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       United States Court of Appeals
                  FOR THE DISTRICT OF COLUMBIA CIRCUIT




Argued December 4, 2003                   Decided February 10, 2004


                               No. 03-7012

      MARIA V. CRUZ, FOR HERSELF AND AS REPRESENTATIVE OF
      GUSTAVO CRUZ AND JOAQUIN RODRIGUEZ MINORS, ET AL.,
                          APPELLANTS

                                     v.

                       AMERICAN AIRLINES, INC.,
                             APPELLEE



          Appeal from the United States District Court
                  for the District of Columbia
                         (No. 96cv02817)



  Leonard N. Bebchick argued the cause and filed the briefs
for appellants.
  Wayne A. Schrader argued the cause for appellee. With
him on the brief was Paul DeCamp.

 Bills of costs must be filed within 14 days after entry of judgment.
The court looks with disfavor upon motions to file bills of costs out
of time.
                                2

     Before: EDWARDS, SENTELLE and TATEL, Circuit Judges.
     Opinion for the Court filed by Circuit Judge SENTELLE.
  SENTELLE, Circuit Judge: Several American Airlines, Inc.
passengers claim that they and others similarly situated lost
their luggage on international American flights. The passen-
gers sued American in federal court seeking damages for
their lost or damaged luggage and various forms of injunctive
and declaratory relief. They sued under the Warsaw Con-
vention, a treaty that governs claims for property damage
arising out of international transportation of people and prop-
erty.1 The individual plaintiffs also moved to certify their
suit as a class action on behalf of two categories of passen-
gers. The district court granted American partial summary
judgment and declined to certify the class. Plaintiffs now
appeal both of those rulings. Because they have shown no
reversible error, we affirm the judgment of the district court.

                         I.   Background

A.     The Cruzes and their luggage
   This case arises from some bad luck the Cruz family
purportedly had with their luggage. (We glean the statement
of facts that follows from the parties’ statements of material
undisputed facts, unless otherwise indicated. See D.D.C.
Local Civ. R. 56.1.) In 1995, five members of the Cruz family
flew on an American Airlines flight from Washington D.C.,
Reagan National Airport to Santo Domingo, the Dominican
Republic, checking two bags each. When they arrived in
Santo Domingo, the Cruzes reported to American that five of
their bags were missing.
  The Cruzes subsequently filed a statement of property loss
with American, claiming that the bags were worth $15,000.
American, however, offered the Cruzes no compensation.
American refused to offer compensation because, according to
  1 Convention for the Unification of Certain Rules Relating to
International Transportation by Air, Oct. 12, 1929, 49 Stat. 3000,
T.S. No. 876, note following 49 U.S.C. § 40105 (2000).
                               3

American’s records, the Cruzes had filed their claims signifi-
cantly more than 30 days after their loss. American’s policy
at the time was not to settle lost-baggage claims voluntarily if
the claimant submitted a lost-property form more than 30
days after the date of loss, though there were (unspecified)
exceptions to this internal policy (we refer to this policy as
the ‘‘30–day rule’’).
  The Cruzes’ luggage travails did not end there. In 1997,
Beato Cruz, who had been on the previous American flight,
again flew on an American flight, this time from the Domini-
can Republic to New York City. When he arrived in New
York, according to Cruz’s deposition testimony, his bag was
badly damaged and was missing its contents.
   The next day, Cruz filed a statement of lost property with
American, declaring that the value of his bag was $3,890.
That same day American gave Cruz a $100 travel voucher.
When he received the form, Cruz signed his name next to the
following statement:
      CUSTOMER RECEIPT AND RELEASE: THE
      ABOVE SUM RECEIVED FROM AMERICAN AIR-
      LINES IS IN FULL SATISFACTION OF ALL
      CLAIMS, LIABILITIES AND DEMANDS THAT I
      MAY HAVE AGAINST SAID COMPANY.
   Several months later, American issued Cruz a check for
$634.90 as compensation for his damaged luggage. The check
came with a letter stating that this figure was the maximum
amount of compensation American was legally obligated to
provide under the terms of its international tariff governing
baggage loss and under the Warsaw Convention. Article 18
of the Warsaw Convention generally provides passengers a
cause of action for damages against international carriers for
lost or damaged checked bags. Under Article 22(2), that
liability is limited to $9.07 per pound of lost or damaged
baggage. American’s international tariffs – which govern the
rates for its international flights and which under federal law
it must file with the Department of Transportation, see 49
U.S.C. § 41504 (2000) – specify a default ‘‘deemed weight’’ for
Caribbean passengers’ lost bags. This deemed weight, under
                                4

