In the

    United States Court of Appeals
                For the Seventh Circuit
                    ____________________
Nos. 23-2840, 23-2846 & 23-2849
UNITED STATES OF AMERICA,
                                                 Plaintiff-Appellee,
                                v.

GREGG SMITH, MICHAEL NOWAK, and CHRISTOPHER JORDAN,
                                  Defendants-Appellants.
                    ____________________

       Appeals from the United States District Court for the
           Northern District of Illinois, Eastern Division.
       Nos. 1:19-CR-00669-1, 2, 4 — Edmond E. Chang, Judge.
                    ____________________

   ARGUED SEPTEMBER 5, 2024 — DECIDED AUGUST 20, 2025
                ____________________

   Before EASTERBROOK, KIRSCH, and KOLAR, Circuit Judges.
    KIRSCH, Circuit Judge. Gregg Smith, Michael Nowak, and
Chrisopher Jordan were precious metals futures traders who
manipulated the market through an unlawful practice called
spoofing, meaning they placed deceptive orders they in-
tended to cancel to push the market price a certain direction.
At trial, they were all convicted of various crimes in connec-
tion with this practice. They appeal their convictions on
2                             Nos. 23-2840, 23-2846 & 23-2849

multiple grounds. Finding none of their challenges persua-
sive, we affirm across the board.
                               I
                              A
   Gregg Smith, Michael Nowak, and Christopher Jordan
once traded precious metals futures contracts on commodities
exchanges operated by the Chicago Mercantile Exchange
Group (CME). They each employed a fraudulent scheme,
known as spoofing, to game the system and manipulate the
prices of the precious metals futures they traded.
    Spoofing is possible because of the nature of commodities
futures trading. A futures contract is a legally binding agree-
ment to buy or sell a commodity at an agreed-upon price on
an agreed-upon future date. Commodities futures traders use
an electronic platform known as Globex to access CME-
operated exchanges. These traders place bids to buy, or offers
to sell, a certain number of futures contracts on Globex at a
specified price or level. Trading on Globex is anonymous, and
while some traders employ computer algorithms to place or-
ders, others enter their orders manually, as Smith, Nowak,
and Jordan did. Globex also permits traders to cancel an or-
der, or an unfilled portion of an order, any time before it is
executed.
    The price of futures contracts is determined by supply and
demand: the price will increase if there is more demand than
supply for a product, and vice versa. But a fundamental as-
sumption on CME exchanges is that every order represents a
legitimate, bona fide order placed with the intent to trade.
Each order visible on Globex therefore impacts the market by
conveying an intent to participate in it at a particular price.
Nos. 23-2840, 23-2846 & 23-2849                                3

    Today, Globex shows every available order, but when
Smith, Nowak, and Jordan were traders, it displayed only the
ten best bids and the ten best offers at any time. And because
larger quantity orders will have a greater effect on price than
smaller orders will, Globex allows traders to break up larger
orders into a number of smaller ones by placing so-called ice-
berg orders. In this way, iceberg orders enable traders to con-
ceal the true size of their order. Although these features were
designed to mitigate the impact that large orders would have
on the market price, they paved the way for fraudulent
schemes to manipulate the market—especially spoofing.
    A spoofing trader places large orders that he does not in-
tend to execute, driving the price in a more favorable direc-
tion by communicating false information that deceives the
marketplace about actual supply and demand. This typically
involves four steps. First, the trader places an order, often an
iceberg order, that he genuinely intends to trade. Second, the
trader places a visible spoof order on the other side of the mar-
ket. The trader never intends to trade this order; rather, it is
designed to push the market price to the benefit of the legiti-
mate order. For instance, if a trader wants to buy at a price
below the market, he will place a large sell order at a low price
(or a series of smaller sell orders at descending prices) to push
the market down. Third, the market reacts to the illusion of
market activity generated by the spoof order, allowing the
trader to execute the genuine order at his desired price.
Fourth, the trader cancels the spoof order before it can be
filled.
   CME rules have long prohibited spoofing. In particular,
CME Rule 432 prohibits traders from manipulating or at-
tempting to manipulate “prices of exchange futures or
4                             Nos. 23-2840, 23-2846 & 23-2849

options contracts”; employing or attempting to employ “any
manipulative device, scheme or artifice to defraud”; and pur-
chasing or selling or offering to purchase or sell “exchange
futures or options contracts or any underlying commodities
or securities for the purpose of upsetting the equilibrium of
the market or creating a condition in which prices do not or
will not reflect fair market values.” Accordingly, the defend-
ants’ employers have policies prohibiting spoofing, both ex-
pressly and implicitly as a form of market manipulation.
                              B
    Nowak and Smith worked at JPMorgan from 2008 to 2016.
Nowak was a managing director who ran the precious metals
trading desk, splitting his time between New York and Lon-
don. Smith was an executive director and sat next to Nowak
in the New York office. He joined JPMorgan after it acquired
Bear Stearns in 2008. Jordan worked as a precious metals
trader in the New York office between 2006 and 2009. After
JPMorgan terminated him in 2009, he moved to Credit Suisse,
where he worked from March to August 2010.
    On multiple occasions, Smith, Nowak, and Jordan each
placed orders mirroring the trading pattern of spoofing. That
conduct eventually led the government to indict them for var-
ious spoofing-related crimes. Smith and Nowak were each
charged with attempted price manipulation, 

