the next several years.
   At some point, Slusser told Kelerchian about an illegal
arms deal in 2008 that Kumstar had instructed him to help
with. Kumstar had acquired machineguns by claiming that
they were for the Sheriﬀ’s Department, but then instructed
Slusser to remove certain parts of these guns and to sell them
over the internet for Kumstar’s personal gain. Slusser testified
that Kelerchian expressed interest in doing a similar deal with
Kumstar and Slusser. The three then plotted the conspiracies
that led to their convictions.
       1. Machinegun Purchases
   The first part of the conspirators’ plan was to purchase ma-
chineguns from international gun importer Heckler & Koch
(“H&K”) under the pretense that the weapons were for the
Lake County Sheriﬀ’s Department. Kelerchian, Slusser, and
Kumstar orchestrated three fraudulent machinegun pur-
chases from H&K.
No. 18-1320                                                   5

    In the first transaction, in December 2008, Kelerchian,
Kumstar, Slusser, and Slusser’s cousin, Ed Kabella, ordered
50 machineguns for $83,026. Kumstar prepared paperwork
saying falsely that the Sheriﬀ’s Department was purchasing
all 50 machineguns. Kelerchian sent this paperwork to H&K,
including statements on Sheriﬀ’s Department letterhead at-
testing that the weapons were for the exclusive use of Lake
County law enforcement. H&K then filed ATF Form 6, assert-
ing that it was importing 50 machineguns for the Lake County
Sheriﬀ’s Department. ATF approved the transaction, and
H&K sent the 50 machineguns to the Sheriﬀ’s Department.
    Slusser then took the machineguns apart, separating the
guns’ lower receivers, which are the regulated portions of the
weapons containing traceable serial numbers. The unregu-
lated upper barrels of the guns were distributed among the
conspirators according to how much money each had contrib-
uted to the purchase. The plan was to refurbish 15 of the reg-
ulated lower receivers into new guns using cheaper parts, and
then to add these new weapons into the Sheriﬀ’s Depart-
ment’s armory. The 35 remaining lower receivers were to be
destroyed. No machineguns ever made it to the Sheriﬀ’s De-
partment, though. The conspirators sold the unregulated ma-
chinegun parts for a substantial profit. Slusser sold his unreg-
ulated machinegun barrels to a dealer named Adam Webber,
who runs a website selling hard-to-acquire H&K machinegun
parts.
    Webber was involved in the next two machinegun pur-
chases. He told Kumstar and Kelerchian that he was inter-
ested in buying additional machinegun parts. In February
2009, using the same procedure as before, Kumstar and Keler-
chian bought nine H&K machineguns, again telling H&K
6                                                 No. 18-1320

falsely that the guns were for the Sheriﬀ’s Department. Once
the machineguns were delivered, Slusser again disassembled
them and sent the unregulated parts to Webber. In exchange,
and relevant to the money-laundering conspiracy charge,
Webber sent Slusser a cashier’s check for $18,900. At Kum-
star’s direction, Slusser deposited that check into his own ac-
count and then sent cashier’s checks to both Kumstar and
Kelerchian. Nine months later, Kelerchian mailed H&K a
check for the machineguns.
   In October 2009, Kelerchian and Kumstar bought twelve
more machineguns from H&K, again telling H&K falsely that
they were for the Sheriﬀ’s Department. Slusser again disas-
sembled the guns and sent the unregulated parts to Webber.
Webber mailed Slusser a $31,200 check, which he cashed.
Slusser wrote Kelerchian a check for $28,200, and Kelerchian
wrote H&K a check for the guns’ $16,800 purchase price.
      2. Demonstration Letters
    In the meantime, the conspirators also used the exception
for importing machineguns as demonstration samples for a
dealer. Kumstar testified that Kelerchian asked him for help
in buying machineguns for his personal collection. Between
October 2007 and March 2010, Kumstar sent five letters to the
ATF stating falsely that the Lake County Sheriﬀ’s Department
was interested in demonstrations of the weapons Kelerchian
wanted for himself. The letters said that Kelerchian had “of-
fered to conduct such demonstration[s]” and “intend[ed] to
demonstrate the operation, identification and safe handling of
the guns” to provide “department personnel a better under-
standing of the capabilities, limitations and diﬀerences of
these guns.” Kumstar testified that neither he nor the Sheriﬀ’s
Department was actually interested in demonstrations of the
No. 18-1320                                                        7

requested machineguns and that he never had discussed a
plan for conducting an actual demonstration with Kelerchian.
Kumstar also testified that the weapons were not guns the De-
partment would use.
   Through this arrangement, Kelerchian was able to buy
nine machineguns. He became the registered owner of these
weapons, and federal law allowed him to sell them at his own
discretion. No demonstrations ever occurred.
    Kelerchian’s testimony disputed Kumstar’s account. He
said that Kumstar had oﬀered on his own to write the first
dealer sales sample letter for Kelerchian and genuinely was
interested in a demonstration. Kelerchian also testified that he
oﬀered to conduct demonstrations for Kumstar and the De-
partment many times between October 2008 and April 2011.
He said that he oﬀered a variety of settings and dates but that
Kumstar never took him up on his oﬀers. The most Kumstar
did, according to Kelerchian, was to come to Kelerchian’s
place of business, take photographs with guns, and pick up a
gun, saying “We did our demo.”
       3. Laser Sight Purchases
     Kelerchian, Kumstar, and Slusser also devised a plan to
buy restricted laser sights from a company called Insight
Technology. Slusser testified that he and Kelerchian wanted
to buy laser sights for their personal collections. The devices
Kelerchian and Slusser wanted did not comply with FDA
safety rules requiring a visible or audible warning. However,
the FDA had granted Insight Technology a variance allowing
it to sell its laser sights (technically, Class IIIb devices) to fed-
eral, state, and local enforcement agencies on the theory that
safety features like a visible or audible warning could
8                                                  No. 18-1320

compromise stealth operations in which oﬃcers need to re-
main unheard and unseen.
    Slusser and Kelerchian used the variance to buy laser
sights on the pretext that they were for the Sheriﬀ’s Depart-
ment. Kelerchian and Slusser told Kumstar which sights they
wanted, and Kumstar then put together a purchase order with
paperwork saying falsely that the Sheriﬀ’s Department was
buying the lasers. In December 2008, Kelerchian sent Insight
Technology this purchase order for 25 sights for $27,103.52.
Using a nearly identical method, in March 2010, the three
bought an additional 22 lasers sights for $30,249.92. Accord-
ing to Slusser, he and Kelerchian placed two more orders for
Insight Technology laser sights by using a friend of Slusser’s
in the Lowell, Indiana Police Department in December 2009
and August 2010. The Lowell orders were for more than 28
Class IIIb laser products costing more than $32,000.
    Kelerchian testified that he was unaware of the FDA’s reg-
ulation of lasers and the variance. He told the jury that an In-
sight Technology employee named Linda Harms told him
that the lasers could be sold to individuals if they went
through a law enforcement department first. Harms testified
at trial that she never would have told a customer that laser
sights were available for individual purchase.
II. Procedural Background
   A federal grand jury returned a nine-count indictment.
Count I alleged that, in buying the machineguns, Kelerchian,
Kumstar, and Slusser violated 18 U.S.C. § 371 by conspiring
to make false statements in records required by the 1968 Act.
See 18 U.S.C. § 924(a)(1)(A). Count II alleged that, in buying
the laser sights, Kelerchian and the others violated 18 U.S.C.
No. 18-1320                                                     9

