 United States Court of Appeals
           FOR THE DISTRICT OF COLUMBIA CIRCUIT



Argued September 11, 2015           Decided December 18, 2015

                         No. 14-7035

    OSCAR SALAZAR, BY HIS PARENTS AND NEXT FRIENDS,
           ADELA AND OSCAR SALAZAR, ET AL.,
                      APPELLEES

                               v.

               DISTRICT OF COLUMBIA, ET AL.,
                       APPELLANTS

 CHARTERED HEALTH PLAN AND D.C. CHARTERED HEALTH
                    PLAN, INC.,
                    APPELLEES


                  Consolidated with 14-7050


        Appeals from the United States District Court
                for the District of Columbia
                    (No. 1:93-cv-00452)


     Richard S. Love, Senior Assistant Attorney General, Office
of the Attorney General for the District of Columbia, argued the
cause for appellants. With him on the briefs were Karl A.
Racine, Attorney General, Todd S. Kim, Solicitor General, and
Loren L. AliKhan, Deputy Solicitor General.
                                2


    Kathleen L. Millian argued the cause for appellees. With
her on the brief were Bruce J. Terris, Zenia Sanchez Fuentes,
Jane Perkins and Lynn E. Cunningham.

   Before: SRINIVASAN and PILLARD, Circuit Judges, and
SENTELLE, Senior Circuit Judge.

   Opinion for the Court filed by Senior Circuit Judge
SENTELLE.

     SENTELLE, Senior Circuit Judge: Appellants the District of
Columbia, the District’s Mayor, and the Director of the
District’s Department of Human Services (collectively, the
“District”) appeal two separate awards of attorneys’ fees and
expenses for work performed from 2010 to 2012 on this 42
U.S.C. § 1983 Medicaid class action. In this consolidated
appeal, the District raises three grounds for its position that the
district court’s decisions amounted to an abuse of discretion.
First, the District argues that the district court abused its
discretion by making targeted reductions in Plaintiff-Appellees’
(“Plaintiffs”) fee requests, as opposed to the District’s requested
across-the-board reductions. Second, the District contends that
the district court abused its discretion in awarding hourly rates
to Plaintiffs based on the Legal Services Index (“LSI”) update
to the Laffey Matrix. See Laffey v. Nw. Airlines, Inc. (Laffey I),
572 F. Supp. 354, 371 (D.D.C. 1983), aff’d in part, rev’d in part
on other grounds, Laffey v. Nw. Airlines, Inc. (Laffey II), 746
F.2d 4 (D.C. Cir. 1984), overruled in part on other grounds en
banc by Save Our Cumberland Mountains, Inc. v. Hodel
(SOCM), 857 F.2d 1516 (D.C. Cir. 1988). Finally, the District
states that the district court improperly ordered the District to
pay for the time Plaintiffs’ counsel spent on a third-party appeal.
We disagree. The district court thoroughly analyzed both
                                 3

parties’ positions in awarding some, but not all, of the requested
fees. For the reasons stated below, we affirm.

                         BACKGROUND

        In 1993, Plaintiffs filed a class action against the District
challenging the District’s provision of medical assistance,
including certain services for all enrolled children, under the
District’s Medicaid program. In 1996, the district court
concluded that the District had violated 42 U.S.C. § 1983 by
depriving Plaintiffs of their statutory and constitutional rights.
Salazar v. District of Columbia, 954 F. Supp. 278, 334 (D.D.C.
1996). In 1999, while the judgment was pending on appeal, the
parties entered into a comprehensive settlement agreement (the
“Settlement Order”).