the tariffs, is used to calculate American’s liability under the
Warsaw Convention. The tariffs, specifically, provide that
the baggage weight of a Caribbean passenger with a single
bag is assumed to be 100 pounds – the bag’s maximum
allowable weight – unless the passenger’s ticket states the
actual weight.
   American calculated the $634.90 it offered Cruz based on a
flawed understanding of the deemed weight of Cruz’s bag.
American computed that figure by multiplying $9.07 by 70
pounds, which it stated was the maximum allowable weight of
Cruz’s bag under its tariffs. The true maximum weight of
Cruz’s bag under the tariffs was 100 pounds. Therefore, the
calculation underestimated the per-bag limit applicable to
Cruz’s lost bag by at least $272.10 ($907 minus $634.90).
   Cruz cashed the $634.90 check. The back of the check had
a legend of release on it, which stated that:
     By endorsement or deposit of this check I (we) hereby
     release American Airlines, Inc., its agents, including oth-
     er airlines providing transportation, its employee’s [sic]
     and representatives from all claims rising in connection
     with the loss, damage or delay of my belongings trans-
     ported or authorized to have been transported on the
     travel date indicated on the remittance advise.
Cruz signed his name next to this statement when he en-
dorsed the check. At that point, Cruz had already retained
his current attorney and was a party to this lawsuit against
American, which at the time only involved the Cruz family’s
1995 trip. Cruz also testified at his deposition that, when he
cashed the check, he believed he could sue American for ‘‘the
additional amount [he] believed [he] was owed,’’ which, ac-
cording to positions he later took, was the bag’s fair value.
Again, Cruz’s position at the time was that the fair value of
his bag was $3,890.

B.   The first phase of litigation
  On December 20, 1996, five Cruz family members, including
Beato Cruz, sued American in federal district court to recover
                               5

the value of their bags. Relying on the Warsaw Convention,
they sought damages equal to the fair value of the contents of
their lost and damaged luggage. They also alleged that
American unlawfully required them to complete a lost-
property form and illegally applied the 30–day rule to them.
The Cruzes accordingly sought both a declaration that these
procedures were illegal and an injunction preventing Ameri-
can from applying the procedures to future passengers.
  The district court dismissed plaintiffs’ declaratory and in-
junctive claims for lack of Article III standing. The court
reasoned that as American admitted, it had incorrectly re-
quired the Cruzes to fill out a claim form, mistakenly applied
the 30–day rule to the Cruzes’ claims, and agreed to process
the Cruzes’ claims as timely filed, the Cruzes personally stood
to gain little from the requested declaratory and injunctive
relief. Moreover, reasoned the court, the possibility that
American would in similar circumstances again misapply
those procedures to the Cruzes was highly improbable. The
district court concluded, therefore, that the Cruzes had no
standing to raise the declaratory and injunctive claims.
  American also moved for partial summary judgment on the
Cruzes’ damages claims to the extent the Cruzes sought
damages in excess of the Warsaw Convention’s $9.07 per-
pound liability limit. American, however, conceded that it
was liable to the Cruzes to the extent of $9.07 per pound of
their lost bags. Consequently, American also moved for
entry of final judgment in the Cruzes’ favor to the extent of
$9.07 times the poundage of the Cruzes’ bags.
   The district court granted both of American’s motions,
holding that American’s liability to the Cruzes under the
Warsaw Convention was limited to $9.07 per pound of lost
luggage. The Cruzes had argued that the Warsaw Conven-
tion’s liability limit did not apply because American had failed
to state the weight of each suitcase on the Cruzes’ baggage
stubs, as required by Article 4(3)(f) of the Convention. The
district court rejected this argument. Because American
conceded liability to the Cruzes and moved for partial judg-
                               6

ment in the Cruzes’ favor, the district court entered a judg-
ment in the Cruzes’ favor to the extent of $9.07 times the
poundage of their bags.
   While American’s summary-judgment motions were pend-
ing, the Cruzes moved to amend their complaint. Their
motion sought to transform their individual claims into class-
action claims on behalf of others who had lost their luggage in
similar circumstances. That motion was pending when the
district court ruled on American’s summary-judgment mo-
tions. After its ruling, the district court dismissed the
Cruzes’ motion to amend as moot.
   The Cruzes successfully appealed the district court’s judg-
ment to this Court. On appeal, the Cruzes attacked, among
other things, the district court’s ruling regarding the Warsaw
Convention’s liability limit. In particular, they argued that
the liability limit did not apply to the Cruzes’ damages claims,
because American had failed to record the baggage weight of
each suitcase on the Cruzes’ baggage stubs. We accepted
that argument and accordingly vacated and remanded the
district court’s judgment. Cruz v. Am. Airlines, Inc., 193
F.3d 526, 528–30 (D.C. Cir. 1999). Cruz did not, however,
address whether the district court’s standing rulings were
correct. Nor did Cruz address whether the district court
correctly dismissed as moot the Cruzes’ motion to amend
their complaint. Cruz merely reinstated the Cruzes’ action to
its prior, pre-summary judgment status and thus revived the
Cruzes’ motion to amend their complaint to a class action.
Id. at 528 n.2.
C.   The second phase of litigation
  After remand, the Cruzes, in April 2000, filed an amended
complaint asserting two class-action claims. The complaint
described the ‘‘Claim I’’ class as
     consist[ing] of all persons who during the period begin-
     ning two years prior to initiation of this suit, December
     20, 1994, and ending on the date of Final Judgment
     herein (the ‘‘Claim I class period’’) (a) checked their
     baggage for transport for an international air journey to
                               7