§ 371 by conspiring to defraud the FDA by interfering with its
lawful government functions of limiting the sale of various
restricted laser sights to military and law enforcement agen-
cies and correctly identifying the buyers of restricted laser
sights.
    Counts III through VII focused on the demonstration let-
ters. Count III charged Kelerchian under 18 U.S.C. § 371 with
conspiring with Kumstar and others to violate 18 U.S.C.
§ 1001 by making false statements to the ATF in the phony
demonstration letters. Counts IV through VII charged Keler-
chian with actual violations of § 1001 in four separate letters.
    Count VIII alleged that Kelerchian committed bribery by
oﬀering Kumstar a shotgun in exchange for his help with sev-
eral of the fraudulent transactions. Count IX alleged that
Kelerchian, Kumstar, and Slusser conspired to launder
money in violation of both 18 U.S.C. § 1956 and § 1957. The
§ 1956 allegation concerned the second machinegun purchase
and the § 1957 allegation concerned the third. The premise of
Count IX is that the conspirators engaged in wire fraud in ob-
taining the machineguns and then laundered the proceeds of
that fraud.
    Slusser, Kumstar, and Kabella pleaded guilty and agreed
to testify for the prosecution. Kelerchian took his case to trial.
After the government rested and again after the close of all
the evidence, Kelerchian moved under Federal Rule of Crim-
inal Procedure 29 for a judgment of acquittal on all counts. At
both stages, the district court denied the motion on Counts I
through VII and took the motion under advisement on
Counts VIII and IX.
10                                                   No. 18-1320

    The jury found Kelerchian guilty on all counts except the
bribery charge in Count VIII. Through a special verdict form,
regarding Count II, the jury specifically found Kelerchian
guilty of conspiring to interfere with both of the two regula-
tory functions of the FDA identified in the indictment.
Through another special verdict form on Count IX, the jury
found Kelerchian guilty of conspiring to launder money in vi-
olation of both 18 U.S.C. § 1956 and § 1957. Kelerchian was
sentenced to 100 months in prison, plus a fine and term of su-
pervised release.
III. Legal Analysis
    Kelerchian challenges all of his convictions on a variety of
grounds. First, he argues that Counts I and II failed to allege
federal crimes. Second, he argues the government failed to
prove the demonstration-letter charges in Counts III through
VII and the money-laundering conspiracy in Count IX. Third,
he contends the district court erred in its jury instructions. Fi-
nally, he claims the prosecution engaged in misconduct in its
closing argument. We find no errors.
     A. Legal Suﬃciency of Counts I and II
        1. Count I—Conspiracy to Violate Gun Control Act Re-
           cording Requirements
    Kelerchian argues that Counts I and II of the indictment
fail to allege federal oﬀenses. We start with Count I, which
charged Kelerchian under 18 U.S.C. § 371 with conspiring to
violate 18 U.S.C. § 924(a)(1)(A), which makes it a crime to
knowingly make “any false statement or representation with
respect to the information required by this chapter to be kept
in the records of a person licensed under this chapter,” includ-
ing federally licensed firearms importers, manufacturers, and
No. 18-1320                                                   11

dealers, including H&K. See Abramski v. United States, 573 U.S.
169, 174–75 (2014). “This chapter” is chapter 44 of Title 18, and
it provides in relevant part that licensees may not sell “any
firearm … to any person unless the licensee notes in his rec-
ords, required to be kept pursuant to section 923 of this chap-
ter, the name, age, and place of residence of such person … or
the identity … of such … corporation or other business en-
tity.” 18 U.S.C. § 922(b)(5). “Person” in this case means the
real buyer or intended recipient of the firearm, not a nominal
or straw purchaser. Abramski, 573 U.S. at 179–82. Regulations
implementing the 1968 Act also require licensees like H&K to
“maintain permanent records of the importation … of fire-
arms, including ATF Forms 6 and 6A.” 27 C.F.R. § 478.129(d).
Count I thus alleged a conspiracy to violate § 924(a)(1) by
leading H&K to create false records for the machinegun pur-
chases—falsely identifying the Lake County Sheriﬀ’s Depart-
ment as the buyer. On this logic, Count I alleged a federal of-
fense.
    To avoid this conclusion, Kelerchian argues that 18 U.S.C.
§ 924(a)(1)(A) and the 1968 Act’s regulations in 27 C.F.R. § 478
do not apply generally to machineguns. He argues that the
1934 Act regulates purchase, possession, importation, regis-
tration, and recordkeeping for machineguns, and that the
only provision of the 1968 Act that applies to machineguns is
18 U.S.C. § 922(o), which criminalizes the transfer and posses-
sion of machineguns, but which was not charged in Count I.
   Kelerchian bases his statutory argument on the two Acts’
diﬀerent definitions of the term “firearm.” The 1934 Act pro-
vides: “The term ‘firearm’ means” a number of categories of
especially dangerous weapons, including short-barreled shot-
guns and rifles, and specifically including “a machinegun.” 26
12                                                            No. 18-1320

U.S.C. § 5845(a). By contrast, the 1968 Act defines a “firearm”
in relevant part much more broadly as “any weapon … which
will or is designed to or may readily be converted to expel a
projectile by the action of an explosive.” 18 U.S.C. § 921(a)(3).
Comparing these definitions, Kelerchian argues that because
the 1968 Act’s definition does not expressly include ma-
chineguns, unlike the 1934 Act’s definition, Congress meant
to distinguish between machineguns and firearms in the 1968
Act, leaving machinegun regulation largely to the 1934 Act.
    Based on both the text and the structure of the 1968 Act,
we reject this argument. First, a machinegun clearly fits into
the 1968 Act’s broad definition of a “firearm” as a weapon that
“will or is designed to or may readily be converted to expel a
projectile by the action of an explosive.” 18 U.S.C. § 921(a)(3).
Machineguns are a subset of “firearms” as defined in the 1968
Act.1
    Second, other provisions of the 1968 Act show that ma-
chineguns are properly treated as a subset of firearms under
that Act. For example, § 924(c)(1) punishes the possession of a
firearm during the commission of a crime of violence or a
drug traﬃcking oﬀense, but § 924(c)(1)(B)(ii) enhances the

     1 In the 1934 Act, the term “‘machinegun’ means any weapon which
shoots, is designed to shoot, or can be readily restored to shoot, automat-
ically more than one shot, without manual reloading, by a single function
of the trigger. The term shall also include the frame or receiver of any such
weapon, any part designed and intended solely and exclusively, or com-
bination of parts designed and intended, for use in converting a weapon
into a machinegun, and any combination of parts from which a ma-
chinegun can be assembled if such parts are in the possession or under the
control of a person.” 26 U.S.C. § 5845(b). The 1968 Act borrows the same
definition for the term where it is used in the 1968 Act. 18 U.S.C.
§ 921(a)(23).
No. 18-1320                                                  13

