 United States Court of Appeals
        FOR THE DISTRICT OF COLUMBIA CIRCUIT



Argued September 21, 2012        Decided December 14, 2012

                       No. 11-7113

  JAMAL J. KIFAFI, INDIVIDUALLY, AND ON BEHALF OF ALL
              OTHERS SIMILARLY SITUATED,
                        APPELLEE

                            v.

        HILTON HOTELS RETIREMENT PLAN, ET AL.,
                    APPELLANTS


                Consolidated with 11-7151


       Appeals from the United States District Court
               for the District of Columbia
                   (No. 1:98-cv-01517)


    Thomas C. Rice argued the cause for appellants-cross
appellees. With him on the briefs were Andrew M. Lacy and
Jonathan K. Youngwood.

    Stephen R. Bruce argued the cause for appellee-cross
appellant. With him on the briefs was Allison C. Pienta.

   Before: SENTELLE, Chief           Judge,   BROWN    and
KAVANAUGH, Circuit Judges.
                                2
    Opinion for the Court filed by Circuit Judge BROWN.

     BROWN, Circuit Judge: In the late 1990s, Jamal Kifafi, an
erstwhile Hilton employee and participant in Hilton’s
retirement plan (“Plan”), noticed a problem with the benefits
calculation on his statement of benefits. Concluding the Plan
violated the Employee Retirement Income Security Act
(“ERISA”) in a number of ways, he sued. Now, almost fifteen
years and twelve district court opinions later, we join the fray
and force the parties a little closer to final resolution of their
dispute. The district court found that the Plan was
impermissibly backloaded and that Hilton failed to calculate
participants’ vesting credit properly, and it imposed relief
accordingly. We affirm because the district court’s handling
of the case was well within its discretion.

                                I

     ERISA guarantees neither a particular benefit nor a
particular method for calculating the benefit. Alessi v.
Raybestos-Manhattan, Inc., 451 U.S. 504, 511–12 (1981). Yet
employers do not have carte blanche.

     ERISA defines the universe of permissible benefit-
accrual rates by requiring defined benefit plans to satisfy
one—and only one—of three rules designed to prevent
backloading, which occurs when a plan awards benefits to
employees in later years of service at a rate disproportionately
higher than the rate for employees in earlier years of service.
See 29 U.S.C. § 1054; H.R. REP. NO. 93-807, at 21 (1974),
reprinted in 1974 U.S.C.C.A.N. 4670, 4688 (defining
“backloading”). The three rules contained in this anti-
backloading provision are known as the 3% rule, the
fractional rule, and the 133 1/3% rule. The 3% rule
“prescribes a minimum percentage of the total retirement
                              3
benefit that must be accrued in any given year.” Alessi, 451
U.S. at 512 n.9. The fractional rule is “essentially a pro rata
rule under which in any given year, the employee’s accrued
benefit is proportionate to the number of years of service as
compared with the number of total years of service
appropriate to the normal retirement age.” Id. The 133 1/3%
rule, meanwhile, “permits the use of any accrual formula as
long as the accrual rate for a given year of service does not
vary beyond a specified percentage from the accrual rate of
any other year under the plan.” Id. Specifically, the “rate of
benefit accrual in any future year may not be more than one-
third greater than the rate in the current year.” Lonecke v.
Citigroup Pension Plan, 584 F.3d 457, 464 (2d Cir. 2009).

     ERISA circumscribes pension plans in other ways as
well, such as by setting minimum vesting standards. Where
accrual relates to “the amount of the benefit to which the
employee is entitled,” vesting relates to when an employee
has a right to the accrued benefit. Holt v. Winpisinger, 811
F.2d 1532, 1536 (D.C. Cir. 1987) (quoting Stewart v. Nat’l
Shopmen Pension Fund, 730 F.2d 1552, 1562 (D.C. Cir.
1984)) (internal quotation marks omitted). Benefit accrual and
vesting are not coextensive concepts, so an employee might
“earn credit toward vesting without accumulating any pension
benefits.” Id. at 1537. Because vesting is tied to length of
employment, this would happen if an employee works
without participating in the plan (“nonparticipating service”),
although the benefits do not actually vest until the employee
begins participating in the plan. ERISA generally requires
employers to count all of an employee’s years of service when
calculating vesting credit, including years completed before
the employee began participating in the plan. See 29 U.S.C.
§ 1053; Holt, 811 F.2d at 1536–37.
                                 4
     This appeal implicates both rules.1 In his complaint,
Kifafi alleged that the Plan’s benefit accrual formula was
impermissibly backloaded and that Hilton, the Plan sponsor
and administrator, violated both ERISA and the Plan by
failing to credit certain years of service when calculating
employees’ vesting credit.

     Unfortunately, the parties were not content to let the
district court decide (relatively) straightforward issues of law.
Instead, as the district court later put it, they “shifted their
burden to the Court to determine which facts are in dispute
between the parties” and they “repeatedly shifted their
arguments such that the Court has consistently been presented
with moving targets.” Kifafi v. Hilton Hotels Ret. Plan, 616 F.
Supp. 2d 7, 22 (D.D.C. 2009) (“Kifafi I”). This included
changing the facts of the case.