    or from the United States in whole or part performed by
    American, (b) sustained the loss of or damage to their
    checked baggage in circumstances where American is
    made liable for such loss/damage under Warsaw Article
    30(3), (c) gave timely notice of such loss/damage consis-
    tent with Warsaw Article 26 or applicable carrier tariff
    rules, (d) made claim for the fair value of such loss/dam-
    age, and (e) suffered the non-processing or rejection of
    their claim because of their alleged failure to comply with
    the requirements of defendant’s 30–day Rule.
Claim I sought, inter alia, a declaration that American’s
‘‘application of its 30–day rule to checked baggage claims’’
was unlawful and an injunction preventing American from
applying the 30–day rule to the claims of future passengers,
and noting damages.
  The complaint defined the ‘‘Claim II class’’ as
    consist[ing] of all persons all persons [sic] who during the
    period beginning two years prior to initiation of this suit,
    December 20, 1994, and ending on March 3, 1999 (the
    ‘‘Claim II class period’’) (a) checked their baggage for
    transport for an international air journey to or from the
    United States in whole or part performed by American
    and without the weight of that baggage having been
    recorded on the passenger’s combined passenger ticket
    and baggage check, (b) sustained the loss of or damage
    to their checked baggage in circumstances where Ameri-
    can is made liable for such loss/damage under Warsaw
    Article 30(3), (c) gave timely notice of such loss/damage
    consistent with Warsaw Article 26 or applicable carrier
    tariff rules, (d) made claim for the fair value of such
    loss/damage, and (e) thereafter received from American
    for such claim a payment of compensation less than the
    claimed fair value of such loss/damage, being an amount
    (usually $634.90 but sometimes $907) which American
    asserted was the limit of its liability for such baggage
    loss/damage under Warsaw’s Article 22(2) liability limit
    and its tariff rules.
                               8

Claim II asked the district court to award this class compen-
satory damages equal to the fair value of their lost or
damaged bags. Claim II also alleged that American had
typically (as it did with Beato Cruz) settled the Claim II class
members’ damages claims for $634.90 per bag, based on
American’s representation that this figure was the limit of its
liability under the Warsaw Convention. As discussed, those
settlement offers (70 pounds times $9.07) erroneously as-
sumed that, for a single bag, the maximum weight provided in
American’s tariff was 70 pounds, not 100.
   American moved for partial summary judgment, arguing,
as it had before the first appeal, that the Claim I plaintiffs
lacked standing to obtain a declaration that American’s 30–
day rule was unlawful and an injunction preventing American
from applying that procedure to future customers. As to
Claim II, American argued that Beato Cruz’s claim was
barred by the two American claim-release forms he signed.
The Cruzes, for their part, moved to certify both Claim I and
Claim II as class actions.
   In their reply to American’s opposition to the Cruzes’
motion to certify the two classes, filed on November 3, 2000,
the Cruzes for the first time requested an additional form of
relief under Claim I, one mentioned in neither their com-
plaints nor their previous certification and summary-
judgment documents. The Cruzes asked the district court to
declare that American had an obligation to ‘‘process’’ the
Claim I class members’ claims without regard to American’s
(since repudiated) 30–day rule, and for American to offer the
Claim I class compensation. The Cruzes requested that the
district court issue an injunction requiring American to do
both of those things.
   The district court granted American’s partial summary-
judgment motion. The court decided to address American’s
summary-judgment motion before addressing the Cruzes’ cer-
tification motion. As to summary judgment, the court con-
cluded that Beato Cruz had released his claim for money
damages by cashing the $634.90 check. Cruz had argued that
this release should be rescinded on grounds of misrepresenta-
                              9

