 United States Court of Appeals
         FOR THE DISTRICT OF COLUMBIA CIRCUIT



Argued January 23, 2019                 Decided July 19, 2019

                         No. 16-3108

                UNITED STATES OF AMERICA,
                        APPELLEE

                              v.

                    MICHAEL M. MONZEL,
                        APPELLANT


        Appeal from the United States District Court
                for the District of Columbia
                   (No. 1:09-cr-00243-1)


    Rosanna M. Taormina, Assistant Federal Public Defender,
argued the cause for appellant. With her on the briefs was A.J.
Kramer, Federal Public Defender.

     Eric Hansford, Assistant U.S. Attorney, argued the cause
for appellee. With him on the brief were Jessie K. Liu, U.S.
Attorney, and Elizabeth Trosman, Elizabeth H. Danello, and
David B. Kent, Assistant U.S. Attorneys.

    Before: ROGERS, MILLETT and KATSAS, Circuit Judges.

    Opinion for the Court filed by Circuit Judge MILLETT.
                                2
     MILLETT, Circuit Judge: Congress has mandated that
those convicted of child pornography offenses pay “full”
restitution to their victims for any injuries they “proximate[ly]”
caused. 18 U.S.C. § 2259 (2012). That directive recognizes
that every perpetrator’s viewing of a child’s image inflicts
distinct harm on that child in that it effects “a repetition of the
victim’s abuse.” See Paroline v. United States, 134 S. Ct.
1710, 1727 (2014).

     In Paroline, the Supreme Court prescribed a general
method and “rough guideposts” for trial courts to follow in
determining a perpetrator’s “relative causal role” in a victim’s
injury. 134 S. Ct. at 1728. This case asks what portion of a
victim’s damages a single, non-distributing possessor can be
ordered to pay. Because the district court followed Paroline in
calculating a restitutionary amount that is reasonably tailored
to the defendant Michael Monzel’s causal role, we affirm.

                                I

     Section 2259(a) of Title 18 requires district courts to
“order restitution for any offense” involving “Sexual
Exploitation and Other Abuse of Children.” 18 U.S.C.
§ 2259(a) (cross-referencing the offenses specified in Chapter
110 of Title 18). So as not to leave any doubt, Congress
declared that “[t]he issuance of a restitution order under this
section is mandatory.” Id. § 2259(b)(4) (emphasis added).
Both distribution and possession of child pornography offenses
fall under Section 2259’s mandatory restitution scheme. See
id. § 2252(a)(2), (4)(B).

     Under Section 2259, convicted defendants must pay their
victim the “full amount of the victim’s losses as determined by
the court[.]” 18 U.S.C. § 2259(b)(1); see also id. § 2259(c)
(defining the victim entitled to restitution as “the individual
                                  3
harmed as a result of a commission of a crime under this
chapter”). The statute, in turn, defines the “full amount of the
victim’s losses” as including “costs incurred” for medical
services (physical, psychiatric, and psychological), therapy,
necessary transportation, temporary housing and child care
expenses, lost income, and attorneys’ fees, as well as “any
other losses suffered * * * as a proximate result of the offense.”
Id. § 2259(b)(3)(A)–(F). The government bears the burden of
“demonstrating the amount of the loss sustained by a victim as
a result of the offense.” Id. § 3664(e) (incorporated by
reference in 18 U.S.C. § 2259(b)(2)).1

                                  II

     In December 2009, Michael Monzel pled guilty to one
count each of distributing and of possessing child pornography.
See United States v. Monzel, 641 F.3d 528, 530 (D.C. Cir.
2011) (“Monzel I”); 18 U.S.C. § 2252(a)(2), (4)(B). The child
pornography collection amassed by Monzel included an image
of “Amy.” See Monzel I, 641 F.3d at 530. Amy is the same
victimized individual who sought restitution in Paroline. 134
S. Ct. at 1716. Her story is, at this point, tragically familiar.
When she was “eight and nine years old, [Amy] was sexually
abused by her uncle in order to produce child pornography.”

     1
       Congress has since amended Section 2259 to both codify
Paroline’s basic approach and to set a restitution floor of $3,000. See
Amy, Vicky, and Andy Child Pornography Victim Assistance Act of
2018, Pub. L. No. 115-299, 132 Stat. 4383 (2018). We agree with
the parties that this amendment does not apply to this case. 18
U.S.C.A. § 2259B(d) (West 2019) (describing “the sense of
Congress” that this amendment does not apply retroactively); Oral
Arg. Tr. 62–63; cf. Landgraf v. USI Film Prods., 511 U.S. 244, 264
(1994) (declining to apply civil law enacted on appeal because “rules
will not be construed to have retroactive effect unless their language
requires this result”) (citation omitted).
                                4
Id. at 1717. She underwent therapy from 1998 through 1999,
and, according to her therapist, was “back to normal” “[b]y the
end of this period.” Id. But then a “major blow to her recovery
came when, at the age of 17, she learned that images of her
abuse were being trafficked on the Internet.” Id. Naturally,
“[t]he knowledge that her images were circulated far and wide
renewed [Amy’s] trauma and made it difficult for her to
recover from her abuse.” Id. By the time Paroline was decided
in 2014, possessors of her image “easily number[ed] in the
thousands.” Id.