     Before Kifafi filed suit,2 the Plan calculated normal
retirement benefits as a function of participants’
compensation and years of service, less the participant’s
“integrated benefits,” that is, benefits payable to that
participant under another pension plan or government-
sponsored system to which Hilton contributed (including half
of the participant’s social security benefits). This calculation
guaranteed, at a minimum, 2% of the participant’s average
monthly compensation multiplied by the participant’s years of
service up to twenty-five years, plus 0.5% of the average

1
     Facts are set out at greater length in the district court’s
opinions. See, e.g., Kifafi v. Hilton Hotels Ret. Plan, 616 F. Supp.
2d 7 (D.D.C. 2009). We recite only those facts relevant to this
appeal.
2
     The Plan underwent a number of amendments before Kifafi
filed suit, but we do not differentiate among them because the last
amendment before Kifafi filed suit that is reflected in the record
applied retroactively.
                               5
monthly compensation for each year after twenty-five years,
minus the integrated benefits offset. The Plan also included
the following language in a separate article titled “Limitation
on Benefits and Payments”: “The method of computing a
Participant’s accrued benefit under the provisions of Article
IV is intended to satisfy the requirements of the 133-1/3 rule
provided in Section 411(b)(1)(B) of the [Internal Revenue]
Code.”

     After Kifafi moved for class certification (but before the
district court ruled on the motion), Hilton amended the Plan
(“1999 Plan”) to eliminate “any controversy regarding the
proriety [sic] of the rate of benefit accruals under the Plan.”
The 1999 Plan modified the benefit accrual formula using a
“greater of” approach: Plan participants would receive the
greater of the benefit determined under the old Plan or the
benefit determined under the 1999 Plan’s modified accrual
formula, which, as the IRS subsequently determined, satisfied
the fractional rule. The 1999 Plan also made two other
retroactive changes: first, it decreased the relevant percentage
of employees’ average monthly compensation during the first
twenty-five years of service from 2% to 1.33%; and second, it
increased the social security offset.

     The district court ultimately certified Kifafi’s proposed
“benefit-accrual class” for the backloading claim—all former
and current Hilton employees whose pension benefits “have
been, or will be, reduced” because of the backloading—but
not Kifafi’s proposed class for the vesting claim. Four years
later, after the parties completed discovery, Kifafi renewed his
motion to certify the vesting claim and sought to include as
class representatives three class members he hoped would
cure any deficiencies in the original class certification motion.
This time, the court granted the certification motion (though it
denied the motion to intervene), certifying for class treatment
                                  6
Kifafi’s claim that Hilton “failed to credit employees with
years of union service for vesting purposes.” The court
ultimately granted summary judgment to Kifafi on both
claims and, eventually, ordered Hilton (1) to amend the Plan’s
benefit accrual formula by capping the social security offset,
thereby bringing the Plan into retroactive compliance with the
133 1/3% rule, and (2) to administer a claim procedure for
crediting participants’ years of union service for vesting
purposes. Both parties appealed.

                                  II

    As an initial matter, Hilton claims the 1999 Plan mooted
Kifafi’s backloading claim, an argument this Court assesses
de novo. Del Monte Fresh Produce Co. v. United States, 570
F.3d 316, 321 (D.C. Cir. 2009).3 As most of the issues in this
case presuppose a live controversy over the backloading
claims, Hilton’s victory on this point would resolve those
other issues quite tidily. Unfortunately for Hilton, its
arguments do not persuade us. See Honeywell Int’l, Inc. v.
NRC, 628 F.3d 568, 576 (D.C. Cir. 2010) (explaining that the
party asserting mootness carries a “heavy burden”).

3
      By pegging mootness determinations to an abuse of discretion
standard, Kifafi oversimplifies the relationship between mootness
and equitable relief. Mootness and its various exceptions implicate
a court’s jurisdiction. Initiative & Referendum Inst. v. U.S. Postal
Serv., 685 F.3d 1066, 1074 (D.C. Cir. 2012). There is, however, a
doctrine of “prudential mootness” under which a court may dismiss
a case in equity despite concluding the case is not in fact moot. See,
e.g., Penthouse Int’l, Ltd. v. Meese, 939 F.2d 1011, 1019–20 (D.C.
Cir. 1991) (explaining that prudential mootness doctrine allows
courts to refrain from exercising equitable authority). Vesting the
district court with discretion to dismiss a case on grounds of
prudential mootness does not alter the standard of review for
determinations of constitutional mootness.
                                 7

     Mootness doctrine “limits federal courts to deciding
actual, ongoing controversies.” Am. Bar Ass’n v. FTC, 636
F.3d 641, 645 (D.C. Cir. 2011) (internal quotation marks
omitted). A case is moot when the court’s decision “will
neither presently affect the parties’ rights nor have a more-
than-speculative chance of affecting them in the future.” Id.
(internal quotation marks omitted). Accordingly, a court must
dismiss a properly-brought case if it is subsequently rendered
moot. Honeywell Int’l, 628 F.3d at 576. Hilton marshals three
arguments to show that happened here: the district court relied
on bad law, the 1999 Plan did not violate ERISA’s “anti-
cutback” provision, and the backloading was eliminated and
would not likely recur.