        Under the terms of the Settlement Order, Plaintiffs’
counsel is entitled to compensation for monitoring the District’s
compliance with the provisions of the Settlement Order, for
representing individual class members to enforce their rights
under federal Medicaid law and the Settlement Order, and for
work not designated as monitoring work, such as enforcement,
attorneys’ fees, and appeals work. Paragraphs 64 and 65 of the
settlement establish certain rates, which are adjusted annually
for inflation, for Plaintiffs’ counsel to monitor and enforce the
District’s compliance with the Settlement Order. For instance,
if a purported member of the class seeks Plaintiffs’ counsel’s
assistance, the reasonable time and expenses of Plaintiffs’
counsel in determining whether the individual is a member of
the class and in providing legal assistance “shall be deemed
compensable monitoring of [the Settlement] Order under 42
U.S.C. § 1988 [at a rate of]” $75/hr. In addition, for rates set
under Paragraphs 64 and 65, the Settlement Order specifies that
those “hourly rates shall be adjusted annually, beginning on
January 1, 1999, based on the U.S. Department of Commerce
                                4

Consumer Price Index for Legal Services.” Under Paragraph 66,
the parties left open the rates for work not specified as
monitoring work under Paragraphs 64 and 65 of the Settlement
Order.

        The Settlement Order provides no further guidance for
determining an appropriate fee award where the rate is
unspecified. However, this Court has developed a three-part
analysis to assess appropriate fee awards under fee-shifting
statutes in cases involving complex federal litigation. See Eley
v. District of Columbia, 793 F.3d 97, 100 (D.C. Cir. 2015)
(citing SOCM, 857 F.2d at 1517). A court must: (1) determine
the “number of hours reasonably expended in litigation”; (2) set
the “reasonable hourly rate”; and (3) use multipliers as
“warranted.” Id. In addition, the “fee applicant bears the burden
of establishing entitlement to an award, documenting the
appropriate hours, and justifying the reasonableness of the
rates,” with the opposing party remaining “free to rebut [the] fee
claim.” Covington v. District of Columbia, 57 F.3d 1101, 1107-
08 (D.C. Cir. 1995), cert. denied, 516 U.S. 1115 (1996).

       Here, the District challenges the district court’s analysis
of the hours Plaintiffs’ counsel spent litigating the multiple
issues arising from the monitoring and enforcement of the
Settlement Order. Broadly, the District argues that the district
court abused its discretion by failing to rein in Plaintiffs’
counsel’s fees further than it did.

        The District also challenges the “reasonable hourly rate”
determination. That determination requires showing at least
three elements: (1) “the attorneys’ billing practices”; (2) “the
attorneys’ skills, experience, and reputation”; and (3) “the
prevailing market rates in the relevant community.” Covington,
57 F.3d at 1107. As to these three sub-elements, the District
                                5

focuses its challenge on the district court’s determination of the
“prevailing market rates in the relevant community.”

        A court calculating a prevailing market rate allows fee
applicants to submit attorneys’ fee matrices as one type of
evidence. Covington, 57 F.3d at 1109. As we have previously
noted in Eley, 793 F.3d at 100, “[t]he most commonly used fee
matrix is the ‘Laffey Matrix’—the schedule of prevailing rates
compiled in [Laffey I].”

        The Laffey Matrix sets out a general guideline for
awarding attorneys’ fees based on experience. See, e.g., Eley,
793 F.3d at 101 (discussing Laffey Matrix rates). For instance,
the Laffey Matrix sets the rate for “experienced federal court
litigators in their 11th through 19th years after law school
graduation” at $150/hr. Id. (citing Laffey II, 746 F.2d at 8 n.14).
But these 30-year-old rates must also be adjusted for inflation.
See Eley, 793 F.3d at 101 (citing SOCM, 857 F.2d at 1525). For
this reason, updated Laffey Matrices developed, including the
two at issue here—(i) the Laffey Matrix as updated by the Legal
Services Index (“LSI”) of the Nationwide Consumer Price Index
(“CPI”) (the “LSI Laffey Matrix”), and (ii) the All-Items CPI for
the Washington, D.C. area (also known as the “USAO Laffey
Matrix”). See also Eley, 793 F.3d at 101-02 (elaborating on the
differences between the LSI and the USAO Laffey Matrices).