     Following Monzel’s conviction, the district court
sentenced him to ten years of imprisonment. Amy then sought
restitution for all of her losses on a theory of joint and several
liability. Monzel I, 641 F.3d at 531. Monzel, on the other hand,
thought Amy should receive only $100 because the
government had failed to show “what portion of [her] losses he
had caused.” Id. at 530. The district court initially awarded
Amy $5,000 of “nominal” restitution. Id. Although “the
Government ha[d] not * * * suggested any rational, evidence-
based procedure for ascertaining the dollar value of the harms”
attributable to Monzel, the district court explained that it had
“no doubt” the $5,000 award was “less than the actual harm”
Monzel had caused. United States v. Monzel, Criminal Case
No. 09-243 (GK), 2011 WL 10549405, at *2–3 (D.D.C. Jan.
11, 2011).

     Amy filed a petition for a writ of mandamus in this court
to challenge the amount of the district court’s award. See 18
U.S.C. § 3771(d)(3) (authorizing mandamus actions by victims
challenging restitutionary awards). This court granted the
petition in part. While we held that the rule of joint and several
liability does not apply to the child-pornography restitution
scheme, we agreed that the district court could not “award[] an
amount of restitution it acknowledged was less than the harm
                                5
Monzel had caused.” Monzel I, 641 F.3d at 539. We directed
the district court on remand to “rely upon some principled
method for determining the harm Monzel proximately caused.”
Id. at 540.

     But, alas, the district court’s quest for a fair causal
benchmark proved unfruitful. “[F]or reasons not of its
making,” the district court explained, the government was
unable to offer anything more than “speculati[on]” as to
Monzel’s individual causal contribution to Amy’s harm. See
United States v. Monzel, Criminal Case No. 09-243 (GK), 2012
WL 12069547, at *6, *4 n.4 (D.D.C. Nov. 6, 2012) (emphasis
added). Recognizing that the result was “most unpalatable,”
the district court ruled that the government had left it no choice
but to deny completely the restitution request. Id. at *6.

    The government appealed, and while that appeal was
pending, the Supreme Court granted certiorari in Paroline. See
Paroline v. United States, No. 12-8561 (cert. granted, Jun. 27,
2013). Because that case involved the same victim, the same
crime, and the same underlying legal question, we held the
appeal in abeyance pending the Supreme Court’s disposition of
Paroline. See Order, In re: Amy, Child Pornography Victim,
No. 12-3093, 1:09-cr-00243-GK-1 (D.C. Cir. June 27, 2013).

     Ten months later, the Supreme Court decided Paroline.
134 S. Ct. at 1710. Paroline rejected Amy’s theory of joint and
several liability, holding instead that restitution is available
“only to the extent the defendant’s offense proximately caused
a victim’s losses.” Id. at 1722.

    This court vacated and remanded for the district court “to
redetermine restitution for Amy consistent with” the Paroline
framework. See Order, In re: Amy, Child Pornography Victim,
No. 12-3093 (D.C. Cir. June 13, 2014).
                               6

    The district court then awarded Amy $7,500 in restitution.
See United States v. Monzel, 209 F. Supp. 3d 73, 77 (D.D.C.
2016) (“Monzel II”). The court began, as Paroline directed, by
calculating Amy’s total losses from the continued trafficking
of her image, finding that they amounted to $3,243,195. Id. at
76. That amount was based on “the Government’s second
request for restitution,” minus $20,563 for certain “specific
expenses.” Id.

     To determine Monzel’s individual causal contribution, the
district court tracked Paroline’s “guideposts,” 134 S. Ct. at
1728. The court adopted the government’s statement that, to
its knowledge, there had been “197 restitution orders on behalf
of Amy.” Monzel II, 209 F. Supp. 3d at 76. The court also
accepted the government’s representation that it lacked
“sufficient, reliable data from which to make reasonable
estimates” of two other Paroline guideposts: the anticipated
number of future convictions related to Amy’s image, or of
“future offenders” who will possess and distribute Amy’s
image while evading conviction. Id.

     Next, the district court found that Monzel’s possession of
a single image of Amy made only a relatively “minor”
contribution to her losses. Monzel II, 209 F. Supp. 3d at 76.
Based on Monzel’s individual role, as well as information
about “prior restitution awards for Amy,” the district court, “in
its discretion, determine[d] that an award of $7,500 in
restitution [was] appropriate.” Id. at 77. That amount, the
district court found, “comport[ed] with [Monzel’s] causal—but
minor—role in Amy’s ongoing losses resulting from the
continued trafficking of her images.” Id.

    Monzel appeals.
                               7
                              III

     We review a restitution order for an abuse of discretion,
and we “examine the factual findings underpinning the order
for clear error.” In re Sealed Case, 702 F.3d 59, 66 (D.C. Cir.
2012). “A district court by definition abuses its discretion
when it makes an error of law.” Koon v. United States, 518
U.S. 81, 100 (1996).