(a)(2); wire fraud, 

; commodities fraud, 

(1); and violating the anti-spoofing provision of
the Dodd-Frank Act, 7 U.S.C. §§ 6c(a)(5)(C) & 13(a)(2). Jordan
was charged with wire fraud, 

. All three were
charged with conspiracy, but none were convicted.
Nos. 23-2840, 23-2846 & 23-2849                               5

                               1
   Smith and Nowak were tried together. They did not mean-
ingfully contest that their trading activity resembled the four-
step pattern of spoofing. Rather, they argued that their trad-
ing was fully consistent with innocent behavior and that the
government could not prove the requisite intent. During a
three-week trial, the government presented substantial evi-
dence to the contrary. Below, we summarize the evidence rel-
evant to this appeal.
    Kumar Venkataraman, a finance expert, explained how
Smith’s and Nowak’s trading patterns and resultant fill ratios
aligned with the typical spoofing pattern. In a set of 100 trad-
ing episodes identified, Smith’s spoof orders had a fill ratio
(meaning the percentage of contracts filled) of 0.18%, com-
pared to a 79.11% fill ratio for his genuine orders. Nowak’s fill
ratios were similar: 0.22% for his spoof orders and 90.11% for
his genuine orders. The defendants’ broader trading showed
this pattern, as well. Despite an abysmal fill ratio on the spoof
orders, Venkataraman testified that Smith and Nowak used
this strategy “again and again.” He concluded that Smith and
Nowak’s trading strategy was “inconsistent with a design” to
fill the genuine orders and was instead “designed” to “push
the price” of the market and execute the order on the other
side. There was no “economically rational” reason for their
patten if they intended to trade the spoof orders, Venkata-
raman said. But because the market perceived the orders as
genuine, they achieved the intended “shock to the market”
and successfully moved the price on the other side.
   The government also presented the testimony of CME in-
vestigator Brian Wika and three of Nowak and Smith’s former
coworkers who admitted to spoofing and cooperated with
6                            Nos. 23-2840, 23-2846 & 23-2849

authorities. John Edmonds sat next to Smith and Nowak at
JPMorgan’s New York office. He testified that he witnessed
Smith and Nowak spoof regularly, at least several times per
day, and that they in fact taught him how to spoof. According
to Edmonds, Smith once told him that they spoofed because
“size moves the market” and would complain “[t]hey’re fuck-
ing hitting me” when spoof orders he placed with the intent
to cancel were executed. After a meeting where JPMorgan
compliance officials warned traders to stop spoofing because
regulators were looking into it, Edwards heard Smith say to
another coworker, “There goes the business.” Edmonds also
reviewed the trading episodes offered by the government and
confirmed that they matched his own spoofing pattern. Based
on his own experience at JPMorgan, he was unaware of any
legitimate non-spoofing explanation for this trading.
    Christian Trunz worked “side by side” with Smith, whom
he described as his mentor. Trunz admitted that he engaged
in spoofing to deceive other market participants. He testified
that he witnessed Smith spoof “all the time” using the same
strategy. Trunz sent a chat to another JPMorgan salesperson
that Smith was “bidding up on the futures trying to get some
off,” and once saw Smith become “angry” and “throw his
glasses against the screen” when his spoof order was exe-
cuted. He further testified that Nowak spoofed while they
worked “back to back” at JPMorgan. And while coaching
Trunz ahead of a compliance review, Nowak once warned,
“Remember, every order we placed, we intended to trade.”
   Corey Flaum sat alongside Smith at Bear Stearns before it
was acquired by JPMorgan in 2008. Flaum also confessed to
spoofing and testified that he saw Smith spoof at least several
Nos. 23-2840, 23-2846 & 23-2849                               7

times per week. Flaum testified that Smith’s trading episodes
were “carbon copies” of his own spoofing pattern.
   At various points, Edmonds, Trunz, and Flaum each de-
fined spoofing in broad strokes and described its purposes
and impact on the market to explain why they spoofed. They
were also shown charts depicting specific trading episodes
and opined that Smith and Nowak lacked an intent to trade
and had been spoofing in those instances. The district court
offered to give a jury instruction that the witnesses would be
serving in a dual role, at times offering an opinion rather than
their personal observations about a particular order. Smith
and Nowak declined the instruction. The government also
submitted various chats between the defendants and other
coworkers discussing the legitimate orders they sought to ex-
ecute, accompanied by data showing that they simultane-
ously placed and quickly canceled large orders on the other
side of the market.
     CME investigator Wika explained what spoofing is, how
traders typically achieve it, how CME investigators identify
it, and why CME rules prohibit it. When asked about his cre-
dentials, Wika stated that he had worked in CME’s investiga-
tions group for 14 years and had been a manager for three or
four. Wika testified that the CME began investigating Smith
after it received a complaint from a market participant. When
discussing the results of his investigation, Wika said that
Smith’s high cancellation rates were “indicative of spoofing
activity—indicative of lack of intent to trade those orders.” He
prepared an investigative report concluding that Smith had
spoofed and identifying specific trading episodes as repre-
sentative examples of Smith’s spoofing behavior. Over the de-
fendants’ objection, the court admitted the report into
8                             Nos. 23-2840, 23-2846 & 23-2849