        In 2013, Plaintiffs filed two fee applications for work
done from 2010 through 2012. The district court granted in part
and denied in part those fee applications, which decisions the
District appeals now. In both decisions, and in spite of the
District’s arguments otherwise, the district court ruled that the
LSI Laffey Matrix provided the appropriate billing rates for
work lacking a specified rate in the Settlement Order. See
Salazar v. District of Columbia (Salazar III), 991 F. Supp. 2d
39, 47 (D.D.C. 2014); see also Salazar v. District of Columbia
                                6

(Salazar IV), 30 F. Supp. 3d 47, 51-52 (D.D.C. 2014) (adopting
analysis of Salazar III). Citing to previous resolutions of other
fee applications in this on-going litigation, the district court
reiterated that “the [LSI-adjusted][ [sic] Laffey index has the
distinct advantage of capturing the more relevant data because
it is based on the legal services component of the Consumer
Price Index rather than the general CPI on which the U.S.
Attorney’s Office matrix is based.” Salazar III, 991 F. Supp. 2d
at 47 (quoting Salazar v. District of Columbia (Salazar I), 123
F. Supp. 2d 8, 14-15 (D.D.C. 2000)) (adopting and citing
Salazar v. District of Columbia (Salazar II), 750 F. Supp. 2d 70,
72-74 (D.D.C. 2011)); see also Salazar IV, 30 F. Supp. 3d at 51-
52. After concluding that the LSI Laffey Matrix was the
appropriate rate index, the district court addressed the District’s
many arguments related to the appropriateness of Plaintiffs’
counsel’s billing. See Salazar III, 991 F. Supp. 2d at 49-64;
Salazar IV, 30 F. Supp. 3d at 52-65.

        The district court awarded some but not all of the fees
and costs Plaintiffs sought; and where the district court found
that Plaintiffs’ counsel’s fees were not reasonable, the court
either reduced the hours sought, or denied the fee request. See,
e.g., Salazar III, 991 F. Supp. 2d at 53 (reducing billing for
some individual claims by 15% as the court found the hours
spent “excessive”); Salazar IV, 991 F. Supp. 2d at 61 (denying
request for fees for categories of work that were “unrelated” to
the case). In the end, the district court awarded Plaintiffs
$655,587.98 for fees and expenses related to the 2011 fee
application, and also awarded Plaintiffs $522,990.63 for fees
and expenses related to the 2012 fee application. J.A. at 2344-
45, 2390-91.
                                 7

                          DISCUSSION

         We review the district court’s fee awards for abuse of
discretion, “and will not upset its hourly rate determination
absent clear misapplication of legal principles, arbitrary fact
finding, or unprincipled disregard for the record evidence.”
Eley, 793 F.3d at 103 (citation and quotation marks omitted).
“This limited standard of review is appropriate in view of the
district court’s superior understanding of the litigation and the
desirability of avoiding frequent appellate review of what
essentially are factual matters.” Id. at 104 (quoting Covington,
57 F.3d at 1110). We do, however, “examine de novo whether
the district court applied the correct legal standard.” Id. (citation
and quotation marks omitted).

                                 A.

         As noted, the District takes issue with the district court’s
calculation of the reasonableness of the attorney hours.
Specifically, the District argues that the district court should
have applied across-the-board reductions to Plaintiffs’ counsel’s
fee applications, in light of purportedly excessive and vague
billing. For example, the District would have preferred the
district court to reduce the 2011 fee application by 20% and the
2012 fee application by 15% rather than the specific reductions
in certain categories of the fee application that the district court
made.