tion or mutual mistake. American, Cruz claimed, mistakenly
represented to Cruz in the letter accompanying the $634.90
offer of settlement that the maximum weight of his bag, as
defined in American’s tariffs, was 70, not 100, pounds. As a
result, American had underestimated the maximum extent of
its Warsaw Convention liability to him. The district court
rejected that argument, in part because American pointed to
Cruz’s deposition testimony showing that this mistake or
misrepresentation did not contribute in any material way to
Cruz’s decision to sign the release. Cruz’s testimony at his
deposition was that, at the time he cashed the $634.90 check,
he was represented by his present attorney and believed that
he could successfully sue American for more than this amount
even after he signed the release.
   The district court also agreed with American that none of
the Claim I putative class representatives had standing to
seek declaratory and injunctive relief to remedy American’s
misapplication of the 30–day rule to them. That relief, the
court reasoned, only would address American’s prospective
application of the rule, and therefore would not redress the
putative representatives’ actual injury – their lost bags.
Moreover, the court continued, the possibility that these same
plaintiffs would again fly on an international American flight,
lose their bags, and have the 30–day rule again applied to
them was simply too speculative an injury to establish Article
III standing. The district court did not address whether the
Cruzes had standing to seek relief under their newly articu-
lated theory – specifically, whether they had standing to seek
a declaration and injunction ordering American to ‘‘process’’
their claims and make offers to them. Having dismissed
much of the Cruzes’ case on the merits, the district court
directed the Cruzes to file a new class-certification motion in
light of the trimmed-down posture of the case.
   The Cruzes filed exactly three post-summary-judgment
motions. First, they renewed their motion to certify the
Claim I class. They claimed that their complaint, even after
the district court’s summary-judgment ruling, still presented
three common issues: (1) whether American was legally
obligated to compensate the Claim I class members; (2)
                              10

whether the district court should issue an injunction requiring
American to process their damages claims on their merits
without regard to the 30–day rule; and (3) whether the
Cruzes were entitled to a declaration that the Warsaw Con-
vention liability limit did not apply to those class members
whose baggage weight American did not record on their claim
tickets.
   Second, the Cruzes requested that the district court recon-
sider its summary-judgment ruling. The sole ground on
which the Cruzes sought reconsideration was that the district
court had mistakenly granted American summary judgment
as to the Claim II representatives’ claims. Specifically, they
repeated their argument that the release signed by the
representatives, contrary to the district court’s ruling, was
fatally tainted by American’s misrepresentation of the
deemed weight of their bags. That motion, however, did not
challenge the district court’s ruling that the Cruzes lacked
standing to assert their Claim I injunctive claims. Because
the Cruzes interpreted the district court’s summary-judgment
ruling to have implicitly denied their motion to certify the
Claim II class, the Cruzes did not formally renew that motion
in their reconsideration petition.
   Finally, the Cruzes filed a motion they styled as a ‘‘contin-
gent motion for disclosure and notification.’’ This motion
asked the district court to direct American to disclose to the
Cruzes the identities of the Claim I putative class members
and to invite them to intervene as plaintiffs, assuming the
district court concluded that ‘‘the existing complement of
plaintiffs seeking to serve as the [Claim I] class representa-
tives requires supplementation or substitution.’’
   The district court denied all three motions. As for the
Cruzes’ claims for declaratory and injunctive relief, the dis-
trict court noted that it had already ruled that the Cruzes
lacked standing to challenge ‘‘the legitimacy of the 30–day
rule.’’ Thus, the court concluded, the Cruzes only had stand-
ing to seek damages for their lost bags. On the issue of
damages, the district court declined to certify a class. The
court relied primarily on Federal Rule of Civil Procedure
                               11

23(a), which requires that there be ‘‘questions of law or fact
common to the class’’ before a court may certify a class. The
court reasoned that the class members’ claims for damages
did not present a common issue. Resolution of any individual
damage claim, the court said, would require a detailed, indi-
vidualized inquiry into the value of each person’s lost luggage,
miring the court in an ‘‘unmanageable series of mini-trials
that would destroy the efficiency rationale undergirding Rule
23.’’ For substantially the same reason, the court concluded,
alternatively, that the Cruzes’ remaining damages claims did
not present ‘‘question[s] of law or fact [that] predominate
over any questions affecting only individual members.’’ Fed.
R. Civ. P. 23(c)(3). The district court also denied the Cruzes’
motion for disclosure and intervention and their motion for
reconsideration of its earlier summary-judgment ruling.
  Following the district court’s disposition, the Cruzes settled
their individual damages claims with American. The district
court accordingly entered an order granting American judg-
ment on Beato Cruz’s Claim II claim and dismissing the
Claim I and Claim II class claims with prejudice. This
appeal followed.