evidence as a business record under Federal Rule of Evidence
803(6).
    After deliberating for a week, the jury announced that it
was deadlocked. Although the defendants sought a mistrial,
the court granted the government’s request for the standard
supplemental jury instruction under United States v. Silvern,

 (7th Cir. 1973) (en banc). Consistent with that de-
cision and the Seventh Circuit pattern instructions, the court
instructed the jurors to “make every reasonable effort to reach
a verdict” and discuss their “differences with an open mind,”
but cautioned them not to “surrender [their] honest beliefs
about the weight or effect of evidence.” The next day, the jury
sent a note expressing “concerns over comments made by a
juror” that suggested that the juror had “made early decisions
regarding the verdict for the defendants” based on the trial’s
opening statements and “saw everything through that lense
[sic].” The government asked the court to dismiss the juror.
Instead, the court reminded the jury “that the lawyers’ state-
ments and arguments are not evidence. If what a lawyer said
is different from the evidence as you remember it, the evi-
dence is what counts.” The next day, the jury found Smith and
Nowak guilty on all substantive counts but acquitted them of
the conspiracy charges. Each moved for acquittal or a new
trial, but the court denied those motions.
                               2
   The government tried Jordan separately and, following
Smith and Nowak’s trial, dropped the conspiracy counts
against him. Jordan, for his part, openly admitted that he
spoofed. Instead, his defense was that he spoofed without the
criminal intent necessary to support a conviction for wire
fraud affecting a financial institution.
Nos. 23-2840, 23-2846 & 23-2849                               9

    FBI Agent Jonathan Luca testified for the government.
Agent Luca had investigated Jordan and interviewed him in
2018. During the interview, Jordan admitted that as a trader
he had placed “small iceberg orders on one side of the market
and larger non-iceberg orders on the other side of the market
in which he intended to cancel” and acknowledged that this
pattern was consistent with spoofing. He explained that he
spoofed “to mislead the market, to outperform the algo-
rithms, and to make—and get the best possible fills for his
boss.” The government characterized this interview as a con-
fession. However, Jordan also told Agent Luca that he “did
not think what he was doing was wrong.” Jordan sought to
admit this statement under a hearsay exception commonly
known as the rule of completeness, Fed. R. Evid. 106, but the
court denied his motion.
    To demonstrate Jordan’s state of mind, the government in-
troduced statements he made during a 2010 deposition before
the Commodity Futures Trading Commission. In stark con-
trast to his interview with Agent Luca, Jordan swore during
the deposition that he never placed an order that he didn’t
intend to execute, and “would only cancel something if [he]
changed [his] mind or if it was put in error.” He further stated
that he never engaged in trading “for the purpose of influenc-
ing the price” of the commodity exchange.
   The director and global head of CME’s rules and regula-
tory outreach group, Erin Middleton, also testified. Middle-
ton said that CME rules require every order to be bona fide—
meaning they must “represent a true intent to buy or sell a
particular price or quantity”—to maintain the integrity of
their markets. She acknowledged, however, that the word
spoofing does not appear in the text of CME Rule 432 and that
10                            Nos. 23-2840, 23-2846 & 23-2849

such language would have clarified that the rule prohibited
spoofing. Representatives from JPMorgan and Credit Suisse
similarly testified that spoofing would have violated the pol-
icies in place when Jordan worked at their banks, even though
they did not explicitly mention spoofing either. Jordan sought
to challenge these statements with post-2010 compliance pol-
icies and CME documents that, unlike the policies in place
when he was an employee, expressly identified spoofing as a
prohibited trading policy. The district court excluded these
exhibits under Federal Rule of Evidence 403, though, finding
that they posed a risk of confusing the jury and erroneously
injecting a mistake of law defense into the case.
    The court also rejected Jordan’s request for a jury instruc-
tion on good faith. Specifically, he sought an instruction that
if he acted in good faith, “then he lacked the intent to defraud
required to prove the offense of wire fraud.” The court found
this instruction unnecessary because Jordan could always ar-
gue that he lacked an intent to defraud and the instruction
posed a similar risk of misleading the jurors into thinking that
mistake of law was a viable defense.
    The court did, however, instruct the jury on the mental
state necessary to show an intent to defraud. The jury was in-
structed that Jordan must have acted knowingly, which the
court defined in part as being “aware of the nature of his con-
duct.” During deliberations, the jury requested clarification
on this definition, and the court responded that “the defini-
tion of ‘knowingly’ … does not mean that the defendant must
be aware of whether his alleged conduct violated federal
law.” The jury returned a guilty verdict, and the court denied
Jordan’s motions for acquittal and a new trial.
Nos. 23-2840, 23-2846 & 23-2849                                  11