punishment “if the firearm possessed … is a machinegun.”
Similarly, § 924(c)(1)(C)(ii) imposes a more severe penalty for
a second § 924(c) conviction “if the firearm involved is a ma-
chinegun.” Section 925(d) provides the Attorney General with
authority over importation of firearms into the United States
and possession of “unserviceable firearm[s], other than … ma-
chinegun[s].” 18 U.S.C. § 925(d) (emphasis added). The 1968
Act also grants qualified law enforcement oﬃcers with the
proper identification the ability to carry concealed firearms,
but specifically excludes machineguns from the definition of
firearm for purposes of just that section. 18 U.S.C. § 926B(e).
The clear implication is that all other provisions of the Act
without such a limit apply to machineguns as a subset of fire-
arms.
   Accordingly, a machinegun counts as a firearm for pur-
poses of 18 U.S.C. § 924, so Count I properly charged Keler-
chian with conspiracy to violate the 1968 Act by submitting
documents falsely telling H&K that the buyer of all the ma-
chineguns would be the Lake County Sheriﬀ’s Department.
       2. Count II—Conspiracy to Defraud the FDA
    Section 371 of Title 18 of the United States Code makes it
a crime not only to conspire to commit “any oﬀense against
the United States,” but also to conspire “to defraud the United
States, or any agency thereof in any manner or for any pur-
pose.” The Supreme Court has “stated repeatedly that the
fraud covered by the statute reaches any conspiracy for the
purpose of impairing, obstructing or defeating the lawful
function of any department of Government.” Tanner v. United
States, 483 U.S. 107, 128 (1987) (internal quotation marks omit-
ted) (collecting cases). Count II charged Kelerchian with vio-
lating § 371 by conspiring to defraud the FDA in carrying out
14                                                 No. 18-1320

its regulatory responsibilities. Kelerchian argues that Count II
charged him with violating only FDA policy as opposed to any
statute or regulation with the force of law. He emphasizes the
text of the indictment charging him with conspiring to de-
fraud the FDA by interfering with and obstructing the lawful
functions of the FDA to:
       a. Limit the sale of various restricted laser aim-
          ing sight devices to the military and law en-
          forcement agencies only;
       b. Correctly identify first line purchasers of
          various laser aiming sight devices which
          were restricted to military or law enforce-
          ment agency purchasers only.
    As Kelerchian sees the case, no law or regulation restricts
laser device sales to law enforcement, so he was charged with
conspiring to violate only the variance the FDA granted In-
sight Technology to sell otherwise-illegal laser sights to law
enforcement. Because this variance, Kelerchian continues,
was not adopted in accordance with the Administrative Pro-
cedure Act, it has no force of law and cannot be used to bind
third parties or to support criminal charges against them.
    The argument misreads the indictment. Count II did not
charge Kelerchian with conspiring to violate the variance but
with conspiring to defraud the FDA, rendering his Adminis-
trative Procedure Act argument irrelevant. Section 371 makes
it a crime to defraud an agency of the United States “in any
manner or for any purpose.” The indictment alleged that
Kelerchian, Kumstar, and Slusser conspired to defraud the
FDA by obstructing the agency’s ability to perform the two
listed regulatory functions. Federal law provides the FDA
No. 18-1320                                                    15

with the authority to regulate the sale of laser devices. See 21
U.S.C. § 360ii. In carrying out its regulatory function, the FDA
promulgated safety and performance standards for laser
sights. 21 C.F.R. § 1040.10. Manufacturers are barred from
selling products that do not comply with the standards the
agency sets. 21 U.S.C. § 360oo(a). That prohibition is in place
unless a valid variance applies to a sale. § 360oo(b).
     The variance is not a regulation, but as the indictment rec-
ognizes, granting these variances is an exercise of the FDA’s
regulatory function over laser products. By deceiving Insight
Technology into selling them non-compliant laser sights,
Kelerchian and the other conspirators defrauded the FDA
into allowing them to possess devices that federal law prohib-
its. They also led Insight to create a false paper trail for these
devices that would make it impossible for the FDA to keep
track of the true owners of these dangerous products, which
the FDA is supposed to do. Such fraud impairs the ability of
the FDA to regulate laser devices to prevent harm to the pub-
lic.
    In United States v. F.J. Vollmer & Co., 1 F.3d 1511 (7th Cir.
1993), we rejected an argument similar to Kelerchian’s. At is-
sue in F.J. Vollmer was a settlement agreement reached be-
tween the ATF and Gun South, Inc., a firearms importer. The
settlement agreement allowed Gun South to sell an otherwise-
banned semi-automatic rifle only to law enforcement oﬃcers
or agencies. Id. at 1514. Kenneth Nevius, a captain on active
duty in the Illinois National Guard, took advantage of this ex-
ception and bought two restricted rifles using his National
Guard stationery. He said he was buying the weapons “in
connection with his oﬃcial duties and not for the purpose of
resale.” Id. He lied. He actually bought the guns to sell them
16                                                 No. 18-1320

to F.J. Vollmer & Company, a firearms dealer. Nevius orches-
trated several such deals. Nevius and F.J. Vollmer were in-
dicted. The company was convicted of mail fraud and con-
spiracy to defraud the United States government.
    On appeal, the company argued that it was charged with
conspiring to violate only the settlement agreement between
the ATF and Gun South, which was being treated as if it were
a “de facto substantive agency rule.” Id. at 1516. We rejected
the argument, explaining that “F.J. Vollmer and Nevius were
not convicted of violating a settlement agreement.” Id. at 1515.
“The indictment … specifically stated the elements” of a § 371
conspiracy, making it evident to the court that this was the
federal crime the defendants were charged with committing.
Id. at 151516. “Further,” we continued, “because the convic-
tions are not based on the violation of the settlement agree-
ment, the defendants’ [APA] argument … is irrelevant.” Id. at
1516. We apply the same reasoning here. Count II properly
charged Kelerchian with a violation of 18 U.S.C. § 371.
     B. Suﬃciency of Evidence
    Kelerchian next argues that the government failed to
prove the charges involving the so-called demonstration let-
ters that enabled Kelerchian to buy machineguns for his per-
sonal collection (Counts III through VII) and failed to prove
the money-laundering conspiracy charge (Count IX). On its
own initiative or upon a defendant’s motion, a trial court
“must enter a judgment of acquittal of any oﬀense for which
the evidence is insuﬃcient to sustain a conviction.” Fed. R.
Crim. P. 29 (a).
   We review de novo the denial of a defendant’s motion for
acquittal, considering the evidence in the light most favorable
No. 18-1320                                                   17

to the prosecution. United States v. Mohamed, 759 F.3d 798, 803
(7th Cir. 2014). We “ask whether any rational trier of fact
could have found the essential elements of a crime beyond a
reasonable doubt,” United States v. Foley, 740 F.3d 1079, 1083
(7th Cir. 2014) (internal quotation marks omitted), and “over-
turn a verdict only when the record contains no evidence, re-
gardless of how it is weighed, from which the jury could find
guilt beyond a reasonable doubt.” United States v. Blassingame,
197 F.3d 271, 284 (7th Cir. 1999) (internal quotation marks
omitted). This is usually a high hurdle for a defendant to clear,
but “the height of the hurdle depends directly on the strength
of the government’s evidence.” United States v. Garcia, 919
F.3d 489, 496–97 (7th Cir. 2019) (reversing denial of Rule 29
motion), quoting United States v. Jones, 713 F.3d 336, 339 (7th
Cir. 2013) (aﬃrming grant of Rule 29 motion).
       1. Demonstration Letters
    Kelerchian argues that the evidence does not support his
convictions for conspiring to make false statements and mak-
ing false statements in the demonstration letters submitted to
ATF. To recap, Count III alleged that Kelerchian violated 18
U.S.C. § 371 by conspiring with Kumstar and Slusser to make
false statements to the ATF by submitting letters falsely claim-
ing that the Sheriﬀ’s Department wanted demonstrations of
otherwise-prohibited weapons that Kelerchian wanted for his
personal collection. Counts IV through VII alleged that the
phony demonstration letters were false statements to the ATF
in violation of 18 U.S.C. § 1001.
    Kelerchian bases his argument on narrow readings of the
text of the demonstration letters as compared to the
indictment. He reads the indictment narrowly to charge him
with conspiring to make and making specific false
18                                                  No. 18-1320