     There are problems with each argument, but at bottom,
the issue comes down to whether a party can deprive a court
of jurisdiction with a wave of its hand.4 It cannot, no matter
how contritely it apologizes for the conduct giving rise to the
litigation. “It is well settled that the voluntary cessation of
allegedly unlawful conduct does not moot a case in which the
legality of that conduct is challenged.” Christian Legal Soc’y
Chapter of the Univ. of California, Hastings Coll. of the Law
v. Martinez, 130 S. Ct. 2971, 3009 n.3 (2010) (Alito, J.,
dissenting). A defendant’s voluntary cessation of allegedly
unlawful conduct moots a case only if (1) “there is no
reasonable expectation . . . that the alleged violation will

4
     Hilton’s attempt to undermine the legal support for the district
court’s finding of non-mootness improperly shifts Hilton’s burden
of showing mootness onto the district court: knocking down an
argument disputing mootness does little to prove the case is moot.
And the 1999 Plan’s compliance with the anti-cutback provision
has only contingent relevance to the mootness analysis, a
completely separate inquiry: compliance with the anti-cutback
provision is not sufficient to moot a case.
                              8
recur,” and (2) “interim relief or events have completely and
irrevocably eradicated the effects of the alleged violation.”
Am. Bar Ass’n, 636 F.3d at 648 (quoting HARRY T. EDWARDS
& LINDA A. ELLIOTT, FEDERAL STANDARDS OF REVIEW—
REVIEW OF DISTRICT COURT DECISIONS AND AGENCY
ACTIONS 114–15 (2007)) (internal quotation marks omitted).

      Hilton’s argument that the backloading will not recur
boils down to its promise not to violate the anti-backloading
provision. See Hilton Br. at 50–51 (arguing it would be
“illogical,” “irrational,” and “absurd” to further violate the
anti-backloading provision because doing so would subject
Hilton to further litigation and might entail adverse tax
consequences). This is insufficient. See United States v.
Concentrated Phosphate Export Ass’n, 393 U.S. 199, 203
(1968) (finding insufficient “appellees’ own statement that it
would be uneconomical for them to engage in [the challenged
activity]”). And even were it sufficient, Hilton has given us
little reason to think its intentions are a good predictor of
reality. When amending the Plan in 1999, for instance, Hilton
flatly asserted its belief “that the Plan satisfied ERISA’s
benefit accrual requirements even without the amendment.”
See also Kifafi I, 616 F. Supp. 2d at 28 (noting that Hilton
“has insisted upon the legality of the challenged practices”).
As the district court concluded—and Hilton now concedes—
this assessment was wrong. Hilton may have made its
erroneous statements in good faith, but that does little to
reassure us that it is “absolutely clear” the backloading could
not reasonably be expected to recur. Friends of the Earth, Inc.
v. Laidlaw Envtl. Servs. (TOC), Inc., 528 U.S. 167, 189
(2000). This is a complicated area of law in which even the
best-intentioned actors may yet do wrong.

     Because Hilton cannot meet its burden of showing there
is no reasonable likelihood of future backloading, we need not
                               9
determine whether the 1999 Plan eradicated the effects of the
backloading. Hilton’s inability to show the first scuttles all
need for the second. See Cnty. of L.A. v. Davis, 440 U.S. 625,
631 (1979).

                              III

     The parties challenge the district court’s remedy and
class certification from a number of angles. We review the
district court’s class certification decisions and its remedial
decisions for abuse of discretion. See, e.g., Garcia v. Johanns,
444 F.3d 625, 631 (D.C. Cir. 2006); SEC v. Banner Fund
Int’l, 211 F.3d 602, 616 (D.C. Cir. 2000). To determine if the
district court applied the wrong legal standard or otherwise
“misapprehended the underlying substantive law,” Brayton v.
Office of the U.S. Trade Representative, 641 F.3d 521, 524
(D.C. Cir. 2011) (quoting Kickapoo Tribe of Indians of the
Kickapoo Reservation in Kan. v. Babbitt, 43 F.3d 1491, 1497
(D.C. Cir. 1995)) (internal quotation marks omitted), we
consider whether the court “failed to consider a relevant
factor” or “relied on an improper factor,” as well as whether
“the reasons given reasonably support the conclusion.” Peyton
v. DiMario, 287 F.3d 1121, 1126 (D.C. Cir. 2002).

                               A

    Hilton first challenges the district court’s general
remedial approach to the backloading claim. In granting
Kifafi summary judgment on the issue, the district court relied
on the pre-1999 Plan’s statement of intent and Hilton’s
representation of compliance with the 133 1/3% rule to the
court and the IRS. Stating that Hilton was “required to
comply with the accrual method it expressly selected,” the
court concluded that “the Plan’s participants are entitled to
receive the benefits they would have accrued had the Plan
                               10
complied with the 133 1/3% rule.” Kifafi I, 616 F. Supp. 2d at
24. It therefore directed the parties to discuss, “at a minimum,
the methodolog[y] that should be used to . . . provide
members of the ‘benefit-accrual class’ with the benefits they
would have accrued under the Plan’s initial benefit accrual
formula, amended only to bring it into compliance with the
133 1/3% rule.” Hilton now argues that requiring the Plan to
comply with the 133 1/3% rule in particular, rather than the
anti-backloading provision generally, was an abuse of
discretion. We disagree.