                                 II
   Smith, Nowak, and Jordan all appeal the denial of their
motions for acquittal and a new trial. They also challenge sev-
eral of the district judge’s rulings at trial. We take their argu-
ments in turn.
                                 A
    All three defendants argue that their fraud convictions
cannot stand because spoofing does not involve a misrepre-
sentation about an essential element of the bargain for futures
contracts. We review this threshold legal challenge de novo.
United States v. Rivers, 

 (7th Cir. 2024) (de
novo review applies to “legal questions wrapped up in chal-
lenges to the sufficiency of the evidence”). Their argument
fails for several reasons.
    Both wire and commodities fraud require as an element “a
scheme or artifice to defraud.” 

 & 1348(1).
The Supreme Court has interpreted this element to prohibit
only deceptive schemes where “money or property was an
object” of the fraud. Ciminelli v. United States, 

(2023) (quotation omitted). Building on this, some circuits pre-
viously drew “a fine line between schemes that do no more
than cause their victims to enter into transactions they would
otherwise avoid” and “schemes that depend for their comple-
tion on a misrepresentation of an essential element of the bar-
gain.” United States v. Shellef, 

 (2d Cir. 2007). In
these circuits, only the latter constituted a scheme to defraud
that violated the fraud statutes. Id.; United States v. Takhalov,

, 1313–14 (11th Cir. 2016); United States v. Guer-
tin, 

, 451–52 (D.C. Cir. 2023); United States v. Bruch-
hausen, 

, 467–69 (9th Cir. 1992). A scheme to
12                             Nos. 23-2840, 23-2846 & 23-2849

defraud, they reasoned, requires a lie about the “nature of the
bargain itself,” such as one concerning “price” or “character-
istics of the good,” Takhalov, 827 F.3d at 1313–14, or some “ex-
plicit promise[]” that had been made, United States v. Schwartz,

 (2d Cir. 1991).
    The defendants ask us to apply the essential element of the
bargain requirement here. Because spoofing misrepresents
market supply and demand, rather than the price or another
characteristic of the futures contract itself, they contend that
the other parties to the transaction “received exactly what
they paid for.” Takhalov, 

 (quotation omitted).
They liken spoofing to misrepresentations about “negotiating
positions” in arm’s length transactions, which are not fraud.
United States v. Weimert, 

 (7th Cir. 2016). Un-
der this theory, spoofing simply does not amount to a scheme
to defraud within the scope of the fraud statutes, even if the
parties would not have otherwise executed the transaction.
    Our task is made easy by the Supreme Court’s decision in
Kousisis v. United States, 

 (2025), which came
down after oral argument in this case. There, the defendant
had secured contracts with the Pennsylvania Department of
Transportation to paint two projects in Philadelphia. 

 at
1388–89. He represented that he would acquire painting sup-
plies from “a prequalified disadvantaged business,” but in
fact used the prequalified disadvantaged business as a mere
pass-through entity to funnel payments. 

. The Court
affirmed the defendant’s wire fraud convictions and directly
abrogated the line of cases that the defendants in this case in-
voke. 

 at 1390–92, 1398; see also United States v. Runner, 

, 154–55 (2d Cir. 2025) (recognizing abrogation). The
wire fraud statute, the Court explained, “is agnostic about
Nos. 23-2840, 23-2846 & 23-2849                                13

economic loss.” Kousisis, 

. Rather, a fraud
conviction can stand if the defendant did no more than “use[]
a material misstatement to trick a victim into a contract that
requires handing over her money or property.” 

.
    Because Kousisis forecloses the defendants’ essential ele-
ment of the bargain argument, we easily conclude based on
well-established precedent that spoofing constitutes a scheme
to defraud within the meaning of the wire and commodities
fraud statutes. United States v. Pacilio, 

, 460 (7th
Cir. 2023); United States v. Chanu, 

, 541 (7th Cir.
2022); United States v. Coscia, 

 (7th Cir. 2017).
    It bears noting that the defendants’ argument would fail
even without Kousisis. Unlike the transactions in Kousisis or
Weimert, where the defendants directly lied to the purported
victims, the deception from spoofing is filtered through third
parties and the market as a whole. Spoofing advances an im-
plied misrepresentation that the fraud statutes prohibit—
“namely the public perception of the intent to trade and the
private intent to cancel.” Pacilio, 85 F.4th at 460. In this way,
spoofing is more akin to theories of securities fraud and
fraud-on-the-market, which predicate liability on misrepre-
sentations that undermine the integrity of the marketplace.
See United States v. Gilbertson, 