        With respect to the district court’s determinations about
the reasonableness of the attorneys’ hours in the fee
applications, the court acted within its discretion. The district
court conducted a comprehensive and careful analysis of the
parties’ positions, and its resolution of the parties’ disputes
concerning the amount of attorney hours was reasonable. See,
e.g., Blum v. Stenson, 465 U.S. 886, 902 n.19 (1984) (“A district
                                8

court is expressly empowered to exercise discretion in
determining whether an award is to be made and if so its
reasonableness.”). Indeed, the district court addressed the
adequacy of the time records at issue, purported overbilling or
excessive billing, and the District’s requested across-the-board
reductions. See Salazar III, 991 F. Supp. 2d at 50, 57, 64; see
also Salazar IV, 30 F. Supp. 3d at 52, 54, 61, 64-65. What is
more, the district court has supervised this case for at least the
last fifteen years, making it well-situated to determine the
reasonableness of Plaintiffs’ counsel’s fees. Accordingly, we
will not disturb the district court’s decisions.

                               B.

         The District also takes issue with the district court’s
determination that the LSI Laffey rates apply in this case. As a
preliminary matter, we reject Plaintiffs’ threshold contention
that the District waived its challenge to the LSI Laffey rates.
Plaintiffs maintain that the law-of-the-case doctrine bars the
District from raising that challenge because the District failed to
appeal the district court’s prior fee decisions applying the LSI
Laffey Matrix, as opposed to the USAO Laffey Matrix, in setting
hourly rates under Paragraph 66 of the Settlement Order. See
Salazar I, 123 F. Supp. 2d at 11-15; Salazar II, 750 F. Supp. 2d
at 72-74. But the law-of-the-case doctrine does not apply here.
Under that doctrine, “a legal decision made at one stage of
litigation, unchallenged in a subsequent appeal when the
opportunity to do so existed, becomes the law of the case for
future stages of the same litigation, and the parties are deemed
to have waived the right to challenge that decision at a later
time.” Kimberlin v. Quinlan, 199 F.3d 496, 500 (D.C. Cir.
1999) (emphasis added) (citation and internal quotation marks
omitted). While the District failed to appeal the district court’s
use of the LSI Laffey Matrix rates in Salazar I or Salazar II, the
District is taking the opportunity now to challenge the
                                9

application of the LSI Laffey Matrix rates to the 2010-2012
attorneys’ fees, which were not at issue in those prior decisions.
Therefore, we consider on its merits the District’s challenge to
the district court’s market-rate determination for 2010-2012.

         The district court did not abuse its discretion. The
district court’s selection of LSI Laffey rates is consistent with
this Court’s intervening decision in Eley. The district court
appropriately required the Plaintiffs to demonstrate the propriety
of the rates they sought (i.e., under the LSI Laffey Matrix). In
Eley, we vacated a district court’s fee award based on evidence
submitted by the District tending to show that, in the particular
context of IDEA claims, there is a submarket in which
attorneys’ hourly fees are generally lower than the rates in either
of the Laffey Matrices. Eley, 793 F.3d at 105. In this case, by
contrast, the District identifies no such submarket, instead
acquiescing in the notion that the litigation at issue qualifies as
complex federal litigation (as to which the Laffey Matrices
apply). See, e.g., Appellant Br. at 48-49 (discussing that “in
complex federal court litigation” the USAO update to the Laffey
Matrix is a more appropriate method for determining the
prevailing market rate).

         Accordingly, unlike in Eley, 793 F.3d at 103, the District
does not argue for rates lower than both of the Laffey matrices,
but instead argues that one Laffey Matrix should apply instead
of the other. See Appellant Br. at 48-54 (arguing that the USAO
Laffey Matrix is the preferable market-rate index). Moreover,
our decision in Eley, 793 F.3d at 104-05, reaffirmed our prior
decision in Covington, 57 F.3d at 1110, in which we held that
the fee applicants “clearly” met their burden of justifying their
requested rates and “were properly accorded a presumption of
reasonableness.” In Covington, the fee applicants’ evidentiary
submissions for the prevailing market rates in complex federal
litigation included “the Laffey matrix, the U.S. Attorney’s Office
                                10

matrix, affidavits attesting to increases in the market rates since
the original Laffey matrix, and memorandum opinions in district
court cases which relied on these matrices.” 57 F.3d at 1110.
The District, in rebuttal, failed to cite any relevant cases
supporting its requested rates. Id. at 1111. Therefore, we
affirmed the district court’s “determination that the relevant
market is that of complex federal litigation.” Id. at 1112.