                         II.   Analysis
   The Cruzes raise two sets of issues on appeal. The first
relates to the district court’s disposition of the motion to
certify the Claim I putative class. As to this claim, the
Cruzes argue that the district court mistakenly found they
lacked standing to pursue declaratory and injunctive relief on
behalf of that class. They also say that the district court
abused its discretion in declining to certify the class. And
they complain that the district court violated Rule 23(d)(2) by
denying their contingent request for the court to order Amer-
ican to disclose the identities of the Claim I putative class
members and to invite those people to intervene in this
action.
  The second set of issues relates to the Claim II class.
Plaintiffs attack the district court’s ruling that Beato Cruz’s
damages claim was released. Plaintiffs also appear to argue
                                  12

in their reply brief that the district court mistakenly declined
to consider the propriety of certifying the Claim II class.
  For the reasons that follow, we reject all of these assertions
and affirm the judgment of the district court. We first
address the Claim I issues, then the Claim II issues.
A.        Claim I issues
   We review de novo the district court’s decision to grant
American summary judgment, viewing the evidence in the
light most favorable to the Cruzes, the nonmoving parties.
The district court’s summary-judgment ruling should be af-
firmed only if American has satisfied its burden of showing
that there is no genuine issue of material fact about whether
it is entitled to judgment. Tao v. Freeh, 27 F.3d 635, 638
(D.C. Cir. 1994). We may reverse a district court’s refusal to
certify a class only if it abused its discretion or applied
incorrect legal criteria in doing so. Hartman v. Duffey, 19
F.3d 1459, 1471 (D.C. Cir. 1994). The district court’s decision
not to order notice to the class is also a matter within the
district court’s ‘‘discretion,’’ Larionoff v. United States, 533
F.2d 1167, 1186 n.44 (D.C. Cir. 1976), and so we will also
reverse that only if the decision was an abuse of discretion.
     1.    Plaintiffs’ challenge to the prospective enforcement of
           the 30–day rule.
  The district court correctly found that the Cruzes lack
Article III standing to obtain an injunction forbidding Ameri-
can from enforcing its 30–day rule and a declaration that this
rule is unlawful. To establish standing, the Cruzes must
show that American’s actions have caused them some con-
crete injury that this declaratory and injunctive relief will
redress. Fla. Audubon Soc’y v. Bentsen, 94 F.3d 658, 663
(D.C. Cir. 1996) (en banc). The Cruzes have made no such
showing.
  In particular, they have not shown that their challenge to
the prospective enforcement of American’s 30–day policy will
redress any concrete injury they have asserted. Plaintiffs
have alleged the loss of their luggage on American flights;
                               13

but a prospective injunction against future applications of the
30–day rule will do nothing to remedy that past harm. There
is a chance that plaintiffs could lose their luggage on a future
American flight; but plaintiffs have not alleged, much less
presented evidence, that they have any such travel plans.
Even if they did, the likelihood that American would, once
again, lose plaintiffs’ luggage is minuscule. And even assum-
ing plaintiffs lost their luggage on another international
American flight, the likelihood that they would again file their
claims late is small, given their previous experience with
American; indeed, Beato Cruz’s actions – he filed his second
claim for reimbursement on time – shows that these once-
wronged plaintiffs are unlikely to file their claims late again.
Even then, it is unlikely that American would again reject any
late-filed claim, given the litigation its 30–day rule spawned
and given that it has disavowed the 30–day rule.
   Plaintiffs’ speculative interest in prospectively challenging
the 30–day rule parallels the one the Supreme Court found
fell short of establishing a concrete interest in City of Los
Angeles v. Lyons, 461 U.S. 95 (1983). In Lyons, a person
whom police officers stopped and applied a chokehold to sued
the City of Los Angeles and the officers for money damages
and an injunction declaring that this practice was unlawful.
Id. at 97–98. The Supreme Court held that the plaintiff
lacked standing to seek the injunctive remedy, since it was
highly unlikely that the plaintiff would be again stopped by
the police and subjected to the same sort of chokehold. Id. at
107–08. Therefore, the Court reasoned, the plaintiff had no
concrete interest in obtaining a prospective injunction.
   The reasoning of Lyons applies to the claims before us. It
is not likely that plaintiffs will again lose their luggage on an
international American flight, much less again be denied
compensation as a result of the misapplication of the 30–day
rule. Though plaintiffs dismiss Lyons as involving a ‘‘wholly
concluded and unlikely to be repeated incident of a police
choke-hold,’’ that characterization aptly describes plaintiffs’
asserted injury as well.
                               14