 (8th Cir. 2020)
(in the context of securities fraud, the “gravamen of manipu-
lation is deception of investors into believing that prices at
which they purchase and sell securities are determined by the
natural interplay of supply and demand, not rigged by ma-
nipulators”) (quotation omitted).
    The defendants also claim the fraud statutes are unconsti-
tutionally vague as applied to their conduct. We have already
14                             Nos. 23-2840, 23-2846 & 23-2849

rejected this argument, Pacilio, 85 F.4th at 460–61, and decline
to revisit that conclusion. Once again, we confirm that spoof-
ing violates the federal wire and commodities fraud statutes,

 & 1348(1).
                                B
    Smith and Nowak argue that even if spoofing amounts to
wire and commodities fraud (it does), the evidence cannot
sustain their convictions because they did not engage in the
practice. They claim that spoofing requires an unconditional
intent to cancel a bid or offer before execution, whereas the
evidence at trial established, at best, a conditional intent to
cancel the orders if the order on the other side was filled.
Smith and Nowak concede, as they must, that each of their
convictions is predicated on the same spoofing conduct,
meaning the convictions all stand or fall with the govern-
ment’s ability to establish that they spoofed. Spoofing not
only violates the federal fraud statutes, as discussed, but the
Dodd-Frank Act provides that any person who knowingly vi-
olates its anti-spoofing provision, 7 U.S.C. § 6c(a)(5)(C), is
guilty of attempted price manipulation under 

(a)(2). According to Smith and Nowak, since the govern-
ment cannot prove that they placed trade orders with the req-
uisite intent for a spoofing conviction, they are entitled to a
judgment of acquittal across the board. Though formally we
review a judgment denying acquittal de novo, “practically
speaking” our “standard of review is that for sufficiency of
the evidence.” United States v. Peterson, 

(7th Cir. 2016); see also Rivers, 

 (de novo review
for threshold legal questions).
   The parties spend considerable time and energy debating
the standard for intent and, frankly, we struggle to
Nos. 23-2840, 23-2846 & 23-2849                                15

understand why. Smith and Nowak won this battle in the dis-
trict court. The court instructed the jury that spoofing requires
an unconditional purpose to cancel the entire bid or offer. The
jury thus considered—and rejected—Smith and Nowak’s ar-
gument that the evidence does not show such unconditional
intent. We measure intent at the moment the order was
placed. Coscia, 

 (a conviction for spoofing re-
quires proving that the defendant “knowingly entered bids or
offers with the present intent to cancel the bid or offer prior to
execution”). If a party possesses a conditional intent to trade,
he necessarily lacks an intent to cancel at the time the order is
placed. The word unconditional is redundant and unneces-
sary.
    The key question in spoofing cases is whether an order is
placed on the opposite side of the commodities market with
the intent to cancel before execution in order to manipulate
the market. Chanu, 40 F.4th at 540. Even if Smith and Nowak
waited to cancel the spoof orders until the legitimate trade
was executed, what counts is that the trades “were designed
specifically to avoid being filled.” Coscia, 

. It
makes sense that a spoofing trader would wait to cancel until
his legitimate order was filled—that’s the whole point of
spoofing. Cf. 

 (defendant’s software program canceled
spoof orders “in three particular circumstances: (1) based on
the passage of time …; (2) the partial filling of the large orders;
or (3) complete filling of the small orders”) (emphasis added). The
“unconditional” semantics aside, the question is whether
Smith’s and Nowak’s “purpose was not to trade on those or-
ders, but rather to use them to shift the market up or down.”

 at 795 & n.45.
16                            Nos. 23-2840, 23-2846 & 23-2849

    More importantly, all that matters is whether a rational
trier of fact could have come to that conclusion. Peterson, 

 (“We consider the evidence in the light most fa-
vorable to the government and affirm the conviction if any ra-
tional trier of fact could find the defendant guilty beyond a
reasonable doubt.”). This hurdle is “nearly insurmountable.”
United States v. Sorensen, 

 (7th Cir. 2025)
(quotation omitted). In particular, Smith and Nowak’s focus
on intent makes our “job relatively easy,” for “once a jury has
weighed the evidence and found guilt beyond a reasonable
doubt, a challenge to the sufficiency of the evidence proving
intent is exceedingly difficult to win.” Pacilio, 85 F.4th at 463
(cleaned up).
    After reviewing the evidence, we are confident that a jury
could have found Smith and Nowak placed spoof orders with
the requisite intent to cancel. The government presented sub-
stantial data evidence depicting the scheme, and the jury
heard extensive testimony from cooperating witnesses, finan-
cial experts, and investigators supporting an inference of
guilt. This evidence was bolstered by contemporaneous chat
messages showing that Smith and Nowak placed (and then
canceled) orders on the opposite side of the market from the
legitimate orders that they intended to execute. Smith and
Nowak argue that this evidence is all circumstantial, as the
government identified no direct evidence of their state of
mind. Even so, “direct evidence of intent is often unattainable,
and specific intent to defraud may be established by circum-
stantial evidence and by inferences drawn from examining
the scheme itself.” Id. at 464 (quotation omitted). Undeterred,
Smith and Nowak counter that the circumstantial evidence
cannot support their convictions because it is equally con-
sistent with their innocence. But Smith and Nowak were free
Nos. 23-2840, 23-2846 & 23-2849                               17

to argue to the jury that there were legitimate explanations for
their trading patterns and to cross-examine the witnesses on
their conclusions and credibility—indeed, that was the heart
of their entire defense at trial. As we have often observed, “the
fact that there existed other possible explanations … that were
fully consistent with innocence did not require a jury to be-
lieve them.” United States v. Maxwell, 