     As the District concedes that the relevant market is that of
complex federal litigation, the only issue is whether Plaintiffs
submitted sufficient evidence for the district court to conclude
that the LSI Laffey Matrix applies. Like the fee applicants in
Covington, 57 F.3d at 1110, Plaintiffs submitted “a great deal of
evidence regarding prevailing market rates for complex federal
litigation.” Plaintiffs submitted evidence for their preferred
Laffey Matrix update, including the affidavit of the economist
that developed the LSI Laffey Matrix—Dr. Michael Kavanaugh.
Dr. Kavanaugh’s affidavit explained why the LSI is a better
measure of the change in prices for legal services in
Washington, D.C. than the USAO update to the Laffey Matrix.
J.A. at 2038-65. The affidavit also noted other federal courts
that have adopted the LSI Laffey Matrix. See J.A. at 2039-40
¶ 6.

     In addition to this evidence, Plaintiffs went further and
submitted more evidence supporting the use of the rates
approved by the district court than the submissions found
adequate in Covington. For instance, Plaintiffs submitted billing
rates tables demonstrating the difference between average
national law firm rates and the LSI update to the Laffey Matrix,
as well as the difference between average national law firm rates
and the USAO update to the Laffey Matrix. J.A. at 2292. As an
example, for lawyers with experience levels between eleven and
nineteen years from the date of law school graduation, the
average national law firm rate in 2012 to 2013 was $672. Id.
                                11

For the same experience level in the same time frame, the LSI
updated rate was closer to the average national law firm rate at
$626, while the USAO updated rate was $445. Id. On average,
the LSI Laffey Matrix rates were 14% lower than the average
national law firm rates for all experience levels in this time
period. See id. On the other hand, the USAO Laffey Matrix
rates were 38% lower than the average national law firm rates.
See id.

     Furthermore, a 2012 National Law Journal Rates Survey
showed that the rates for partners in Washington, D.C. on the
high-end of the market far exceeded the rates in the LSI update.
See J.A. at 2293. With these numbers and submissions in the
record, the district court’s point that “the LSI-adjusted matrix is
probably a conservative estimate of the actual cost of legal
services in this area,” does not appear illogical. See Salazar III,
991 F. Supp. 2d at 48 (citation and internal quotation marks
omitted). The District, neither below nor on appeal, rebuts this
logic with relevant arguments. The District makes much about
the fact that this prolonged litigation is depleting public funds in
a case in which Plaintiffs no longer need to pay LSI updated
Laffey rates to “attract competent counsel.” Appellant Br. at 49.
But as the district court correctly noted, and as we have made
clear, “fees should be neither lower, nor calculated differently,
when the losing defendant is the government.” Salazar III, 991
F. Supp. 2d at 49 (quoting Copeland v. Marshall, 641 F.2d 880,
896 (D.C. Cir. 1980) (en banc)).1




1
 The District’s argument that other courts within this Circuit have
applied the USAO update to the Laffey Matrix is not compelling. The
cases cited by the District are district court cases, not binding
precedent for this Court or the trial court we review.
                                 12

                                 C.

    As to the final matter on appeal, the District takes issue with
the district court’s order requiring the District to pay for the time
Plaintiffs’ counsel spent responding to an appeal involving an
effort to obtain information used by one of the District’s
contractors. See Salazar III, 991 F. Supp. 2d at 59-60 (awarding
Plaintiffs’ appeal fees). We affirm the award of fees for this
work, despite the District not entering an appearance in the
appeal. See id. at 60. In the particular circumstances of that
appeal, where the information was necessary for Plaintiffs’
counsel to litigate some of the claims underlying the Settlement
Order, see id., the award of fees was not inappropriate.

                           CONCLUSION

    For the foregoing reasons, and based on the particular facts
of this case, the decisions of the district court are affirmed.


                                                        So ordered.