statements—requests for demonstrations of machineguns.
Nowhere in the essentially identical demonstration letters,
Kelerchian contends, however, is there specific language,
false or otherwise, actually requesting a demonstration.
Because the indictment charged Kelerchian not with
conspiring to make and making any false statement to the ATF
but with conspiring to make and making specific false
statements to the ATF, the government was required to
produce evidence showing that the specific false statements
were in fact made and failed to do so. We disagree.
    The letters said the Sheriﬀ’s Department was “interested
in a demonstration” of several listed guns and had found a
dealer, Kelerchian, who had “oﬀered to conduct such a
demonstration.”       The     letters   explained     that    the
“demonstration[s] will give [the] department personnel a
better understanding of the capabilities, limitations, and
diﬀerences of these [requested] guns.” From the content of
these letters, a reasonable jury could find that these were false
requests for demonstrations. The letters could have had no
other purpose. In addition, Kelerchian’s own testimony
characterized the letters as a “request to demonstrate”
machineguns. Kumstar also testified that each of the letters
was “a demonstration request,” that Kelerchian had not
oﬀered demonstrations, and that the Sheriﬀ’s Department
was not really interested in any. In short, there was suﬃcient
evidence to support Kelerchian’s convictions for conspiring
to make and actually making false statements in the
demonstration letters that he and his co-conspirators drafted.
       2. Money-Laundering Conspiracy
   Kelerchian’s challenge to his conviction for conspiring to
commit money laundering poses the closest question in this
No. 18-1320                                                   19

appeal. The money-laundering conspiracy charge stems from
the conspirators’ second and third fraudulent machinegun
purchases. The indictment charged Kelerchian with conspir-
ing to launder money in violation of 18 U.S.C. § 1956(h),
which makes it a crime to conspire to commit any of the
money-laundering oﬀenses defined in § 1956 or § 1957.
    The indictment specified that Kelerchian conspired to vio-
late this statute in two ways. First was a conspiracy to engage
in a financial transaction using the known proceeds of an un-
lawful activity (wire fraud to obtain the machineguns) to con-
ceal the ownership and control of the proceeds from the spec-
ified unlawful activity in violation of § 1956(a)(1)(B)(i). Sec-
ond was a conspiracy to use the proceeds of the wire fraud to
engage in a monetary transaction exceeding $10,000 in viola-
tion of § 1957. The jury found Kelerchian guilty of both al-
leged conspiracies. We focus on the conspiracy to violate
§ 1957, which we find was proven, so we need not address the
theory under § 1956(a)(1)(B)(i). See United States v. Joshua, 648
F.3d 547, 553 (7th Cir. 2011).
    A money-laundering violation under either § 1956 or
§ 1957 requires proof of two distinct acts: the unlawful activ-
ity that generated “proceeds” and then the monetary transac-
tion conducted with the criminal proceeds. United States v.
Seward, 272 F.3d 831, 836 (7th Cir. 2001), quoting United States
v. Mankarious, 151 F.3d 694, 705 (7th Cir. 1998). The underly-
ing unlawful activity here was wire fraud. “To establish wire
fraud under 18 U.S.C. § 1343, the government must prove the
defendant (1) participated in a scheme to defraud, (2) in-
tended to defraud, and (3) used interstate wires in furtherance
of the fraud.” United States v. Buncich, 926 F.3d 361, 366 (7th
Cir. 2019). The wire fraud oﬀense was completed during the
20                                                  No. 18-1320

second and third machinegun transactions when Kelerchian
and the others sent materially false statements to H&K assert-
ing that the machineguns were being purchased by the Lake
County Sheriﬀ. See United States v. Aslan, 644 F.3d 526, 545–46
(7th Cir. 2011) (wire fraud statute “punishes the scheme, not
its success”) (collecting cases); accord, e.g., United States v.
Kennedy, 707 F.3d 558, 566–67 (5th Cir. 2013) (wire fraud dis-
tinct from money laundering of proceeds); United States v.
Halstead, 634 F.3d 270, 280–81 (4th Cir. 2011) (health care fraud
distinct from money laundering of proceeds). The ma-
chineguns were the proceeds of that wire fraud. According to
the government, the way in which Kelerchian and Kumstar
sold these weapons to dealer Adam Webber constituted
money laundering.
    The government’s theories for the money-laundering con-
spiracy are that, after completing the fraud in the second pur-
chase of machineguns, Kelerchian and Kumstar conspired to
conceal the fact that machinegun parts were intended for
dealer Adam Webber in violation of § 1956(a)(1)(B)(i) and con-
spired to engage in one or more transactions in criminally de-
rived proceeds worth more than $10,000 in violation of § 1957.
Kelerchian and Kumstar used Slusser as a middleman in their
dealings with Webber to obscure the true ownership of the
guns. In particular, Slusser sold the parts to Webber for
$18,900 and received a check in his name as payment. He was
instructed to deposit that check in his own account and then
to issue cashier’s checks to Kelerchian and Kumstar for $9,450
each. Kelerchian then waited nine months before paying H&K
for the weapons. The intention, the government argued, was
to make it appear as though the Sheriﬀ’s Department bought
and retained control over the weapons. Further, Kelerchian
waited months to pay H&K to distance himself from the
No. 18-1320                                                               21

Webber sale, making it look as though he was unaware of the
connection between the money sent to H&K and the check he
received from Slusser. The wire fraud theory thus holds to-
gether.
    But the government’s explanation of its theory raised a
new issue in the law of wire fraud. The government must
show that the scheme to defraud was aimed at some form of
money or property. Cleveland v. United States, 531 U.S. 12, 19
(2000).2 In his opening appellate brief, Kelerchian argued that
the wire fraud the government alleged was not a transaction
distinct from the sale of the fraudulently obtained
machinegun parts to Webber. The government responded
that the wire fraud was complete as soon as the defendants
sent the purchase packets with fraudulent statements to
H&K, so that the later sale of the parts was a distinct oﬀense.
We agree with that point, but Kelerchian argued in his reply
brief that the government’s solution to the distinct-transaction
problem posed a diﬀerent fatal problem for the money-
laundering conspiracy charge. Submitting the fraudulent
statements to H&K to obtain the machineguns, Kelerchian
argued, did not amount to wire fraud because Kelerchian and
his co-conspirators did not deprive anyone of a “property
interest” as required under Cleveland.
  This property interest issue takes us to the edges of federal
mail and wire fraud law and poses Kelerchian’s strongest