                               A

     We are not the first, and surely will not be the last, court
to wrestle with giving practical effect to Section 2259’s
proximate-cause test for mandatory restitution in the context of
child-pornography offenses. While “every viewing” of a
child’s pornographic image itself re-inflicts “the victim’s
abuse,” Paroline, 134 S. Ct. at 1727, no “discrete, readily
definable incremental loss” can easily be traced to each
individual possessor’s exploitation of the image, id. 1726. As
a result, there can be no “precise algorithm” for computing
individual restitution awards. Id. at 1728.

     Here, as in Paroline, the defendant was a non-distributing
possessor of an image that thousands have trafficked.
Paroline, 134 S. Ct. at 1727. In such cases, the perpetrator’s
relative share “[sh]ould not be severe,” but neither should it be
“token or nominal.” Id. Instead, it should be “reasonable and
circumscribed,” geared to the statute’s dual purposes of
“helping the victim achieve eventual restitution for all her
child-pornography losses and impressing upon offenders the
fact that child-pornography crimes, even simple possession,
affect real victims.” Id.

     To that end, Paroline identified seven “rough guideposts”
that district courts “might consider” in navigating between the
                              8
Scylla and Charybdis of prohibited “severe” and “nominal”
awards. 134 S. Ct. at 1728. The considerations identified by
the Court include:

        •    “[W]hether the defendant reproduced or
            distributed images of the victim”;
        •   “[W]hether the defendant had any connection to
            the initial production of the images”;
        •   “[H]ow many images of the victim the defendant
            possessed”;
        •   “[T]he number of past criminal defendants found
            to have contributed to the victim’s general losses”;
        •   “[R]easonable predictions of the number of future
            offenders likely to be caught and convicted for
            crimes contributing to the victim’s general
            losses”;
        •   “[A]ny available and reasonably reliable estimate
            of the broader number of offenders involved (most
            of whom will, of course, never be caught or
            convicted)”; and
        •   “[O]ther facts relevant to the defendant’s relative
            causal role.”

Id. The Court added that “restitution sought and ordered in
other [like] cases” could also be informative. Id. at 1729.

    The Supreme Court stressed that those factors are neither
a mandatory checklist nor a “rigid formula,” but instead are
meant to guide the sentencing court’s “wide discretion” and
“sound judgment.” Paroline, 134 S. Ct. at 1728, 1729. Once
a sentencing court has made its best judgment about a
defendant’s relative share of causal blame, the resulting
amount—if it is both “reasonable and circumscribed”—is then
“deemed the amount of the victim’s general losses”
proximately caused by the offense. Id. at 1728.
                               9

                               B

     The district court’s decision in this case reflects a
reasonable exercise of discretion guided by the Paroline
guideposts and principles of analysis. The court began, as it
should have, by calculating Amy’s general losses from the
trafficking of her image. Monzel II, 209 F. Supp. 3d at 76. The
court then marched carefully through each of Paroline’s factors
and delineated Monzel’s individual contribution to and
responsibility for Amy’s losses. Id.; see also Paroline, 134 S.
Ct. at 1727–1729. The court emphasized that Monzel
possessed “only one single image of Amy.” Monzel II, 209 F.
Supp. 3d at 76. There was no evidence he distributed her
image, knew her, attempted to discover her identity or to
contact her in any way, sought out her image in particular, paid
for or sold her image, or “groom[ed] other minors for sexual
exploitation” using her image. Id. In view of Monzel’s real,
but still “minor,” role, the court’s chosen award of $7,500 was
neither “severe,” nor “nominal,” but rather “reasonable and
circumscribed” to fit Monzel’s contribution to Amy’s
damages, Paroline, 134 S. Ct. at 1727. That is all that Paroline
requires.

                               C

     Monzel’s arguments on appeal fall into three general
buckets. First, he argues that the government failed to carry its
burden of proving “the amount of the loss sustained by a victim
as a result of the offense.” 18 U.S.C. § 3664(e) (incorporated
by reference in 18 U.S.C. § 2259(b)(2)). Second, he asserts
that the district court’s explanation for its award was
insufficient and unreviewable. And he contends, thirdly, that
the district court made several fatal factual mistakes. None of
those challenges succeeds.
                               10

                                1

      Monzel offers a laundry list of asserted deficiencies in the
government’s proof of the amount of Amy’s losses.
Specifically, he objects that the government failed (i) to
identify a particular amount of restitution, (ii) to formulate a
discrete methodology for the district court to follow, (iii) to
submit evidence about total offenders and future prosecutions,
(iv) to disaggregate Amy’s initial-abuse losses from her general
loss figure, and (v) to update the 2008 loss projections relied
upon by the district court. Monzel’s Br. 40–45. Those
objections misunderstand the Paroline mission.