  2.   Plaintiffs’ request for a retrospective injunction order-
       ing American to process their claims and offer to settle
       their claims.
   Plaintiffs argue that the district court’s decision to grant
American summary judgment failed to consider a separate
claim for injunctive relief – a claim for a retrospective injunc-
tion ordering American to ‘‘process’’ plaintiffs’ compensation
claims without regard to American’s 30–day rule. This asser-
tion challenges the district court’s summary-judgment ruling
that the Cruzes lacked standing to assert their Claim I
requests ‘‘for declaratory and injunctive relief regarding
[American’s] 30–day rule.’’ The district court never ad-
dressed plaintiffs’ request for a retrospective, as opposed to a
prospective, injunction and declaration, but that was because
the Cruzes’ lawyer failed to apprise the district court of it
sufficiently. We therefore decline to address its merits.
   We root this decision in our well-established discretion not
to consider claims that litigants fail to raise sufficiently below
and on which district courts do not pass. See Singleton v.
Wulff, 428 U.S. 106, 120–21 (1976). The issue is whether, in
light of the policy of this rule to ‘‘encourage[ ] parties to
communicate with each other and the trial judge,’’ Edmond v.
U.S. Postal Serv., 949 F.2d 415, 422 (D.C. Cir. 1991), plaintiffs
apprised the district court with sufficient clarity of this chal-
lenge to its summary-judgment ruling.
   They did not. Plaintiffs never mentioned this request in
their pleadings. Their revised complaint, in particular, con-
tained no hint of this odd request for an injunction, as
plaintiffs’ counsel conceded when pressed at oral argument.
Nor did their summary-judgment papers, although those
papers did stress the uncontroversial (and distinct) proposi-
tion that American has a duty to compensate passengers
whose luggage it loses. The first clue plaintiffs gave the
district court of their new theory came in their reply to
American’s opposition to their motion to certify the Claim I
class – filed nearly four years after the Cruzes’ filed their
initial complaint.
                              15

   This tardy, oblique assertion of the claim was not sufficient
to apprise the district court of the need to address this issue
in its summary-judgment ruling. Because plaintiffs asserted
it only in their class-certification papers, rather than their
summary-judgment papers, they did not give the district
court a square chance to decide the question at the summary
judgment stage. Plaintiffs, in particular, never made the
argument that they had standing to assert this claim, and
thus that American’s motion to dismiss the Claim I claims for
injunctive relief should have been denied.
   Nor did plaintiffs make this argument clear to the district
court after the district court entered its order dismissing
Claim I to the extent it requested ‘‘declaratory and injunctive
relief regarding [American’s] 30–day rule.’’ Plaintiffs, most
damningly, never raised their retrospective injunctive claim
as a reason for the district court to reconsider its summary-
judgment ruling, although plaintiffs moved for reconsidera-
tion on other grounds. True, plaintiffs, in their renewed
motion for class certification, identified the claim as a com-
mon issue that might warrant certifying the class. By then,
however, the district court had granted American’s motion for
summary judgment as to Claim I injunctive relief related to
the 30–day rule, removing those claims from the case. When
plaintiffs belatedly argued that their new injunctive claim
presented a common issue ripe for class adjudication, the
district court, understandably, rejected it on the ground that
it had already dismissed plaintiffs’ injunctive claims. The
district court properly treated the unchallenged portions of
its summary-judgment order as the law of the case. Sum-
mary-judgment motions could not perform their function of
simplifying and narrowing disputed issues if district courts
had an obligation to reconsider, in light of the implications of
other positions taken by litigants, such rulings sua sponte.
   Plaintiffs’ attempt to excuse their 11th-hour change of
course does not succeed. They attempt to assign the blame
to American, asserting that their shift simply reacted to
‘‘American’s assertion, first made in its summary judgment
papers, that it was free, as a matter of business policy, to
reject or refuse to process, class member damage claims,
                              16

whether or not its 30–day rule was unlawful or properly
applied.’’ This is both backward and wrong. It is wrong
because American, to our knowledge, has never made such an
assertion. American conceded below, in its brief, and at oral
argument, that it may have a duty to compensate some (but
not all) class members whose claims it rejected on the basis of
its (now-abandoned) 30–day rule, and thus that it was not
‘‘free’’ to reject those claims.
   It is backward because plaintiffs, not American, are the
ones who shifted course. Nothing prevented the Cruzes from
making this argument either in the four years that passed
before the district court granted summary judgment against
them or in their reconsideration motion. This inaction moves
us, in our discretion, to decline to consider the merits of the
issue now.
   Finally, it is appropriate for us to determine that the claim
was not sufficiently raised below, and therefore is not proper-
ly before us, without addressing whether plaintiffs have Arti-
cle III standing to raise the claim. This approach is entirely
consistent with the rule that courts must address issues
relating to subject matter jurisdiction before reaching the
merits of a case. See Steel Co. v. Citizens for a Better Env’t,
523 U.S. 83, 101–02 (1998). As the Supreme Court has
explained, ‘‘a court that dismisses on other non-merits
grounds TTT makes no assumption of law-declaring power
that violates the separation of powers principles’’ underlying
the Steel Company rule. Ruhrgas AG v. Marathon Oil Co.,
526 U.S. 574, 585 (1999) (internal quotation marks and cita-
tion omitted). By declining to consider plaintiffs’ retrospec-
tive injunctive claim, we are, within our discretion, simply
declining to exercise jurisdiction over it. As Steel Company
itself recognized, it is permissible to do that without deter-
mining whether plaintiffs have Article III standing to assert
their claim for a retrospective injunction. See 523 U.S. at 100
n.3.
  3.   Class certification
   Because plaintiffs’ claim for retrospective injunctive relief
is not properly before us, we can easily dispose of plaintiffs’
                                17