     Whether a plan satisfies the anti-backloading provision—
and which anti-backloading rule it satisfies—turns on the
nature of the plan. In other words, the terms of the plan will or
will not be amenable to analysis under any given rule as a
matter of fact. See, e.g., Tomlinson v. El Paso Corp., 653 F.3d
1281, 1290 (10th Cir. 2011) (noting party concession the plan
“must qualify under the ‘133 1/3 percent’ test if it qualifies at
all”); Hurlic v. S. Cal. Gas Co., 539 F.3d 1024, 1033 n.4 (9th
Cir. 2008) (disclaiming need to consider plan’s ability to
satisfy fractional or 3% rules because plan satisfies the
133 1/3% rule); Carollo v. Cement & Concrete Workers Dist.
Council Pension Plan, 964 F. Supp. 677, 681 (E.D.N.Y.
1997) (noting party agreement that “the 133 1/3% Rule is the
only standard the Plan is capable of satisfying”). A plan must
be measured not against the anti-backloading rule it says it is
following, but against ERISA’s general provision for plans to
satisfy any one of the three anti-backloading rules. As Hilton
points out, it would be absurd to find a plan that in fact
satisfies one of the anti-backloading rules to be backloaded
because it “intends” to comply with a different rule.

     Such is not the case here because the Plan did not satisfy
any of the anti-backloading rules, but that does not change the
fact that the Plan’s statement of intent is irrelevant to the
                              11
backloading analysis. The 133 1/3% rule delimits only a
range of possibility; to comply, plans must still set out the
benefit accrual rate. See 29 U.S.C. § 1102(b)(4); Kennedy v.
Plan Adm’r for DuPont Sav. & Inv. Plan, 555 U.S. 285, 300
(2009); Curtiss-Wright Corp. v. Schoonejongen, 514 U.S. 73,
83 (1995). And once a plan sets out an accrual rate, the rate is
directly testable against the various anti-backloading rules.
Kifafi’s claim that statements of intent are “clearly”
enforceable terms therefore overstates the analogy between
ERISA plans and contracts where intent is relevant either
under the substantive law or to clarify ambiguity. See, e.g., In
re Palmdale Hills Prop., LLC, 457 B.R. 29, 44–45 (B.A.P.
9th Cir. 2011) (invoking language of intent in order to
determine parties’ intent). Certainly, no one has claimed the
accrual formula is ambiguous.

     But this does not mean the district court abused its
discretion. Once the court determined the Plan violated
ERISA, it entered the world of equity. See 29 U.S.C.
§ 1132(a)(3); CIGNA Corp. v. Amara, 131 S. Ct. 1866, 1875,
1879–80 (2011) (concluding that 29 U.S.C. § 1132(a)(3)
authorized district court’s reformation of plan and injunction
requiring the plan to pay corresponding benefits). And
Hilton’s premise that a plan’s prospective compliance with
ERISA’s anti-backloading mandate circumscribes a court’s
remedial options in the face of past violations cannot be
sustained. We see no reason why the court’s remedy need be a
perfect reflection of the legal violations supporting the
remedy; the district court exercised a discretion informed by
much more than just the ERISA violation. See Cobell v.
Salazar, 573 F.3d 808, 813 (D.C. Cir. 2009); Sheaffer v.
Warehouse Emps. Union, Local No. 730, 408 F.2d 204, 206–
                                12
07 (D.C. Cir. 1969). Hilton misses this distinction.5 No doubt
a plan may alter its accrual formula to comply with a different
anti-backloading rule than the one it had hitherto complied
with (assuming it does not violate ERISA in other ways); the
IRS accordingly concluded the 1999 Plan satisfied the
fractional rule, even though the pre-1999 Plan had failed to
satisfy any of the anti-backloading rules. But the standard for
prospective compliance does not ipso facto establish the
adequacy of a retroactive amendment or court-imposed relief.
To reduce the district court’s remedy to nothing more than a
demand that Hilton comply with any of the anti-backloading
rules would—like evaluating a movie by analyzing a single
frame—ignore too much.

     First, the parties did not make things easy for the district
court. After Kifafi filed suit, for example, Hilton amended the
Plan into compliance with the anti-backloading provision,
simultaneously making two changes to the benefit accrual
formula unfavorable to Plan participants, and over the next
few years, Hilton amended the Plan additional times in
response to Kifafi’s various legal claims. This, in addition to
freezing the Plan’s benefit accruals in 1996, which Kifafi’s
actuarial expert explained had a material impact on the Plan’s
ability to comply with the various anti-backloading rules. The
court expressed its frustration when, in its summary judgment
opinion, it referred to the parties’ arguments as “moving

5
     For this reason, Hilton’s reliance on Lonecke and Revenue
Ruling 2008-7 is misplaced. Neither says anything about retroactive
amendments; they purport to deal only with prospective
compliance. See, e.g., Lonecke, 584 F.3d at 465, 469 (upholding
plan granting participants sufficient additional benefits to comply
with the fractional rule “upon the termination of the period of
employment” if the rate of benefits accrual failed the 133 1/3%
rule, and explaining that the fractional rule explicitly ties the
accrued benefit to the employee’s separation from employment).
                              13
targets.” Kifafi I, 616 F. Supp. 2d at 22. In short, more than a
decade passed after Kifafi filed suit before the district court
granted summary judgment, what the court referred to as “an
extraordinary amount of judicial time.”