     At the outset, Monzel’s argument that the government’s
asserted evidentiary omissions preclude any award at all misses
the mark. Monzel does not dispute that the district court put
the burden of proof where it belonged—on the government. He
makes no claim, for instance, that the district court erroneously
assigned him the burden of proof for any aspect of the case.
Nor does Monzel dispute the government’s evidentiary
showing that he possessed an image of Amy, and that Amy has
“outstanding losses caused by the continuing traffic in those
images.” Paroline, 134 S. Ct. at 1727.

     Given that showing by the government and the court’s
agreement with it, an award of restitution was mandatory. 18
U.S.C. § 2259(b)(4). The only question, then, is whether the
district court abused its discretion in calculating the award
based on the record before it. See United States v. Dillard, 891
F.3d 151, 161 (4th Cir. 2018) (faulting the district court for
denying recovery even though the government had proven the
defendant possessed the victim’s image and that the victim had
outstanding losses from trafficking) (citing Paroline, 134 S. Ct.
at 1728); United States v. Rothenberg, 923 F.3d 1309, 1336–
                               11
1337 (11th Cir. 2019) (agreeing with Dillard that, once the
government proves possession and outstanding losses,
restitution must issue).

     So while the purported evidentiary gaps that Monzel has
identified might bear upon the “reasonableness” of the amount
awarded, they would not let him off scot free. Cf. United States
v. Sainz, 827 F.3d 602, 607 (7th Cir. 2016) (explaining that
failure of proof with respect to some Paroline factors “should
not be a barrier to all compensation for victims of child
pornography”).

      Viewed as challenges to the reasonableness of the
restitution award, all five of Monzel’s evidentiary arguments
fail.

     First, Monzel complains that the government did not
request a specific amount of restitution on Amy’s behalf. But
that is neither here nor there. A party’s claim for a particular
amount of restitution is not proof of causation. Instead, Section
3664(e) requires the government to “demonstrat[e] the amount
of the loss,” not to propose a mathematical calculation or to
specifically assert a dollar amount. 18 U.S.C. § 3664(e)
(emphasis added). So the question on appeal is not what the
government asked for, but what the district court found. We
are, after all, reviewing the district court’s judgment, not the
United States’ briefs. And the lack of a particular dollar
amount in the government’s request does not, by itself,
establish as a matter of law the “unreasonableness” of the
district court’s order.

    Second, Monzel faults the government for failing to
proffer, and the district court for failing to adopt, a formulaic
methodology for computing the restitution award. No dice.
What Paroline requires is that courts issue “reasonable and
                               12
circumscribed” awards. 134 S. Ct. at 1727. Beyond that,
Paroline was explicit that the district court’s judgment “cannot
be a precise mathematical inquiry”; “algorithm[s]” and “rigid
formula[s]” are not required. Id. at 1728 (emphasis added); see
also United States v. Rogers, 758 F.3d 37, 39 (1st Cir. 2014)
(per curiam) (affirming award in apparent absence of any
formula); Dillard, 891 F.3d at 161 (district court made
“fundamental error” when it decided not to order restitution
because it disagreed with government’s proposed formula); cf.
United States v. Halverson, 897 F.3d 645, 650 & n.1, 654 (5th
Cir. 2018) (endorsing a diversity of calculation methods
because the Paroline factors “need not be converted into a rigid
formula”).

     Third, Monzel faults the government for failing to provide
estimates on two of the Paroline factors—the number of future
convictions and the total offenders predicted to possess Amy’s
image.

     Again, Paroline says otherwise. Those numbers were only
two among a number of “rough guideposts” flagged in
Paroline. 134 S. Ct. at 1728. Those particular factors are not
“rigid” evidentiary requirements that the government is bound
to satisfy, or that the district court is obliged to analyze, in
every restitution case. United States v. Bordman, 895 F.3d
1048, 1059 (8th Cir. 2018) (quoting Paroline, 134 S. Ct. at
1728), cert. denied, 139 S. Ct. 1618 (Apr. 29, 2019). Instead,
the factors are permissive, and a district court is generally free
to disregard them if it reasonably concludes they are
unknowable or otherwise uninstructive. See id.; Sainz, 827
F.3d at 606 (“We do not read Paroline as requiring district
courts to consider in every case every factor mentioned.”);
United States v. Knapp, 695 F. App’x 985, 988 (8th Cir. 2017)
(“Paroline does not require an analysis of each of its
permissive factors.”).
                               13

     Of course, it may not be reasonable for a district court to
disregard those guideposts that describe the essential character
of the individual perpetrator’s offense, such as the number of
images possessed and the number of acts of distribution. Those
facts would generally seem to be indispensable to evaluating a
defendant’s relative causal role.