, 858 (7th
Cir. 2025) (quotation omitted). We find more than sufficient
evidence to justify the jury’s conclusions.
    Briefly, Smith and Nowak also challenge the anti-spoofing
statute, 7 U.S.C. § 6c(a)(5)(C), as void for vagueness. As with
fraud, our precedent squarely forecloses this argument.
Coscia, 866 F.3d at 793–95. The spoofing statute is not uncon-
stitutionally vague, and ample evidence supported Smith’s
and Nowak’s convictions under it.
    In short, Smith and Nowak’s sufficiency of the evidence
challenge fails as to all convictions. There was more than suf-
ficient evidence that Smith and Nowak engaged in spoofing
in violation of 7 U.S.C. § 6c(a)(5)(C). And because spoofing
constitutes a scheme to defraud under the wire and commod-
ities fraud statutes, 

 & 1348(1), and amounts
to attempted price manipulation, 

(a)(2), there was
sufficient evidence that they committed those crimes as well.
Because the jury’s verdict is supported by substantial evi-
dence on all charges, they are not entitled to a new trial on
these grounds either. Peterson, 

; United States
v. Conley, 

, 399–400 (7th Cir. 2017) (when motions
for acquittal and for a new trial are based on the same claim
that the government failed to prove the elements of the of-
fenses beyond a reasonable doubt, we will affirm both if suf-
ficient evidence supports the guilty verdict).
18                              Nos. 23-2840, 23-2846 & 23-2849

                                C
    Smith and Nowak next turn their attention to the district
court’s decision to admit much of the evidence discussed
above. They claim the court’s rulings were erroneous and ask
for a judgment of acquittal or a new trial in the alternative. We
review the district court’s evidentiary rulings for an abuse of
discretion. Pacilio, 85 F.4th at 464. We will only reverse if we
are “left with the definite and firm conviction that a mistake
has been committed.” Id. (quotation omitted). Smith and
Nowak assert that the district court abused its discretion by
admitting: (1) lay opinion testimony from the three cooperat-
ing witnesses, (2) Wika’s lay opinion testimony, and (3)
Wika’s investigative report.
    To begin, we confirm that Nowak may also challenge the
latter two rulings. Although the report and some of Wika’s
testimony pertained specifically to Smith, Wika also testified
about spoofing and CME policies more broadly. Particularly
in light of the joint conspiracy charge, even though this evi-
dence focused on Smith, the jury could consider it against
Nowak as relevant and in accordance with any limiting in-
structions. See United States v. Lopez, 

 (7th Cir.
1993) (in joint trials, juries will “sort through the evidence”
and “follow instructions from the court” about separate con-
sideration of evidence). Nowak joined Smith's objections to
Wika's testimony and report and, importantly, did not receive
or request a limiting instruction that the jury could only con-
sider them against Smith.
   Turning to the merits, none of these decisions was an
abuse of discretion. Federal Rule of Evidence 701 permits lay
witnesses to testify as to “their opinions and inferences, even
about ultimate issues in the case.” United States v. Locke, 643
Nos. 23-2840, 23-2846 & 23-2849                              

 (7th Cir. 2011). They may even testify about an-
other person’s mental state, so long as the testimony is helpful
to the jury under Rule 701 and appropriate under Rule 403’s
balancing test. 

 at 239–40. Though lay witnesses may not
offer legal conclusions or opine on the application of statutory
elements, United States v. Noel, 

 (7th Cir.
2009), they can use words “in a colloquial sense” that “em-
ploy[] the vernacular of their financial professions,” even if
those words mirror legal standards, Locke, 643 F.3d at 241–42
(approving of lay witnesses’ use of the words fraud and mis-
representation).
    The lay testimony was proper under this standard. Smith
and Nowak take issue with the witnesses’ use of the word
spoofing to describe their trading activity, argue that they im-
properly characterized spoofing as fraud and price manipu-
lation, and claim that the witnesses inappropriately opined on
Smith’s and Nowak’s intent based on technical knowledge.
But the witnesses’ use of the word spoofing was consistent
with the colloquial vernacular of the trading industry, id. at
242, and any testimony about Smith’s and Nowak’s mental
states was properly framed as an opinion drawn from the
trading data in light of the witnesses’ own experience, see
United States v. Winbush, 