     Second, Hilton represented its compliance with the
133 1/3% rule to Kifafi, the IRS, and the district court. We do
not, as Hilton charges, think this constitutes the predicate for
estoppel. Rather, this suggests the Plan was more amenable to
analysis under the 133 1/3% rule than under the fractional or
3% rules. See, e.g., Carrabba v. Randalls Food Mkts., Inc.,
145 F. Supp. 2d 763, 773 (N.D. Tex. 2000) (requiring plan
without accrual rate to satisfy 133 1/3% rule, which, the court
concluded, “most appropriately recognizes the objectives of
the [plan] in an ERISA context,” based on the actual
progression of benefits), aff’d, 252 F.3d 721 (5th Cir. 2001)
(per curiam) (calling the district court opinion “conscientious”
and “well-reasoned”). Indeed, as Kifafi’s actuarial expert
attested in an affidavit, “The progression of the Plan’s
existing accrual rates lends itself to compliance with [the
133 1/3%] rule.”

     Read in this context, we understand the district court’s
remedial order to be an attempt to pin Hilton down, denying it
the opportunity to avoid the consequences of its ERISA
violations. The district court certainly used language
suggesting it thought that as a matter of law Hilton could not
comply with any anti-backloading rule other than the
133 1/3% rule. But like the court’s reliance on the statement
of intent, most such statements occurred in the context of the
court’s conclusion that the original Plan was backloaded
under any of the anti-backloading rules. The court also stated,
in the context of rejecting Hilton’s mootness argument, that
Plan participants are entitled to what they would have
received had the Plan complied with the 133 1/3% rule. But it
                               14
continued: “If this were not so, Hilton and all other employers
that have unlawfully backloaded benefit accruals could
simply ‘amend away’ their ERISA violations.” Kifafi I, 616 F.
Supp. 2d at 25. And as it emphasized in a later proceeding,
the 1999 Plan’s compliance with the fractional rule came at
the expense of “substantial modifications to the benefits that
would be paid to participants.” Kifafi v. Hilton Hotels Ret.
Plan, 736 F. Supp. 2d 64, 73 (D.D.C. 2010) (“Kifafi II”). This
was enough to support its remedy. See, e.g., Shahriar v. Smith
& Wollensky Rest. Grp., Inc., 659 F.3d 234, 251–52 (2d Cir.
2011); In re Grand Jury Investigation, 545 F.3d 21, 26 (1st
Cir. 2008). Just as an employer would not remedy its failure
to pay overtime by “retroactively revising the base rate of pay
down from $10 per hour to $6.50 per hour and offering to
multiply the reduced rate by the required ‘time and one-half,’”
Kifafi Br. at 36, the district court did not abuse its discretion
by requiring Hilton to provide a remedy it considered
meaningful. See, e.g., Hecht Co. v. Bowles, 321 U.S. 321, 329
(1944) (tying the injunctive process to deterrence); H.R. REP.
101-386, at 433 (1989) (Conf. Rep.), reprinted in 1989
U.S.C.C.A.N. 3018, 3036 (stating congressional intent that
courts fashion remedies for ERISA violations “that not only
protect participants and beneficiaries but deter violations of
the law as well”).

                               B

     Hilton next invokes the statute of limitations to argue the
district court should have dismissed the claims of Plan
participants who received benefits more than three years
before Kifafi filed this suit. Although ERISA is not entirely
silent with respect to statutes of limitations, see, e.g., 29
U.S.C. § 1113, there is no applicable limitations period for the
type of claims Kifafi brought. See Kifafi I, 616 F. Supp. 2d at
35 (noting Kifafi brought his class claims under 29 U.S.C.
                                   15
§ 1132). We accordingly apply “the most closely analogous
statute of limitations from the state in which the court sits.”
Connors v. Hallmark & Son Coal Co., 935 F.2d 336, 341
(D.C. Cir. 1991). Fortunately, the parties agree on the
appropriate limitations period (three years), as well as the
appropriate standard for determining when the limitations
period begins (the discovery rule). They disagree, however,
about whether the district court properly applied these
principles. We think it did.6

     Statutes of limitations ordinarily begin running when “the
factual and legal prerequisites for filing suit are in place.”
Norwest Bank Minn. Nat’l Ass’n v. FDIC, 312 F.3d 447, 451
(D.C. Cir. 2002). It will not always be obvious when this
happens. In such cases, and absent a contrary congressional
directive, this Court applies the discovery rule, which
provides that the statute of limitations begins when the
plaintiff “discovers, or with due diligence should have
discovered,” the injury supporting the legal claim. Connors,
935 F.2d at 341, 343.