     In addition to the nature of the perpetrator’s role, the
number of images involved, and the number of acts of
distribution, there can be “other facts relevant to the
defendant’s relative causal role,” Paroline, 134 S. Ct. at 1728,
which often will include: (i) the frequency of views and shares,
because “every viewing * * * is a repetition of the victim’s
abuse,” id. at 1727; (ii) the means by which the images were
acquired (e.g., the trading of other images in exchange, the
payment of money encouraging the abuse, requests for images
of escalating levels of abuse); (iii) any stalking or attempts at
victim contact; (iv) the defendant’s individual contribution to
the market for the victim’s image over time—that is, whether
he sought out this particular victim’s images, the length of his
involvement in child pornography, whether he displayed a
pattern of offenses, and whether he has distributed other
images; and (v) the use of images to groom other children for
abuse or exposure to pornography. Additional considerations
may also include the imperative of ensuring that the individual
perpetrator is internalizing the costs of harm to the victim, and
the need to deter recidivism by encouraging the perpetrator to
express remorse, to obtain treatment, or to otherwise pursue
rehabilitative steps that will prevent him from generating
further demand for child pornography.

     But the factors Monzel cites—those seeking to predict the
future behavior of third parties—will often have less salience.
For starters, those factors are aimed mainly at preventing over-
                              14
compensation of the victim, which is not an issue in this case
(or in many cases).

     Beyond that, many courts have concluded that, as
restitution factors, future convictions and total offenders are
“virtually unknown and unknowable.” United States v.
Crisostomi, 31 F. Supp. 3d 361, 364 (D.R.I. 2014); see United
States v. Hite, 113 F. Supp. 3d 91, 96 (D.D.C. 2015); United
States v. DiLeo, 58 F. Supp. 3d 239, 245 (E.D.N.Y. 2014);
United States v. Wencewicz, 63 F. Supp. 3d 1238, 1246 (D.
Mont. 2014), vacated and remanded on other grounds, United
States v. Grovo, 653 F. App’x 512 (9th Cir. 2016); United
States v. Moody, CR 417–256, 2018 WL 3887506, at *3 (S.D.
Ga. Aug. 15, 2018); United States v. Reddick, CASE No. 2:17-
CR-208-WKW, 2018 WL 445112, at *6 (M.D. Ala. Jan. 16,
2018); United States v. Ayer, Case No. 2:15-cr-86-APG-NJK,
2015 WL 7259765, at *2 n.2 (D. Nev. Nov. 17, 2015); United
States v. Romero-Medrano, 2017 WL 5177647, at *4 (S.D.
Tex. Nov. 8, 2017); United States v. Schultz, CRIMINAL
ACTION NO. 14-10085-RGS, 2015 WL 5972421, at *2 (D.
Mass. Oct. 14, 2015); United States v. Gamble, No. 1:10–CR–
137, 2015 WL 4162924, at *2 (E.D. Tenn. July 9, 2015);
United States v. Campbell-Zorn, No. CR–14–41–BLG–SPW,
2014 WL 7215214, at *6 (D. Mont. Dec. 17, 2014); United
States v. Bellah, No. 13–10169–EFM, 2014 WL 7073287, at
*3 (D. Kan. Dec. 12, 2014); United States v. McIntosh, No.
4:14cr28, 2014 WL 5422215, at *6 (E.D. Va. Oct. 22, 2014);
United States v. Daniel, No. 3:07–CR–142–O, 2014 WL
5314834, at *2 (N.D. Tex. Oct. 17, 2014); United States v.
Reynolds, No. 12–20843, 2014 WL 4187936, at *6 (E.D. Mich.
Aug. 22, 2014); United States v. Watkins, No. 2:13–cr–00268
LKK AC, 2014 WL 3966381, at *6–7 (E.D. Cal. Aug. 13,
2014); accord Sainz, 827 F.3d at 607 (This information “may
not even be reliably known.”); United States v. Grovo, 826 F.3d
                               15
1207, 1221 (9th Cir. 2016) (same); United States v. Evans, 802
F.3d 942, 950 (8th Cir. 2015) (same).

     The bottom line is that that Paroline provided a “starting
point” for the district courts’ analyses. The Supreme Court did
not carve its permissive guideposts into doctrinal stone. See
Paroline, 134 S. Ct. at 1728. In many cases, the district courts
have concluded that total offenders and future convictions are
unknowable and uninstructive. The government in this case
stated that it lacked “sufficient, reliable data from which to
make reasonable estimates” of the number of future
convictions likely to involve images of Amy. Monzel II, 209
F. Supp. 3d at 76. The government added that it has no way to
estimate the broader number of offenders who possess images
of Amy. Id. The district court accepted both representations.
Id. Under these circumstances, the district court did not abuse
its discretion by focusing instead on the more defendant-
focused and market-perpetuating factors, as well as the
practical impact of the award. See id. at 77.

     Fourth, the district court relied upon a 2008 economic
report that estimated Amy would suffer $512,681 in future
treatment expenses and $2,751,077 in future vocational losses.
Monzel argues that the government was obligated to update the
report with the actual rather than predicted cost projections for
the period between 2009 and 2015, and to adjust the report’s
future projections based upon more recent developments in
Amy’s treatment patterns.