 (7th Cir. 2009). As
for the claim that the testimony improperly equated spoofing
with fraud and price manipulation, the witnesses were simply
explaining why they spoofed, what they had pled guilty to,
or (in Wika’s case) why the CME prohibits spoofing. That
Smith and Nowak declined a jury instruction that the wit-
nesses were serving in a dual role only solidifies our conclu-
sion that no abuse of discretion occurred.
20                              Nos. 23-2840, 23-2846 & 23-2849

    Smith and Nowak also argue that Wika should have testi-
fied as an expert, rather than a lay witness. Investigators such
as Wika can testify about their role in an investigation and
provide their impressions of the case without crossing into ex-
pert territory. United States v. Rollins, 

, 832–33 (7th
Cir. 2008). This is permissible even if an investigator’s “spe-
cialized knowledge informed his mental state.” United States
v. Oriedo, 

 (7th Cir. 2007). While informed by
his background experience, Wika’s testimony was limited to
his investigation and what it revealed to him. Even if it argu-
ably “approaches the line dividing lay opinion testimony
from expert opinion testimony,” this testimony remained ad-
missible, and the district court did not abuse its discretion in
allowing it. Rollins, 

. At the very worst, the gov-
ernment’s other evidence of Smith’s and Nowak’s guilt was
so extensive that even if Wika’s testimony “had crossed the
line” it would have been harmless error. 

 Nor was it erro-
neous to admit Wika’s investigative report: investigative re-
ports may come in as public records under Federal Rule of
Evidence 803(6) if the authoring officer or investigator testifies
at trial, as Wika did. United States v. King, 

, 672–
73 (7th Cir. 1980); United States v. Blackburn, 

(7th Cir. 1993) (“So long as the maker of the report is available
for cross-examination, … admitting the reports themselves
does not contravene Rule 803(8).”).
                                D
    For their final challenge, Smith and Nowak argue that the
district court’s supplemental instructions to the jury were er-
roneous and impermissibly coercive. We review the district
court’s decision to provide supplemental jury instructions, in-
cluding its decision to read (or reread) a Silvern instruction,
Nos. 23-2840, 23-2846 & 23-2849                                21

for abuse of discretion. United States v. Cardena, 

 (7th Cir. 2016) (Silvern instruction); United States v. Sims,

 (7th Cir. 2003) (supplemental instructions
generally).
    It was appropriate for the district court to reread the Sil-
vern instruction. Silvern instructions are “perfectly content-
neutral and carr[y] no plausible potential for coercing the
jury.” United States v. Beverly, 

 (7th Cir. 1990)
(quotation omitted). Rather, the district court followed our
clear, established procedure and provided the model instruc-
tion to a deadlocked jury. United States v. Collins, 

,
508–09 (7th Cir. 2000).
    It was similarly within the court’s discretion to remind the
jury that lawyers’ statements are arguments, not evidence.
The court pulled the language from a pattern instruction and,
despite Smith and Nowak’s arguments to the contrary,
crafted it carefully to avoid singling out the problematic juror.
The court also refused to ask the jury whether it remained
deadlocked, precisely to avoid any intrusion on their deliber-
ations. Under the circumstances, the court proceeded
thoughtfully and exercised its discretion wisely. Nowak and
Smith may not like the verdict the jury reached after receiving
these instructions, but that does not mean they were issued in
error.
                               III
   Recall that Jordan was convicted of only wire fraud under

. Jordan challenges various aspects of his sep-
arate trial. Before turning to them, we first dispense with his
own sufficiency of the evidence claim. Jordan joined Smith
and Nowak’s argument that spoofing cannot sustain a fraud
22                             Nos. 23-2840, 23-2846 & 23-2849

conviction because it lacks a misrepresentation about an es-
sential element of the bargain. Because Jordan concedes that
he spoofed, his argument hinges entirely on that theory. Since
we rejected that argument in Section II.A, Jordan’s sufficiency
of the evidence challenge is a nonstarter.
                                A
    Jordan’s primary remaining argument concerns the dis-
trict court’s decision to exclude his statement to Agent Luca
that he “did not think what he was doing was wrong.” Jordan
sought to admit that statement under Federal Rule of Evi-
dence 106, often referred to as the rule of completeness. Rule
106 provides that “[i]f a party introduces all or part of a state-
ment, an adverse party may require the introduction, at that
time, of any other part—or any other statement—that in fair-
ness ought to be considered at the same time.” They “may do
so over a hearsay objection.” Fed. R. Evid. 106.
    Rule 106 requires a complete statement “to be read or
heard when it is necessary to (1) explain the admitted portion,
(2) place the admitted portion in context, (3) avoid misleading
the trier of fact, or (4) insure a fair and impartial understand-
ing.” United States v. Lewis, 

 (7th Cir. 2011)
(quotation omitted). In United States v. Haddad, 

(7th Cir. 1993), for instance, the court admitted the defend-
ant’s statement, “Yes, I knew of the marijuana” but excluded
the remainder that said, “but I had no knowledge of the gun.”

. The gun was located right next to the marijuana,
so the admitted statement suggested that the defendant knew
about the gun as well. 