assertion that the district court abused its discretion in not
certifying the Claim I class. As discussed more fully above,
the district court declined to certify the Claim I class because
the class members’ damages claims presented individualized
issues not common to all class members. Plaintiffs do not
challenge this conclusion on appeal. Instead, plaintiffs assert
that their injunctive claims, rather than their damages claims,
are common issues that can be adjudicated class wide.
  Those claims, however, are out of this case now that we
have concluded that plaintiffs either lack standing to raise
their injunctive claims or have not preserved them for appeal.
These conclusions therefore also refute plaintiffs’ certification
argument. The district court neither erred nor abused its
discretion in declining to certify the class on a ground that
plaintiffs do not challenge on appeal.
     4.    Notice
   The district court did not abuse its discretion in denying
plaintiffs’ ‘‘contingent motion for disclosure and notification’’ –
in essence, a request that the district court order notice,
pursuant to Rule 23(d)(2), to a non-certified class. We doubt,
as a threshold matter, that a district court has any discretion
to order notice ‘‘in the conduct of [an] action[ ]’’ in which it
has declined to certify any class whatsoever, for such an
action may well not be one ‘‘to which [Rule 23] applies.’’ Fed.
R. Civ. P. 23(d)(2). Setting that point aside, however, the
district court, at a minimum, did not abuse its discretion by
declining to order notice to this putative class given that it
found the remaining issues in the case were unsuitable for
class treatment at all, and given that there was no reversible
error in that finding.
B.        Claim II issues
   We also affirm the district court’s decision to grant Ameri-
can summary judgment on Beato Cruz’s individual damages
claim and to deny his motion to certify the Claim II class. As
to the summary-judgment issue, the district court concluded
that Cruz’s individual damages claim was barred by the
release Cruz signed in exchange for American’s $634.90 pay-
                               18

ment to him. Cruz challenges this ruling on appeal, claiming
that the release is voidable because American, in its letter
accompanying that payment, mistakenly represented the ex-
tent of its liability to Cruz under the Warsaw Convention.
Cruz also appears to argue in his reply brief that the district
court erroneously declined to address whether the Claim II
class should have been certified given that it granted Ameri-
can summary judgment on the representative plaintiffs’ indi-
vidual claims. We reject both challenges.
  1.   The validity of the release
  The parties disagree on the law applicable to the issue of
the validity of the release. Cruz argues that federal common
law applies; American says, and the district court agreed,
that state law applies. In any event, American continues,
Cruz’s release is valid regardless whether state law or federal
common law applies.
   We agree with American that there is no conflict of law for
this Court to resolve. The parties have identified only three
possible sources of law: Maryland, Virginia, and federal
common law. Cruz argues that the federal common law rule
of decision to apply is the rule of the Second Restatement of
Contracts. That rule, as Cruz quotes approvingly in his brief,
is that ‘‘[a]n agreement is voidable’’ on grounds of mutual
mistake ‘‘where both parties were mistaken as to a basic
assumption of the agreement which has a material effect on
the exchange of performances.’’ Restatement (Second) of
Contracts § 152. In like fashion, Cruz relies on the Second
Restatement’s unilateral misrepresentation rule. That rule,
as stated in his brief, is that the release is voidable if Cruz’s
manifestation of assent was induced by a material misrepre-
sentation by American that ‘‘substantially contributed’’ to
Cruz’s decision to sign the release. Id. §§ 164, 167.
  In American’s view, under the law of Virginia and Mary-
land, Cruz may rescind the agreement on the ground of
mistake if he agreed to it with a mistaken belief concerning a
fact of significance. As for misrepresentation, American’s
understanding of the law of Virginia and Maryland is that
                               19

Cruz may rescind the agreement if he reasonably relied on
American’s material misrepresentation.
   The standards advocated by the parties do not conflict in
any respect relevant to our resolution of this appeal. While
the standards are not linguistically identical, all place the
burden on Cruz to make out this defense to enforcing the
release. The only difference is that the mutual mistake
standard labels whether Cruz relied on the misrepresentation
in terms of whether the mistake had a ‘‘material effect on the
exchange of performances’’ or whether the mistaken belief
concerned a ‘‘fact of significance,’’ rather than in terms of his
‘‘reliance’’ on the misrepresentation. These formulations all
go to whether the misrepresentation or mutual mistake was
important to Cruz in his decision to accept the release.
Therefore, the distinctions among them, in our view, make no
substantive difference, at least in this case, and so we need
not make a choice of law.
   Turning to the merits, Cruz has shown no triable issue of
fact as to whether he relied on American’s mistaken misrep-
resentation. To review: American’s letter that accompanied
its $634.90 check to Cruz understated the limit of its Warsaw
Convention liability by $272.10. It is true, as Cruz points out,
that this was indeed a misrepresentation or mistake; but
Cruz has not established a triable issue of fact on the
essential element of Cruz’s reliance on this misrepresentation
or mistake.
   Uncontradicted evidence in the summary-judgment record
establishes that this is not a triable issue. Cruz testified that,
at the time he signed the release, he believed that the release
would not prevent him from recovering even more money
from American. That belief demonstrates that he did not
rely on American’s representations about the state of the law
of Warsaw Convention liability. If Cruz, in accepting the
release, had relied on American’s representation about the
limit of its liability, he would not have believed that he could,
in his words, recover an ‘‘additional amount.’’ Rather, he
would have thought that American’s payment fully discharged
its payment obligation. That is because American paid him
                              20