     Hilton’s sole argument is that its payment of backloaded
benefits to Plan participants amounted to a repudiation of the
participants’ right to additional benefits, the implication being

6
      It is irrelevant whether we review Hilton’s statute of
limitations argument de novo or for abuse of discretion: Hilton
loses either way. Ordinarily, a district court’s application of a
statute of limitations demands de novo review. See Jung v. Mundy,
Holt & Mance, P.C., 372 F.3d 429, 432 (D.C. Cir. 2004). Here,
though, the statute of limitations issue might be conceived as a
piece of the district court’s class certification decision, see Kifafi I,
616 F. Supp. 2d at 37 (“[T]he Court finds that modification of the
class definitions to exclude claims based on the statute of
limitations is unnecessary and inappropriate.”), a decision entrusted
to its discretion.
                               16
that the participants should have discovered from these
payments that their benefits were backloaded. Courts have
indeed held that repudiation can trigger ERISA’s statute of
limitations if it is clear and made known to the plan
beneficiary. See, e.g., Thompson v. Ret. Plan for Emps. of S.C.
Johnson & Son, Inc., 651 F.3d 600, 604 (7th Cir. 2011);
Miller v. Fortis Benefits Ins. Co., 475 F.3d 516, 520–21 (3d
Cir. 2007); Davenport v. Harry N. Abrams, Inc., 249 F.3d
130, 134–35 (2d Cir. 2001); Union Pac. R. Co. v. Beckham,
138 F.3d 325, 330 (8th Cir. 1998); see also Connors, 935
F.2d at 342 (noting consistency of discovery rule and “time of
injury” rule). But the requirement that the repudiation be clear
and made known to the plan beneficiaries is not an idle one.
Whether repudiation may trigger the limitations period
depends on what the prospective plaintiff should have
understood from the miscalculated benefit payments. Where
the miscalculated benefits comprise a single lump-sum
payment, it might make sense to hold plan participants
responsible for their failure to notice the miscalculation,
although we do not decide the issue. See Thompson, 651 F.3d
at 606 (holding that receipt of lump-sum distribution served
as an “unequivocal repudiation of any entitlement to benefits
beyond the account balance” because it was clear that “no
additional benefits would be forthcoming”). The same might
be true for miscalculated periodic payments. See Miller, 475
F.3d at 521–22 (explaining that beneficiaries ordinarily
should know if a benefit award is improperly low). But if so,
the miscalculation must still be such that the beneficiary
should recognize it. See id. at 523 (“[T]he need for Miller to
be vigilant was triggered only when his receipt of benefits
alerted him that his award had been miscalculated.”). Miller
involved “a simple calculation of sixty percent of [the
beneficiary’s] salary,” id. at 522, and if one thing in this case
is clear, it is that Hilton’s miscalculation was anything but
simple. To catch the backloading, Plan participants would
                               17
have needed to apply complex law to complex facts. If Hilton
itself admits the Plan “did not appear to be backloaded,” it
makes no sense to ask the participants to navigate the
complexity of ERISA’s anti-backloading provision
immediately upon receipt of their first benefits payment. They
are the parties least likely “to have a clear understanding of
the terms of the pension plan and their application to [the]
case.” Novella v. Westchester Cnty., 661 F.3d 128, 146 (2d
Cir. 2011).

                               C

     Having failed to circumscribe the scope of the district
court’s remedy by excluding participants who received
benefits more than three years before Kifafi filed suit, Hilton
tries to contain the remedial fallout by challenging the district
court’s determination that the Plan’s retroactive compliance
with the 133 1/3% rule should apply to participants who
separated from service before the controversial statement of
intent was added to the Plan in 1994 (with retroactive effect).
This argument also fails. The district court determined that the
Plan had never complied with the anti-backloading provision
and that the benefits accrual formula did not substantially
change in 1994, findings Hilton does not challenge. If the
Plan violated the anti-backloading provision after 1994, and it
violated the anti-backloading provision essentially the same
way before 1994, then we see no reason to distinguish
between pre- and post-1994 separation dates, particularly
given our conclusion that the statement of intent is irrelevant
to the backloading violation.

                               D

    Kifafi, in turn, argues the district court improperly
accepted Hilton’s theory that participants can “outgrow” the
                               18
backloading merely by participating in the Plan for a
sufficiently long period of time. As Kifafi puts it,

    if a plan offers a $5 per month per year of
    participation rate of accrual for years 1-7, and a $10
    per month rate of accrual in years 8-25, the 133%
    rule is violated in years 1-7, no matter how much
    longer the participant works, e.g., whether the
    participant works one more year or 18 more years. A
    participant who works for 25 years, and has 18 years
    at the $10 rate, does not ‘grow out’ of the
    backloading violation because his or her accruals for
    years 1-7 continue to be only $5 per month per year
    of participation.

Kifafi Br. at 56–57. According to Kifafi, the district court
should have increased the early-year accrual rates without
touching the later-year accrual rates. Translated into his
hypothetical plan, this would mean offering a $7.50 rate of
accrual for the first seven years while leaving everything else
about the plan unchanged. We disagree.