    2 Although Cleveland and other Supreme Court cases establishing this
rule involve the mail fraud statute, 18 U.S.C. § 1341, as opposed to the wire
fraud statute, we have explained that “the elements of wire fraud under
18 U.S.C. § 1343 directly parallel those of the mail fraud statute” so that
“cases construing one are equally applicable to the other.” United States v.
Leahy, 464 F.3d 773, 786 (7th Cir. 2006).
22                                                    No. 18-1320

challenge to any of his convictions. In McNally v. United States,
the Supreme Court explained that the federal mail fraud stat-
ute is “limited in scope to the protection of property rights.”
483 U.S. 350, 360 (1987), superseded by statute on other grounds,
18 U.S.C. § 1346. To establish mail fraud, the government thus
must “prove as an element of the oﬀense … that the defendant
deprived the victim of a property right.” United States v. F.J.
Vollmer & Co., 1 F.3d 1511, 1520 (7th Cir. 1993), citing McNally,
483 U.S. at 359–61. Kelerchian argues that the government
failed to identify a victim whom the defendants intended to
deprive of a recognized property interest. He argues that nei-
ther the ATF’s regulatory interest in the transfer of firearms
nor H&K’s interest in the legal disposition of its guns quali-
fies. The government’s interest will not suﬃce, but H&K’s in-
terests will support the wire fraud theory.
    As discussed above, F.J. Vollmer & Co. involved a scam in
which an Illinois National Guard captain, Kenneth Nevius,
defrauded a weapons manufacturer into selling him re-
stricted guns under the pretense that he was purchasing the
weapons “in connection with” his oﬃcial duties. 1 F.3d at
1514. Nevius then resold the weapons to F.J. Vollmer & Com-
pany, a business dealing in the sale of firearms. Id. at 151314.
Nevius and F.J. Vollmer were convicted of mail fraud in vio-
lation of § 1341. F.J. Vollmer argued that the mail fraud charge
was insuﬃcient because it “did not allege that the govern-
ment had a property interest in the guns as is required by
McNally.” Id. at 1520. As in this case, at F.J. Vollmer’s trial “the
government did not allege in the indictment, present evidence
at trial, nor was the jury instructed on the deprivation of a
property right.” Id.
No. 18-1320                                                  23

    We agreed with F.J. Vollmer, concluding that the govern-
ment was not deprived of a qualifying property interest.
Vollmer, 1 F.3d at 1521. The government argued that its “right
to control the disposition of … firearms is a property interest”
of which Nevius and F.J. Vollmer deprived it through mail
fraud. We rejected this argument, holding that “the govern-
ment’s regulatory interests are not protected by the mail fraud
statute.” Id. (emphasis added), citing, among other cases,
United States v. Bruchhausen, 977 F.2d 464 (9th Cir. 1992).
    We conclude here, however, that the government proved
that Kelerchian and his co-conspirators committed wire fraud
against H&K, which had a suﬃcient property interest of
which they schemed to deprive it. Kelerchian finds support
for his position, though, in the Ninth Circuit’s Bruchhausen de-
cision. We consider first that case and then decisions of this
court and the Second Circuit that adopt a broader view of
property interests when parties are induced to enter into ille-
gal sales, especially of weapons.
    In Bruchhausen, the defendant was charged with a scheme
to defraud American manufacturers by buying sophisticated
technology, promising falsely that the purchased equipment
would be used only in the United States, and then smuggling
the goods to countries in the Soviet Bloc. “Representatives
from these companies testified that they would never have
sold to Bruchhausen had they known the truth.” 977 F.2d at
466. On appeal the Ninth Circuit held that Bruchhausen had
not defrauded the manufacturers of “property interests”
within the meaning of the wire fraud statute. The court rea-
soned: “The manufacturers received the full sale price for
their products,” and “While they may have been deceived
into entering sales that they had the right to refuse, their
24                                                 No. 18-1320

actual loss was in control over the destination of their prod-
ucts after sale.” Id. at 467. The Ninth Circuit wrote that while
“the manufacturer may have an interest in assuring that its
products are not ultimately shipped in violation of law … that
interest in the disposition of goods it no longer owns is not
easily characterized as property.” Id. at 468. Accordingly, the
court held “that the interest of the manufacturers in seeing
that the products they sold were not shipped to the Soviet
Bloc in violation of federal law is not ‘property’ of the kind
Congress intended to reach in the wire fraud statute.” Id.
    If that view were correct, then it would be diﬃcult to af-
firm Kelerchian’s money-laundering conspiracy conviction.
Bruchhausen is not the final word on the issue, however. The
government’s Rule 28(j) letter cited cases from this circuit and
the Second Circuit that support its view that Kelerchian and
the others defrauded H&K of a property interest suﬃcient to
allow use of wire fraud as “unlawful activity” to support
Kelerchian’s money-laundering conspiracy conviction, and
that view is consistent with the way the jury instructions and
the government’s closing argument framed Count IX for the
jury at trial.
    We start with United States v. Leahy, 464 F.3d 773 (7th Cir.
2006), in which defendant Duﬀ was convicted of defrauding
the City of Chicago. A Chicago ordinance required the city to
establish a goal of awarding not less than 25% of the annual
dollar value of all city contracts to qualified minority-owned
businesses and 5% of the annual dollar value to qualified
women-owned businesses, and set aside certain contracts for
such businesses. Id. at 778. To take fraudulent advantage of
the ordinance, Duﬀ, a white man, obscured the ownership
and control of two of his businesses to give the city the false
No. 18-1320                                                    25

impression that his mother and a black man were running
them. Id. at 77981. Through this fraud, Duﬀ was able to win
lucrative contacts with the city. Duﬀ and others were eventu-
ally convicted of wire fraud, in addition to other oﬀenses. The
defendants appealed, arguing that the indictment could not
support a conviction under the applicable mail and wire
fraud statutes because “the only loss Chicago suﬀered was to
its regulatory interests—an intangible right unprotected by
these statutes.” Id. at 786.
    We rejected that argument. We noted that the object of the
wire fraud was in fact property—money paid under con-
tracts. Id. at 78788. We distinguished Cleveland, where the Su-
preme Court held that for mail-fraud purposes, Louisiana did
not have a property interest in state permits or licenses it is-
sued for video poker machines. See 531 U.S. at 21–23. Unlike
the fraud to obtain the licenses in Cleveland, in Leahy “the
fraud was committed both against Chicago as a regulator and
also against the city as a property holder.” 464 F.3d at 788.
This “scheme precisely and directly targeted Chicago’s coﬀers
and its position as a contracting party.” Id. We concluded that
Chicago suﬀered a property loss “in that it paid for a service
provided by [a minority-owned business] or [women-owned
business] that it did not receive.” Id. We aﬃrmed the mail and
wire fraud convictions.
     Leahy is not precisely on point—the fraud there was aimed
at the buyer, not the seller, of products and services—but it is
instructive. First, in both cases, the object of the fraud was
property—money in Leahy and here machineguns. Second, in
both cases one party to a contract deceived the other to induce
it to enter into the contract. In Leahy the city was deceived into
contracting with businesses controlled by Duﬀ rather than by
26                                                   No. 18-1320

minorities or women, as the ordinance called for. Here, H&K
was induced to sell machineguns to a buyer it thought was
lawful (the Sheriﬀ’s Department) when the real buyers were
the defendants, who could not lawfully buy the machineguns.
Kelerchian’s fraud deprived H&K of the ability to ensure that
its products were sold in compliance with federal law. As
Kelerchian points out, H&K was paid the full price for the ma-
chineguns. In Leahy, too, however, the city received the ser-
vices it paid for, yet not from the sorts of businesses it thought
it was paying for them. 464 F.3d at 788. We treated that sort of
loss as suﬃcient, noting that the object of the fraud “was
money, plain and simple, taken under false pretenses from
the city its role as a purchaser of services.” Id.
    The government also finds support from Second Circuit
cases. In United States v. Schwartz, the defendants purchased
night-vision equipment from Litton Industries. 924 F.2d 410
(2d Cir. 1991). The Arms Export Control Act restricted the sale
of this equipment to certain countries (including Argentina,
then fighting the United Kingdom in the Falklands War), so
Litton sought assurances that the defendants would not ex-
port purchased equipment to restricted countries. Id. at 414.
The sales contracts required the buyers to assure that they
would comply “with all laws and regulations pertaining to
the export of night vision goggles.” Id. As the defendants
placed additional orders, Litton sought further assurances
and documentation that the equipment was not destined for
restricted countries. The defendants signed the contracts and
promised to abide by applicable laws but then exported reg-
ulated night-vision goggles to Argentina, where they were
used against British forces. Id. The defendants were convicted
of wire fraud, among other crimes. Id. at 420.
No. 18-1320                                                      27