     But a determination of Monzel’s relative causal role does
not require a perpetual nickeling and diming of the victim
through the imposition of a never-ending accounting
requirement—a mandate that would force the victim to
constantly confront the growing number of offenders who trade
in her image.
                                16

     In any event, Monzel has not shown that, without his
requested adjustments, there would be a significant temporal
gap or a material dollar disparity between the initial projection
and actual costs. For example, the projected treatment costs for
the 2009 to 2015 period constituted only a minute fraction of
Amy’s losses. And even then, the record reveals no clear
disparity between the report’s projections and the costs actually
incurred. Cf. FED. R. CRIM. P. 52(a). As for Amy’s future
treatment, the record confirms the core assumptions that
underlay the 2008 projections. In other words, on this record,
demanding an update for the sake of an update would not be
worth the candle.

     Fifth, Monzel argues that the district court was required to
formally backout of Amy’s lifetime of psychological treatment
and social and vocational impacts those future damages
attributable to both her initial abuse and the initial distribution
of her image. That argument, again, seeks to impose a
mathematical rigidity that Paroline eschews. The Supreme
Court made “connection to the initial production of the images”
one of several factors that could be considered. See Paroline,
572 U.S. at 460. Here, the district court expressly took into
account that Monzel was in no way “connected to the initial
production” of Amy’s images. Monzel II, 209 F. Supp. 3d at
76. Paroline requires no more than that.

    The argument also proves too much. Courts already
consider whether the defendant’s conduct was connected to
“the initial production of the images.” Paroline, 134 S. Ct. at
1728. Monzel’s demand that courts also mathematically
disaggregate the losses from before the images entered the
marketplace simply blinks away the compounding effects of
demand for child-pornography images on their production in
the first place. It also ignores the distinct harm that Amy
                                17
suffered upon learning that the images of her already-
completed abuse were being viewed for pleasure by
perpetrators like Monzel. Paroline, 134 S. Ct. at 1717. For the
type of long-term harms at issue here, courts cannot be
expected to formally disaggregate the intertwined. See
Bordman, 895 F.3d at 1059 (explaining that it would transform
Paroline’s “rough guideposts” into a “rigid formula” to treat
initial-abuse disaggregation as a threshold requirement)
(citation omitted); Rothenberg, 923 F.3d at 1333–1334 (same);
cf. United States v. Miner, 617 F. App’x 102, 103 (2d Cir.
2015) (explaining that, in the disaggregation context, Paroline
does not require a “detailed accounting”).

     The Ninth Circuit has taken the opposite tack. See United
States v. Galan, 804 F.3d 1287, 1290 (9th Cir. 2015) (reading
Paroline as “plainly perceiv[ing] a need for separation”). But
in our view, that court’s categorical test demands a level of
forensic precision in the causal analysis that fails to account for
the synergistic effect of possessors’ demand for images on the
harms unleashed by production. The complexity of the Ninth
Circuit’s approach also demands in most cases more linear
precision than a comparative “relative” causal role seeks to
measure. Not to mention the continuing need to ensure,
through the award, that each perpetrator internalizes the costs
of his actions. See Paroline, 134 S. Ct. at 1727 (describing goal
of “impressing upon offenders the fact that child-pornography
crimes, even simple possession, affect real victims”).

     The test’s difficulties are seemingly reflected in the large
number of district court cases within the Ninth Circuit in which
victims have been denied restitution because the government
cannot meet its “impossible [evidentiary] task” of
disaggregating, in a coherent way, a victim’s lifetime of costs
from the marketing of her images. See United States v. Chan,
CR No. 15-00224 DKW, 2016 WL 370712, at *2 (D. Haw.
                                  18
Jan. 29, 2016) (denying recovery because government could
not surmount the “monumental difficulty associated with * * *
disaggregation”); accord United States v. Kugler, No. CR 14-
73-BLG-SPW, 2016 WL 816741, at *3 (D. Mont. Feb. 29,
2016) (same); cf. United States v. Young, 703 F. App’x 520,
521 (9th Cir. 2017) (unpublished decision reversing for failure
to disaggregate); United States v. Massa, 647 F. App’x 718,
721 (9th Cir. 2016) (same); United States v. Blurton, 623 F.
App’x 318, 319 (9th Cir. 2015) (same); Campbell-Zorn, 2014
WL 7215214, at *4 (Disaggregation “only seems possible in
the rather unique situation presented in Paroline where there is
some kind of demarcation between the losses from the initial
abuse and the losses from continued trafficking.”) (emphasis
omitted).2

                                  2

     In addition to those evidentiary objections, Monzel takes
aim at the district court’s reasoning. He argues, first, that the
opinion is so devoid of analysis as to be unreviewable for all
intents and purposes. Monzel’s Br. 46. Monzel contends,
secondly, that the district court wrongly failed to address “any”

     2
       Certain statements from the Tenth Circuit’s decision in United
States v. Dunn, 777 F.3d 1171 (10th Cir. 2015), could also be read to
endorse a categorical disaggregation requirement. See, e.g., id. at
1181. But context is everything, and the Tenth Circuit made its
statements in the course of overturning a trial court decision that had
held a distributor jointly and severally liable with the abuser for the
entirety of the outstanding losses. So disaggregation, as Dunn
deployed the concept, may have meant simply that distributors and
possessors should pay only for their relative roles. See Rothenberg,
923 F.3d at 1333 (“Dunn must be read in the factual context of a
reversal of a district court’s ruling that a defendant was jointly and
severally liable with all other defendants, including the abuser, for
the entirety of the victim’s * * * total losses[.]”).
                               19
of his mitigation arguments. Id. at 47. Both challenges are
mistaken.