     Backloading is nothing more than the improper allocation
of benefit accrual rates; the concept does not necessarily say
anything about the amount of benefits participants ultimately
accrue. Fixing a backloaded plan might entail increased
benefits, but it need not. A participant in Kifafi’s hypothetical
plan, for instance, accrues $2,580 after twenty-five years of
service. Amending the plan to comply with the 133 1/3% rule
by offering $7.50 each month for the first seven years, as
Kifafi suggests, would yield participants an additional $210
after twenty-five years of service. But the plan could satisfy
the 133 1/3% rule while still yielding only $2,580; this would
happen if, say, the plan offered $8 per month rate of accrual in
the first seven years and (approximately) $8.83 in the next
                                19
eighteen, or if it offered $8.60 every month for all twenty-five
years. The district court did not abuse its discretion when it
chose which of these counterfactual accrual formulas the
backloading remedy should track.7 As Revenue Ruling 2008-
7, 2008-7 I.R.B. 419, explains, if a plan becomes backloaded
because of a decreased interest crediting rate, the plan could
be amended into compliance with ERISA by increasing “the
hypothetical pay credits at the earlier ages,” reducing the
credits at the higher ages, or a combination of both.

     According to Kifafi, IRS regulations prohibit the district
court’s “average rate of accrual” methodology. See Treas.
Reg. § 1.411(b)-1(b)(2)(iii) (Example 3) (explaining that a
plan under which a participant accrues benefits at the rate of
2% for each of the first five years, 1% for each of the next
five years, and 1.5% for every year thereafter violates the
133 1/3% rule because 1.5% is more than 133 1/3% of 1%).
This is beside the point. The regulations purport to address
base compliance with the anti-backloading provision; we now
deal only with the remedy for an undisputedly backloaded
formula. Though there may be situations where the proper
remedy for backloading involves additional benefits, this is
not one of them. See Kifafi II, 736 F. Supp. 2d at 72 (finding
that over time, some participants in fact recovered from any
benefits deficiency they may have initially suffered). Given
that the benefit-accrual class is limited to “employees whose
benefits ‘have been, or will be, reduced’” because of the
backloading, id., and that the Plan could have yielded the

7
     Kifafi implicitly concedes this when, in his reply brief, he
notes—in contrast to his initial claim that a participant in the
hypothetical plan does not outgrow the backloading violation by
working for the full twenty-five years—that the effects of
backloading are eliminated “if a participant has worked long
enough . . . to earn the Plan’s full ‘normal retirement benefit’ as
described in ERISA § 204(b)(1)(B).”
                                 20
same amount of total benefits to participants while complying
with the anti-backloading provision, the district court’s refusal
to apply its remedy to employees whose benefits were not
reduced by the backloading—to penalize Hilton for the fact of
the backloading—is far from an abuse of discretion. See
Mertens v. Hewitt Assocs., 508 U.S. 248, 257 n.7 (1993)
(noting that punitive damages were not a “major issue” when
ERISA was enacted). Equitable relief—the only kind of relief
at issue here—may very well mean “something less than all
relief.” Id. at 258 n.8.

                                 E

     Finally, Kifafi challenges the district court’s approach to
his union service vesting claim. The court found that Hilton
violated the Plan’s vesting provisions by failing to credit
employees’ years of union service, and it molded its remedial
relief around the contours of that finding. Kifafi complains
this contravenes both ERISA and the Plan itself. His argument
goes like this: because both ERISA and the Plan require
crediting all nonparticipating service and, under the Plan,
union membership is not the only type of nonparticipating
service,8 the district court erred by addressing Hilton’s failure
to count years of union service but not its failure to count
years of nonunion nonparticipating service, either in its class
certification decision or its remedial order. This is an
impractical approach, he continues, because Hilton failed to

8
     We again ignore the chronology of the various Plan
amendments. Kifafi’s complaint alleged failure to count his 1985
union service, and the district court responded by broadly finding
that “Hilton failed to properly credit union service for vesting
purposes.” Hilton likewise discusses the Plan’s vesting provisions
in present tense. Since no one has differentiated among the different
Plan amendments’ treatment of the issue in a meaningful way, we
will not be the first to do so.
                              21
maintain any records about employees’ union service, so
participants end up bearing the burden of proving uncredited
union service years after the fact when the district court could
have avoided this by broadening its perspective to encompass
Hilton’s general failure to count nonparticipating service.

     We reject Kifafi’s arguments. The district court’s
approach to Kifafi’s vesting claim is not just a matter of law;
it reflects the parties’ respective actions throughout the
litigation and effected the court’s determination about how
best to manage the shape-shifter shackled to the parties’
dispute. In this light, we see no abuse of discretion.