    In challenging their wire fraud convictions for the Argen-
tine sales, the defendants argued that Litton did not suﬀer any
economic harm and thus could identify no qualifying prop-
erty interest. Id. The Second Circuit upheld the convictions be-
cause the defendants’ “misrepresentations went to an essen-
tial element of the bargain between the parties and were not
simply fraudulent inducements to gain access to Litton equip-
ment.” Id. at 421. The court explained that “the fact that Litton
was paid for its night vision goggles does not mean that Litton
received all it bargained for. In fact, it did not.” Id. The “de-
fendants’ conduct deprived Litton of the right to define the
terms for the sale of its property … and cost it, as well, good
will because equipment Litton … sold was exported illegally.”
Id.
    In later cases, the Second Circuit has clarified the test it ap-
plied in Schwartz. The court has acknowledged that “[t]he
‘right to control one’s assets’ does not render every transac-
tion induced by deceit actionable under the mail and wire
fraud statutes.” United States v. Binday, 804 F.3d 558, 570 (2d
Cir. 2015), quoting United States v. Wallach, 935 F.2d 445, 463
(2d Cir. 1991). Its “cases have drawn a fine line between
schemes that do no more than cause their victims to enter into
transactions they would otherwise avoid—which do not vio-
late the mail or wire fraud statutes—and schemes that depend
for their completion on a misrepresentation of an essential el-
ement of the bargain—which do violate the mail and wire
fraud statutes.” Id., quoting United States v. Shellef, 507 F.3d 82,
108 (2d Cir. 2007). This is a fine distinction, but Kelerchian and
his co-conspirators fell on the wrong side of it, as the defend-
ants in Schwartz did with their fraud to obtain arms for illegal
export.
28                                                 No. 18-1320

    In Shellef, for example, the defendants persuaded a com-
pany to sell them hundreds of thousands of pounds of a
highly regulated chemical by falsely representing that they
would not resell the solvent within the United States. 507 F.3d
at 8990. The court distinguished Schwartz by focusing on the
diﬀerent misrepresentations made in the cases. In Shellef, the
misrepresentations induced the seller only “to enter into a
transaction it would otherwise have avoided,” whereas in
Schwartz, the defendants had misrepresented “an essential el-
ement of the bargain.” Id. at 109, quoting Schwartz, 924 F.2d at
421. In explaining this distinction further, the Second Circuit
later said that it “reject[s] application of the mail and wire
fraud statute where the purported victim received the full
economic benefit of its bargain,” and upholds “convictions …
where the deceit aﬀected or the victim’s economic calculus or
the benefits and burdens of the agreement.” Binday, 804 F.3d
at 570.
    The Second Circuit opinions and our opinion in Leahy
show that schemes to defraud a party into entering a contract
it would not enter if it had been told the truth, but where the
fraudsters deliver the agreed money, goods, or services are
close to the edge of the reach of the wire and mail fraud
statutes. We do not attempt here, in this money-laundering
conspiracy case, to establish a comprehensive guide on the
scope of the mail and wire fraud statutes. We concentrate on
the case before us, focused on illegal imports of highly
regulated and dangerous machineguns. On the strength of
our decision in Leahy and the Second Circuit’s in Schwartz,
which is remarkably close to our facts and persuasive, we
conclude that the government proved that the scheme to
defraud H&K involved a suﬃcient property interest to
No. 18-1320                                                      29

support using wire fraud as the underlying unlawful activity
for a money-laundering conspiracy charge.
    As in Leahy, the scheme to defraud induced one party here
to contract with others who were not legally entitled to enter
into the contract. And as in Schwartz, this case involves much
more than the seller’s preferences about the terms of the deals.
As in Schwartz, an arms manufacturer was defrauded into
making a sale to buyers who were legally prohibited from
buying the goods. We agree with the Second Circuit’s expla-
nation in Schwartz that, in such a deal, the fact that the seller
was paid full price does not mean it received all it bargained
for and is not decisive. The Bruchhausen view fails to take into
account the damage to goodwill from the illegal sale and, we
add, the legal and regulatory risk that the seller faces in such
deals. If Litton (in Schwartz) and H&K (here) had known the
true facts of the sales, those companies would have faced
criminal liability. Even the investigation of the criminal trans-
actions posed costs and legal risks for the sellers.
   In the language of the Second Circuit, the destination of
the machineguns—a law enforcement agency—was an
“essential element of the bargain” between H&K and the
supposed buyer. Without the Sheriﬀ’s Department stationery,
Kelerchian and the others could not even have approached
H&K about buying these machineguns. The sale required
submitting the ATF forms and an application certifying that
the purchaser of the guns was a law enforcement agency.
Although H&K did not lose any money in the machinegun
transaction itself, by illegally selling firearms it opened itself
up to risks it did not bargain for: risks of liability, of increased
government scrutiny, and negative publicity, all of which in
turn could jeopardize future sales. These are serious
30                                                   No. 18-1320

repercussions central to H&K’s calculus of the “benefits and
burdens” of this transaction.
    Comparing the Ninth Circuit’s decision in Bruchhausen
with the Second Circuit’s decisions in Schwartz and its prog-
eny, we think the Second Circuit has the better reading of the
mail and wire fraud statutes. Although “property” in these
statutes is not broad enough to encompass intangible interests
like government regulatory interests, “property” is not so nar-
row as to exclude any tangible good or service for which fair
market value is paid. In Bruchhausen, the Ninth Circuit re-
jected the idea that a seller could have a cognizable property
interest “in assuring that its products are not ultimately
shipped in violation of law” because that would mean the
manufacturer’s interest is “in the disposition of goods it no
longer owns.” 977 F.2d at 468. We respectfully disagree. The
seller’s interest is not only in shipping goods legally, but also
in not selling products in violation of federal law. That interest
exists before the seller relinquishes ownership. As the concur-
rence in Bruchhausen explained: “The strictures an owner puts
on his willingness to sell an item are not mere ephemera.
When a prospective buyer lies in order to evade those stric-
tures, a fraud has been committed upon the owner of the item
just as surely as if the buyer had issued a rubber check.” Id. at
469 (Fernandez, J., concurring).
    H&K sold the machineguns to Kelerchian and his co-
conspirators only because of their deceit. Because this fraud
deprived H&K of a cognizable property interest in avoiding
illegal sales of its products, the government established a
violation of § 1343. This is as far as we need to go to aﬃrm
Kelerchian’s conviction on conspiracy to launder money in
violation of § 1957.
No. 18-1320                                                    31