 We concluded that Rule 106 required
the admission of the exculpatory statement, in part to avoid
any misleading inference. 

 “The completeness doctrine
does not, however, require introduction of portions of a
Nos. 23-2840, 23-2846 & 23-2849                                23

statement that are neither explanatory of nor relevant to the
admitted passages.” Lewis, 

 (quoting United
States v. Marin, 

 (2d Cir. 1982)).
    The district court was correct that Rule 106 did not compel
it to admit Jordan’s statement. Jordan’s claim that he did not
think he was doing anything wrong does not change the fac-
tual nature of the statement that he placed bids with the intent
to cancel for the purpose of misleading the market. Nor does
it correct or clarify any misleading impression about the ad-
mitted statement: mistake of law is not a defense to wire
fraud, and it is irrelevant whether Jordan knew that spoofing
was illegal or, as he put it, wrong. United States v. Blagojevich,

 (7th Cir. 2015). Rather, the court rightly
noted that Jordan was free to take the stand and testify that he
did not think he was doing anything wrong. United States v.
Faruki, 

 (7th Cir. 2015) (agreeing with the dis-
trict court that “the appropriate vehicle for the introduction of
such evidence would have been for [the defendant] himself to
have taken the stand,” rather than Rule 106). Defendants often
try to justify their actions when speaking with FBI agents and
other law enforcement officials by disclaiming criminal intent.
Such an exculpatory statement has nothing to do with Rule
106.
                                B
    Next, Jordan claims that the district court abused its dis-
cretion by excluding certain exhibits he sought to use for im-
peachment. The trial concerned Jordan’s trading when he
worked at JPMorgan and then Credit Suisse until August
2010. Although the policies in place at the time did not explic-
itly mention spoofing, government witnesses testified that the
practice was nonetheless prohibited by their terms. To
24                            Nos. 23-2840, 23-2846 & 23-2849

controvert this testimony, Jordan moved to admit post-2010
compliance policies and CME documents that had been re-
vised to expressly forbid spoofing. However, the district court
excluded this evidence under Rule 403. The policies were re-
vised to reflect the Dodd-Frank Wall Street and Consumer
Protection Act, 

 Stat. 1376, which Con-
gress passed in July 2010. Though spoofing already violated
the general wire fraud statutes, the Dodd-Frank Act amended
the Commodity Exchange Act to explicitly recognize spoofing
as an unlawful disruptive practice amounting to price manip-
ulation. 7 U.S.C. §§ 6c(a)(5)(C) (defining spoofing as practice
“commonly known to the trade” of “bidding or offering with
the intent to cancel the bid or offer before execution”) &
13(a)(2). Given this background, the district court thought the
offered evidence posed a risk of confusing the jury and erro-
neously injecting a mistake of law defense into the case and
excluded it.
    Jordan argues that these exhibits were highly probative
and directly responsive to the witnesses’ testimony, making
the district court’s decision to exclude them under Rule 403
an abuse of discretion. We disagree. Jordan conducted exten-
sive cross-examination of the witnesses, which elicited clear
testimony that the pre-2010 documents did not mention
spoofing even though they could (and possibly should) have.
The actual documents themselves were thus of limited addi-
tional probative value. And as the district court noted, evi-
dence of the after-the-fact, post-Dodd-Frank policies could
have led the jury to think that the wire fraud statutes were not
sufficient to criminalize spoofing. The court was justified in
this concern—defendants in other cases have made this same
(albeit incorrect) argument. See Chanu, 40 F.4th at 534.
Nos. 23-2840, 23-2846 & 23-2849                                  25

    Because “[t]he balancing of probative value and prejudice
is a highly discretionary assessment,” we give “great defer-
ence” to a district court’s decision to exclude evidence under
Rule 403 and “only disturb[] it if no reasonable person could
agree with the ruling.” Pacilio, 85 F.4th at 465 (quotation omit-
ted). Given the limited probative value of the documents and
valid concerns of jury confusion, Jordan does not overcome
this extremely deferential standard.
                                 C
    Last, Jordan says the district court erred in declining to ad-
minister a so-called good faith instruction. Specifically, Jordan
sought an instruction that if he acted in good faith “then he
lacked the intent to defraud required to prove the offense of
wire fraud.” Though we review challenges to jury instruc-
tions de novo, “the district court is afforded substantial dis-
cretion with respect to the precise wording of instructions so
long as the final result, read as a whole, completely and cor-
rectly states the law.” Chanu, 40 F.4th at 542 (cleaned up).
    We already addressed and rejected this same argument in
Chanu. As the district court noted, a good faith instruction is
unnecessary in wire fraud cases because a lack of good faith
is a part of the charge. Id. at 543. To be sure, district courts are
free to provide one if they wish. But “the rule is clear” that
defendants such as Jordan cannot demonstrate that “the fail-
ure to include the good faith instruction denied [them] a fair
trial.” Id. (cleaned up). Jordan admitted he spoofed, and a jury
convicted him of wire fraud after a fair, properly conducted
trial.
                                                         AFFIRMED