     To start, the court could reasonably have concluded that
Kifafi was best able to represent a class limited to union
participation. As Kifafi’s original complaint made evident, his
claim to representative status on the nonparticipating service
issue derived from his “service as a union employee prior to
1985.” The complaint thus listed as one of the two legal
questions “common to the members of the class and subclass”
whether Hilton may “fail to credit years in unionized
employment with Hilton,” and it mentioned only union
service in the relevant complaint count. Kifafi subsequently
amended the complaint, expanding the scope of the proposed
class to include Hilton employees who “have not been
credited with all years of service with Hilton, including years
in unionized employment,” but he continued to suggest that
his claim remained tied to union service. For example, when
describing the nature of the case at the beginning of the
complaint, he alleged that Hilton “violated ERISA by not
crediting his years of union service,” and in his claim for
relief, he alleged only that Hilton “violated the Retirement
Plan by not counting years of service in union employment.”
                               22
In his renewed motion to certify the class,9 Kifafi asserted that
“the common legal thread that binds the class is Hilton’s
failure to count all years of service,” but he did little else to
advance that broader argument. Though referring generally to
nonparticipating service and citing Hilton’s admission that it
failed also to credit certain nonparticipating service other than
union service, the motion otherwise focused on union service,
tying general nonparticipating-service references to union
service. Indeed, the motion’s list of “individuals whose union
or other non-participating service was not counted for
vesting” included only three individuals, each listed for his or
her uncredited years of union service; and the three class
members Kifafi sought to include as class representatives
likewise asserted that their uncredited years consisted of
union service. Even if it would have been reasonable to
certify a broader nonparticipating service class, the district
court’s actual certification decision was no less reasonable.
The same is true of its later refusals to expand the certified
subclass. See, e.g., Kifafi I, 616 F. Supp. 2d at 30 n.18; Kifafi
II, 736 F. Supp. 2d at 74.

     Kifafi cites two cases where a court of appeals found an
abuse of discretion in the district court’s class certification.
Abrams v. Communications Workers of America, 59 F.3d
1373 (D.C. Cir. 1995), involved a challenge to the adequacy
of a union’s notice of the non-union members’ right to object
to paying dues. We reversed the district court’s refusal to
certify a class of all nonmember employees—including both
employees who had objected and employees who merely
might object—explaining that every employee had an interest

9
     We conflate two versions of Kifafi’s renewed motion because
our discussion, like its object, traverses a period of time. In
actuality, the district court denied Kifafi’s first renewed motion
without prejudice, asking Kifafi to rebrief the issue.
                               23
in adequate notice because “the union must provide notice in
advance of an employee’s decision to object.” Id. at 1378.
And in Green v. Ferrell, 664 F.2d 1292 (5th Cir. 1982), the
Fifth Circuit required the district court to broaden the class of
convicted prisoners to include pretrial detainees because
“those rights and the conditions of confinement that impact
upon those two groups at the same county jail facility are
sufficiently    common       to     warrant    contemporaneous
consideration in a single judicial proceeding under the
circumstances present here.” Id. at 1295. Yet in both cases,
the excluded group of proposed class members necessarily
belonged to the included group: a challenge to notice
procedures affects anyone who ought to receive that notice; a
challenge to jail conditions affects anyone who is or will be
held in that jail. Here, by contrast, Hilton’s alleged failure to
count nonunion nonparticipating service potentially affects
individuals other than those affected by its failure to count
union service. That Hilton apparently treated union service as
a mere subset of nonparticipating service, ignoring both
entirely, does not mean it could not have counted one but not
the other. The extent to which Hilton treated the two groups
of employees the same is a question of fact, as is whether
Hilton’s alleged blanket policy affected any employees for
reasons unrelated to union service. And where changed jail
conditions or notice procedures necessarily provide relief for
all potential class members regardless of their identities, this
case involves detailed actuarial determinations and
individualized remedies.

     Rather than agreeing with Kifafi’s argument, then, we
commend the district court for its exemplary work on this
case. The court managed and reasonably disposed of this
litigation—juggling a voluminous record and ably balancing
competing considerations—despite shouldering much of the
burden that should have been carried by counsel, and despite
                               24
facing arguments it characterized as “moving targets.” Along
the way, the district court fashioned a remedy that hewed
closely to its class certification decision—and that makes
sense. Indeed, the court had promised as much when it stated
at the summary judgment phase that “[i]n resolving the
parties’ claims, the Court shall not allow Kifafi to expand his
Amended Complaint.” Kifafi I, 616 F. Supp. 2d at 23. Once it
limited the scope of the dispute, the district court could quite
reasonably restrict relief to those parameters. See Aviation
Consumer Action Project v. Washburn, 535 F.2d 101, 108
(D.C. Cir. 1976).

     For similar reasons, we reject Kifafi’s assertion that the
claim procedure ordered by the district court was “completely
unnecessary” and improperly shifts the burden onto the
plaintiff class. The district court considered using
nonparticipating service as a proxy for union service because
Hilton’s records were incomplete, but it rejected the idea in
order to prevent Kifafi from using the procedure to evade the
court’s class certification decision. The court instead required
Hilton to fund and administer a claim procedure open to all
participants whose vesting status turns on nonparticipating
service. As part of this, the district court not only required
Hilton to provide Kifafi information submitted by claimants
so Kifafi can challenge Hilton’s claim-process decisions, but
it expressly permitted Hilton to credit all nonparticipating
service if it wants to avoid the administrative costs incident to
its mandated record searches and the claim procedure. This
seems both fair and reasonable. While it is unfortunate for the
burden to fall on innocent parties rather than the employer
who failed to perform its statutory duties, that is not enough to
turn the district court’s otherwise-competent performance into
an abuse of discretion.
                           25
                           IV

For the reasons stated, the district court’s orders are

                                                   Affirmed.