     As for reviewability, district courts generally are required
to “articulate the specific factual findings underlying * * *
restitution order[s] in order to enable appellate review.” United
States v. Fair, 699 F.3d 508, 513 (D.C. Cir. 2012) (citations
omitted); cf. Chavez-Meza v. United States, 138 S. Ct. 1959,
1965 (2018) (with respect to 18 U.S.C. § 3553(a)’s sentencing
factors, district court’s explanation must be sufficient “to allow
for meaningful appellate review” in “the circumstances of the
particular case”).

    The district court’s opinion here easily passes that test.
The court discussed each of the Paroline factors, emphasizing
and delineating Monzel’s relatively “minor” role. Monzel II,
209 F. Supp. 3d at 76–77. Whether or not those record-based
determinations are correct, they are certainly amenable to
appellate review.

     Monzel insists the district court opinion must leave “some
way for [us] to trace the derivation of the court’s $7,500
award[.]” Monzel’s Br. 46 (second emphasis added). The
question, however, is not whether the district court showed
every step of its homework. The decision being made is one of
reasoned judgment, not formulaic computation. Cf. Chavez-
Meza, 138 S. Ct. at 1964 (In sentencing, “[t]he appropriateness
of brevity or length, conciseness or detail, when to write, what
to say, depends upon circumstances.”) (quoting Rita v. United
States, 551 U.S. 338, 356 (2007)).

     So we ask only whether the district court reasonably
exercised its discretion in weighing the Paroline and other
relevant factors, applying them to the record in this case, and
then choosing a “circumscribed” award that is consistent with
                              20
the restitutionary purposes of the statutory scheme. See
Paroline, 134 S. Ct. at 1727; Massa, 647 F. App’x at 720
(upholding restitution award even though “[i]t would have been
helpful for the court to have provided more detail as to how it
reached the $8,000 figure for each victim,” because “the
awards appear ‘reasonable and circumscribed,’ and neither
‘token or nominal’ nor ‘severe’”); accord United States v.
Beckmann, 786 F.3d 672, 683 (8th Cir. 2015). The district
court did just that, discussing the relevant factors and
emphasizing Monzel’s limited role as the possessor of a single
image. Monzel II, 209 F. Supp. 3d at 76–77.

     Taking a 180-degree turn, Monzel next argues that the
district court was too mathematical in its approach. Monzel
speculates that the district court randomly selected five post-
Paroline awards, averaged the amounts to $7,432.63, and
rounded that figure “to an even $7,500.” Monzel’s Br. 37, 45.
But that reconstruction of the district court’s reasoning is as
implausible as it is uncharitable. First, Monzel concedes that
his argument fudged the math. His calculation relied upon the
$7,500 that was in fact “award[ed]” in United States v. Bellah,
No. 13–10169–EFM, 2014 WL 7073287 (D. Kan. Dec. 12,
2014), rather than the $7,000 figure cited by the district court
below. Monzel’s Br. 37 n.15.

     Anyhow, the district court here explained that its decision
was based on “the parties’ arguments, the relevant Paroline
factors, * * * and * * * information provided regarding prior
restitution awards for Amy,” and not on the small and random
sampling of post-Paroline awards stressed in Monzel’s
briefing. See Monzel II, 209 F. Supp. 3d at 77 (emphasis
added). We take the district court at its word. For more than a
decade, the court has been immersed in this litigation and,
throughout, has consistently demonstrated a good-faith effort
to properly implement the evolving legal standard for
                               21
restitution awards. See, e.g., id.; Monzel, 2012 WL 12069547,
at *4; Monzel, 2011 WL 10549405, at *2. There is no basis for
imputing a hidden and arbitrary decisionmaking process to the
court.

      Monzel’s next objection is that the district court “did not
address any of [his] arguments in mitigation[.]” Monzel’s Br.
47. That argument falls flat. A sentencing court must generally
consider all “nonfrivolous arguments for mitigation.” See
United States v. Bigley, 786 F.3d 11, 12, 14 (D.C. Cir. 2015);
accord United States v. McKeever, 824 F.3d 1113, 1125–1126
(D.C. Cir. 2016). And that is what the district court did here.
It acknowledged Monzel’s “minor” role, and it specifically
emphasized the lack of evidence that Monzel (i) knew Amy,
attempted to discover her identity, or attempted to contact her;
(ii) sought out images of Amy in particular; (iii) paid for or
received anything of value for her images; or (iv) groomed
other minors with her images. See Monzel II, 209 F. Supp. 3d
at 76. With all of those considerations factored into the
ultimate award, id. at 77, Monzel fails to identify any material
mitigation arguments that the district court did not address.

                               3

    Finally, Monzel offers a laundry list of factual errors he
deems fatal to the district court’s judgment. None are.