    Kelerchian also argues that the government failed to prove
that he conspired “to conceal or disguise the nature, the loca-
tion, the source, the ownership, or the control of the proceeds
of” the wire fraud in the second machinegun purchase. See 18
U.S.C. § 1956(a)(1)(B)(i). Although such evidence is needed to
sustain a § 1956 conviction, we need not decide whether the
government proved this allegation. As discussed above, the
jury expressly found Kelerchian guilty of conspiring to violate
both § 1956 and § 1957. That means that Kelerchian must
show that the evidence was insuﬃcient under either theory to
overturn his conviction on Count IX. Because a rational jury
could find Kelerchian guilty of conspiracy to violate § 1957,
we aﬃrm his conviction on Count IX.
   C. Jury Instructions
       1. Standard of Review
    Kelerchian raises several objections to the jury instruc-
tions. “We review de novo whether jury instructions accurately
summarize the law, but give the district court substantial dis-
cretion to formulate the instructions provided that the in-
structions represent a complete and correct statement of the
law.” United States v. Edwards, 869 F.3d 490, 496 (7th Cir. 2017),
quoting United States v. Daniel, 749 F.3d 608, 613 (7th Cir.
2014). We review jury instructions as a whole and in context.
United States v. al-Awadi, 873 F.3d 592, 598 (7th Cir. 2017).
       2. Conspiracy Instructions
    Kelerchian challenges the jury instructions on three dis-
tinct conspiracy charges. Count I alleged that he conspired to
make false statements regarding the records required to be
kept by a licensed firearms dealer. Making the false state-
ments violated 18 U.S.C. § 924(a)(1)(A), which is the
32                                                  No. 18-1320

substantive crime. Similarly, making false statements to the
ATF in violation of 18 U.S.C. § 1001 was the substantive crime
of Count III’s conspiracy charge, and money laundering in vi-
olation of § 1956 and § 1957 was the substantive oﬀense in
Count IX’s conspiracy charge.
    To establish a conspiracy to commit an oﬀense against the
United States in violation of § 371, the government must
prove “(1) an agreement to commit an oﬀense against the
United States; (2) an overt act in furtherance of the conspiracy;
and (3) knowledge of the conspiratorial purpose.” United
States v. Soy, 454 F.3d 766, 768 (7th Cir. 2006). The government
must show only “that the conspirators agreed that the under-
lying crime be committed. … In other words, each conspirator
must have specifically intended that some conspirator commit
each element of the substantive oﬀense.” Ocasio v. United
States, 136 S. Ct. 1423, 1432 (2016). “[T]he fundamental char-
acteristic of a conspiracy is a joint commitment to an ‘en-
deavor which, if completed, would satisfy all the elements of
[the underlying substantive] criminal oﬀense.’” Id. at 1429,
quoting Salinas v. United States, 522 U.S. 52, 65 (1997) (altera-
tion in original).
    Kelerchian asked the district court to instruct the jury that
the government had to prove every element of the substantive
oﬀenses underlying the § 371 charges. The court declined to
give that instruction and instead, for each of the three relevant
conspiracy counts, gave the Seventh Circuit’s Pattern Jury In-
struction, telling the jurors that that government had to
“prove each of the following elements beyond a reasonable
doubt:”(1) that the conspiracy charged in the indictment ex-
isted; (2) that the defendant knowingly joined the conspiracy
with the intent to advance it; and (3) that one of the
No. 18-1320                                                   33

conspirators committed an overt act to advance the charged
conspiracy. See 7th Cir. Pattern Criminal Jury Instr. § 5.08(A)
(2018). For each conspiracy count, the court also gave the ju-
rors an Eighth Circuit Pattern Instruction at the Government’s
request: “To help you decide whether the defendant con-
spired to commit” the relevant substantive oﬀense, the jury
“should consider the elements of the [substantive oﬀense].”
The court then listed the elements of each of the substantive
oﬀenses and instructed the jurors that they “should consider
these elements in determining whether the defendant con-
spired to commit” the underlying oﬀense at issue.
    Kelerchian argues that these instructions misled the jurors
into thinking that they were not obliged to consider the ele-
ments of the substantive oﬀenses to convict Kelerchian on the
conspiracy charges against him. In particular, he asserts that
the use of “should” as opposed to “must” was problematic.
He argues that the word “should” suggested that the jury
could disregard entirely the elements of the substantive
crimes in the conspiracy charges and convict on a finding that
a generic conspiracy existed, rather than a conspiracy to com-
mit a specific, defined crime. The problem was exacerbated,
Kelerchian contends, by instructions saying that the govern-
ment must prove the elements of conspiracy beyond a reason-
able doubt.
    These instructions were not erroneous. We have said be-
fore that “should” and “must” are interchangeable in this con-
text: “[B]oth words are imperative when used to instruct a
jury,” and “it is hardly plausible that a jury would reach a dif-
ferent verdict based on the use of ‘should’ or ‘must.’” United
States v. Davis, 724 F.3d 949, 955 (7th Cir. 2013). That is how
the district court used the terms throughout its instructions
34                                                  No. 18-1320

here. The jurors were instructed that, in deliberations, they
“should” or “should not” do a variety of things that are man-
datory or prohibited. For example, the jurors were told that
they “should not consider the possible punishment for the de-
fendant who is on trial,” “should rely on your independent
recollection of the evidence,” “should not be unduly influ-
enced by the notes of other jurors,” and “should find the de-
fendant not guilty” if the government failed to prove all ele-
ments of an alleged oﬀense beyond a reasonable doubt. We
see no meaningful diﬀerence between the framing of these in-
structions and the instructions to which Kelerchian objects.
   The instructions communicated correctly that to convict
on the conspiracy counts, the jury needed to find that Keler-
chian “agree[d] with [the] others to commit the acts which
constitute the substantive oﬀense[s]” defined by
§ 924(a)(1)(A), § 1001, and §§ 1956 and 1957. United States v.
Craig, 573 F.2d 455, 486 (7th Cir. 1977). There was no error.
       3. Demonstration Letter Instruction
    Kelerchian also argues that the district court erroneously
instructed the jury regarding ATF’s requirements for demon-
stration letters. His issue is with Instruction 27, which said in
relevant part:
       Machine guns may also be imported as dealer
       samples if a dealer can establish to the Bureau
       of Alcohol, Tobacco, Firearms and Explosives
       by specific information:
          o that there is a governmental customer
            requiring a demonstration of the
            weapons; and
No. 18-1320                                                35

          o the weapons are available to fill sub-
            sequent orders.
      In addition, the governmental entity must pro-
      vide a letter expressing a need for a particular
      model or interest in seeing a demonstration of a
      particular weapon.
      If a dealer requests more than one machine gun
      of a particular model, he must also establish his
      need for the quantity of samples sought to be
      imported.
    Kelerchian contends that this instruction selectively
pulled a phrase from 27 C.F.R. § 479.112(c), which governs the
registration of imported firearms, including those acquired
pursuant to demonstration letters, to create the erroneous im-
pression that “dealer sales samples required a demonstration
of the weapons” to take place. The government responds that
Kelerchian is focusing on the wrong regulation. Instruction 27
addressed 27 C.F.R § 479.105, which applies to the transfer,
rather than the importation, of machineguns, and subsection
(d) specifically deals with demonstration letters. In short,
§ 479.112(c) applies to importation of firearms for demonstra-
tions and § 479.105(d) applies to domestic transfers of ma-
chineguns for the same purpose. Kelerchian was alleged to
have conducted dealer sample purchases involving the im-
portation of machine guns only in Count IV. The remaining
counts involved domestic transfers.
   Regardless of which regulation Instruction 27 is based on,
Kelerchian’s challenge fails because the instruction did not
say that the dealer must actually perform a demonstration. It
said that a dealer must show “that there is a governmental
36                                                  No. 18-1320