exactly what it represented it owed him. The fact that he
thought he was owed more shows that he did not believe that
representation, i.e., American’s view of the law.
   Therefore, Cruz’s deposition testimony, together with the
fact that he was represented by his current lawyer at the
time, proves that he accepted a totally different measure, one
that did not depend on deemed weight. This evidence shows
that at the time – no doubt influenced by advice from his
lawyer in the pending litigation against American – Cruz
believed that he could recover the full $3,890 value of his bag
regardless of its weight, deemed or otherwise. That is clear
enough from positions his lawyer later took on his behalf, and
given the summary-judgment record the parties compiled, it
is not reasonable to read the record any other way. Because
Cruz did not accept deemed weight as a method for calculat-
ing liability at all, he could not have cared that American got
the deemed weight wrong. Cruz’s belief shows that he
accepted the release for totally different reasons, ones that
had nothing to do with American’s mistaken representation as
to deemed weight, and thus as to the limit of its liability
under the Warsaw Convention. Cruz’s failure to produce any
evidence creating a genuine issue as to this fact entitles
American to summary judgment on the question of this
defense to enforcing the release.
   We recognize, as Cruz takes pains to highlight in his brief,
that the mistake at issue in this case is different from the one
in Curtin v. United Airlines, Inc., 275 F.3d 88 (D.C. Cir.
2001), but this distinction does not require a different result
in this case. In Curtin, United Airlines had offered to settle
the lost-baggage claims of certain of its passengers and, in
connection with these offers, had represented to these pas-
sengers that its liability was limited to $635 under the War-
saw Convention. Id. at 89–90. This Court held that this
representation did not allow the passengers who had settled
their claims with United to rescind the releases on the ground
of mutual or unilateral mistake. Id. at 96–97. American
made the representations before Cruz was decided, the Court
reasoned, when the law regarding the limit of American’s
liability under the Warsaw Convention was unsettled. Be-
                                21

cause that representation was reasonable in light of the
unsettled state of the law at the time the parties agreed to
the release, American made no ‘‘mistake,’’ the Court held.
Id.
   Cruz is right that, unlike Curtin, American, in light of its
understanding of the law at the time of the release, made a
mistake. Given American’s belief that the Warsaw Conven-
tion liability limits applied, and its view of how to calculate
those liability limits, American mistakenly stated the limit of
that liability. We rest our holding not on the fact that
American made no ‘‘mistake,’’ but rather on the fact that that
Cruz has not established genuine issues of material fact about
whether he relied on that mistake, given that he did not think
American’s liability was limited at all.
  2.   Claim II class certification
   Cruz does not argue in his opening brief that the district
court mistakenly declined to address whether the Claim II
class should be certified given that it dismissed only the
representative plaintiffs’ claims on the merits at the summary
judgment stage, rather than all of the claims of the Claim II
putative class. Although we may discern a hint of such an
argument after a close reading of plaintiffs’ reply brief (albeit
not a hint supported by both citations to authority and
argument, as is required by Federal Rule of Appellate Proce-
dure 28(a)(9)), plaintiff was required to present, argue, and
support this claim in his opening brief for us to consider it.
See, e.g., Nat’l Lime Ass’n v. EPA, 233 F.3d 625, 633 (D.C.
Cir. 2000). We are not ‘‘self-directed boards of legal inquiry
and research, but essentially TTT arbiters of legal questions
presented and argued by the parties.’’ Carducci v. Regan,
714 F.2d 171, 177 (D.C. Cir. 1983).
  We therefore do not consider whether the district court
correctly declined to address the propriety of certifying the
Claim II class after it dismissed the individual plaintiff’s
damages claims. Although we do not decide the point, we
note that many of the reasons the district court gave in
declining to certify the Claim I class equally apply to whether
the Claim II class should have been certified. Once the
                             22

injunctive claims are gone, the issues in both Claim I and
Claim II are individualized.

                     III.   Conclusion
  For the reasons expressed above, the judgment of the
district court is affirmed.