     First, he argues that the district court wrongly read Monzel
I as setting a $5,000 floor below which his restitution payment
could not go. And that erroneous starting point, Monzel
contends, tainted the ultimate $7,500 award.

    That argument is doubly flawed. As an exegetical matter,
the district court’s construction of Monzel I was quite
reasonable. This court was explicit that it was “grant[ing]
                                22
[Amy’s] petition” because “the $5,000 the court awarded was,
by [the district court’s] own acknowledgement, less than the
amount of harm Monzel caused Amy[.]” Monzel I, 641 F.3d at
534 (emphasis added). While the district court could have
found that the dollar amount changed, the admonition not to
order restitution in an amount less than what Monzel caused
remained in place.

     As a factual matter, the district court never indicated in any
way that the $5,000 floor tied its hands in the wake of Paroline,
somehow forcing it to award more restitution than warranted.
See Order, In re: Amy, Child Pornography Victim, No. 12-3093
(D.C. Cir. June 13, 2014) (directing the district court “to
redetermine restitution for Amy consistent with” the causation
framework set out in Paroline). Monzel points to nothing in
the district court’s opinion that even hints that its post-Paroline
analysis proceeded with a $5000 weight already on the
damages scale.

     Second, Monzel claims the district court made a pair of
factual errors, subtracting both too much and too little from
Amy’s general loss figure. According to him, the court should
have subtracted $7,186 to exclude damages incurred prior to
Monzel’s arrest in 2009, and also should not have subtracted
$20,563 in attorney’s fees because Amy’s submission
consisted exclusively of vocational and treatment expenses. As
to the purported $7,186 over-inclusion of loss, the impact—if
any—in determining Monzel’s share of Amy’s more than $3
million in losses is at best de minimis, and at worst incalculable.
And as to the asserted underestimation of Amy’s general
losses, that could only have inured to Monzel’s benefit. See
FED. R. CRIM. P. 52(a) (reversal only for prejudicial error). No
harm, no foul.
                              23
     Third, Monzel faults the district court for failing to
mention the amount of Amy’s then-to-date recovery. That
argument asks the wrong question. Under Paroline, restitution
reflects not Monzel’s share of Amy’s unpaid balance, but rather
his contribution to her “general losses”—“the aggregate losses,
including the costs of psychiatric treatment and lost income,
that stem from the ongoing traffic in her images as a whole.”
Paroline, 134 S. Ct. at 1722. The harm that Monzel caused
does not change just because other sources of compensation
may have surfaced. Cf. 18 U.S.C. § 2259(b)(4)(B) (barring
district courts from “declin[ing] to issue [restitution] because
of * * * the fact that a victim has, or is entitled to, receive
compensation for his or her injuries from the proceeds of
insurance or any other source”).

    Lastly, Monzel returns to the “math.” He claims that
$7,500 cannot represent his actual contribution to Amy’s losses
because it “essentially assumes that Mr. Monzel is one of 432
people ($3,243,195/$7,500) who have harmed and will harm
Amy,” when in fact thousands continue to trade in her image.
Monzel’s Br. 52. Any effort to apportion Amy’s losses evenly
among the full universe of offenders would, by Monzel’s
account, yield something between fifteen dollars and less than
a penny.

     That is exactly the reasoning that Paroline rejected. See
134 S. Ct. at 1734 (Roberts, C.J., dissenting) (finding it “hard
to see how a court fairly assessing this defendant’s relative
contribution could do anything” other than “impose ‘trivial
restitution orders’”) (citation omitted). Under Paroline,
restitution is a matter of “discretion and sound judgment,” not
an exercise in long division. 134 S. Ct. at 1728 (majority op.)
(no “trivial” awards); id. at 1744 (Sotomayor, J., dissenting)
(“[A] truly proportional approach to restitution would lead to
an award of just $47 against any individual defendant.
                              24
Congress obviously did not intend that outcome, and the Court
wisely refuses to permit it.”) (citation omitted).

                           *****

     Restitution in child pornography cases is meant to address
the very real and reverberating trauma that attends each
perpetrator’s acquisition and viewing of a victim’s image.
“[C]hild pornography is ‘a permanent record’ of the depicted
child’s abuse, and ‘the harm to the child is [only further]
exacerbated by [its] circulation.’” Paroline, 134 S. Ct. at 1717
(third alteration in original) (quoting New York v. Ferber, 458
U.S. 747, 759 (1982)); cf. Osborne v. Ohio, 495 U.S. 103, 111
(1990) (Child pornography “haunt[s] [the victim] in years to
come.”). What Monzel’s slide-rule approach fails to come to
grips with is that the harm to Amy became greater, not less,
when he joined the ranks of perpetrators, reinflicting and
perpetuating her trauma. To value that pain in pennies would
make the restitution statute an insult to the victims. It would
also wrongly allow the individual possessor to hide among the
sea of wrongdoers. The district court was correct to hold
Monzel accountable for the harm that he caused by acquiring
and viewing for personal pleasure the image of Amy’s abuse.

    The judgment of the district court is affirmed.

                                                      So ordered.