customer requiring a demonstration.” Another instruction
told the jury: “The law does not require a dealer who receives
a machine gun for use as a sale sample to do a demonstration
of the machine gun.” The instructions as a whole correctly
stated the law.
     D. Closing Argument Issues
   Kelerchian also argues that the government committed
prosecutorial misconduct and improperly amended the in-
dictment. Neither argument is persuasive.
        1. Prosecutorial Misconduct
    We review claims of prosecutorial misconduct in two
steps. “First, we determine whether the prosecutor’s com-
ments were improper standing alone. Second, we ask whether
the remarks in the context of the whole record denied the de-
fendants the right to a fair trial.” United States v. Durham, 766
F.3d 672, 684 (7th Cir. 2014), citing United States v. Bell, 624
F.3d 803, 811 (7th Cir. 2010). To evaluate the relevant state-
ments in context to determine whether they deprived a de-
fendant of a fair trial, we consider “1) the nature and serious-
ness of the misconduct; 2) the extent to which the comments
were invited by the defense; 3) the extent to which the preju-
dice was ameliorated by the court’s instruction to the jury;
4) the defense’s opportunity to counter any prejudice; and 5)
the weight of the evidence supporting the conviction.” United
States v. Common, 818 F.3d 323, 333 (7th Cir. 2016).
   At trial, Kelerchian did not object to the prosecution’s ar-
guments in closing that he now argues are improper. We
therefore review only for plain error. “On plain-error review,
we may reverse if: (1) an error occurred, (2) the error was
plain, (3) it aﬀected the defendant’s substantial rights, and (4)
No. 18-1320                                                   37

it seriously aﬀected the fairness, integrity, or public reputa-
tion of the proceedings.” United States v. Pierson, 925 F.3d 913,
919 (7th Cir. 2019), citing United States v. Olano, 507 U.S. 725,
73238 (1993). Together, these inquiries mean that Kelerchian
“must demonstrate that the comments at issue were ‘obvi-
ously’ or ‘clearly’ improper … [such] that not only was [he]
deprived of a fair trial, but also that the outcome of the trial
probably would have been diﬀerent absent the prosecution’s
remarks.” United States v. Hills, 618 F.3d 619, 640 (7th Cir.
2010) (internal citation omitted). In essence, the question is
whether the argument was so egregious that the trial judge
was required to intervene without a defense objection.
    Kelerchian argues that the government’s rebuttal improp-
erly appealed to the jurors’ emotions and invited them to con-
sider the societal consequences of their verdict. Some back-
ground is needed on relevant testimony solicited during trial.
There was testimony throughout trial that the machineguns
Kelerchian and his co-conspirators requested for dealer sales
samples were not appropriate for use by the Sheriﬀ’s Depart-
ment. They included a “multipurpose belt-fed machine gun
… typically used on top of a Humvee or maybe on the door
of a helicopter” and a “light-weight, belt-fed machinegun,”
“designed for the Navy SEAL teams for warfare.” Testimony
of this nature helped show that the dealer sales sample letters
were fraudulent because the Sheriﬀ’s Department had no use
for the sample firearms.
   In closing, defense counsel responded by pointing out that
the ATF agreed to allow H&K to provide these weapons to
Kelerchian to demonstrate to the Sheriﬀ’s Department:
       I want to talk now about the demonstration let-
       ters. Count 3 is charged as a conspiracy. Counts
38                                                   No. 18-1320

        4 through 7 are charged as making the actual
        statement, the false statement. Every letter at is-
        sue in this case says, well, basically the same
        thing … approximately seven letters on the Lake
        County Sheriﬀ’s Department letterhead re-
        questing firearms demonstrations of machine
        guns from Kelerchian knowing the same to con-
        tain a materially false, fictitious, and fraudulent
        statement because Vahan Kelerchian very well
        knew in fact, no demonstration was going to oc-
        cur.
        First of all, ladies and gentlemen, every single
        one of those letters was accepted by the ATF,
        was signed oﬀ by numerous people from the
        ATF as justifying the transfer of those guns. This
        whole discussion about these guns not being
        appropriate for the Lake County Sheriﬀ’s De-
        partment is completely undercut by ATF sign-
        ing oﬀ and indicating that, in fact, these are the
        kinds of weapons that are justifiable in a
        demonstration letter.
Defense counsel emphasized the point a second time in clos-
ing: “ATF found [these] letter[s] acceptable.”
     In rebuttal, the government responded:
        There is no way on earth that these types of
        guns, any department would require a demon-
        stration because they’re belt-fed machine guns
        … [T]hese guns are so far outside the bounds of
        what regular law enforcement uses that there is
        no legitimate reason to have them
No. 18-1320                                                    39

       demonstrated. They’re belt-fed machine guns
       with ammunition that is three inches long.
       There’s no reason on earth why any law en-
       forcement agency would want them to be
       demonstrated. Mr. Kelerchian wants those. He
       told you that, but there’s no reason an agency
       would want them demonstrated. … That’s why
       the demonstration letters are utter nonsense be-
       cause the weapon is so far out of bounds it
       doesn’t make any sense. Under their rationale,
       the Lake County Sheriﬀ’s Department, Mr.
       Kelerchian, could demonstrate a tank, and he
       would get to keep it. How absurd is that? The
       law isn’t meant to function in absurdities. It’s
       meant to be applied by rational people such as
       you to determine what’s acceptable.
    Kelerchian argues that the prosecution’s use of the word
“acceptable” invited the jury to decide what is socially ac-
ceptable as opposed to what is legal. According to the govern-
ment, its use of the term “acceptable” in context was meant
only to remind the jury that its job was to determine whether
the letters requesting demonstrations were legitimate. In re-
jecting a similar claim of plain error in closing argument, we
have noted that “[l]awyers sometimes are not as precise as
they should be when giving extemporaneous closing argu-
ments.” United States v. Thomas, — F.3d —, — , 2019 WL
3490675, at *6 (7th Cir. Aug. 1, 2019). This jury was instructed
to focus on the instructions and to remember that lawyers’ ar-
guments are not evidence. The government’s use of the am-
biguous term “acceptable,” which did not even draw an ob-
jection, did not deny Kelerchian a fair trial or rise to the level
of plain error.
40                                                 No. 18-1320

       2. Constructive Amendment
    A constructive amendment of an indictment occurs in vi-
olation of the Fifth Amendment when the jury is allowed “to
convict for an oﬀense outside the scope of the indictment.”
Pierson, 925 F.3d at 91920. Kelerchian argues that the govern-
ment’s closing attempted to change its theory of liability as to
the demonstration letter charges in Counts III through VII.
The government argued in rebuttal:
       In Instruction Number 27, it tells you how you
       get these guns into the country for purposes of
       a demonstration. You know, it’s sales samples.
       That’s what it’s called, dealer samples. There’s a
       couple requirements. It’s pretty loose. I’ll grant
       you that. And there certainly doesn’t have to be
       any demonstration—and I mentioned that to
       you in the first part of my closing—but whether
       or not one occurs is sort of helpful to know
       whether or not they intended one. And it says
       that you have to have a document with specific
       information that there was a governmental cus-
       tomer requiring a demonstration of the weapon.
    Again, there was no objection to this argument. On appeal,
Kelerchian argues that the reference to “‘a document with
specific information’ … led the jury to underst[and] that the
‘document’ the government referred to in relation to Instruc-
tion No. 27, [was], in fact the [demonstration] letters refer-
enced in Counts 3–7.” Although Kelerchian does not spell this
out clearly, he implies that the government changed its theory
for Counts III through VII, arguing now that the “false state-
ments” were in an unspecified document submitted to H&K
No. 18-1320                                                41

as opposed to in the demonstration letters as alleged in the
indictment.
    We see no error, let alone a plain error. The government
was always clear that the demonstration letters were the basis
for Counts III through VII. They were the documents that con-
tained the “specific information” asserting “that there is a
governmental customer requiring a demonstration of the
weapons.” The government’s closing did not indicate other-
wise simply because in this excerpt it uses the term “docu-
ment” as opposed to “demonstration letter.”
   The judgment of the district court is
                                                 AFFIRMED.
