Opinion for the Court filed PER CURIAM.
PER CURIAM:Appellants seek review of a final determination of the Copyright Royalty Judges, setting rates and terms relating to web-casting. See Digital Performance Right in Sound Recordings and, Ephemeral Recordings (“Order”), 72 Fed.Reg. 24,084 (May 1, 2007). Webcasting is the process of transmitting sound recordings over the Internet. This case consolidates five separate appeals. A group of “commercial webeaster” appellants led by the Digital Media Association (“DiMA”) argues that the rates for commercial webcasters set by the Judges were unreasonable and that the absence of a cap on minimum fees paid per licensee was arbitrary and capricious. Several “small commercial web-caster” appellants argue that the Judges’ refusal to permit them to pay royalties as a percentage of revenues was arbitrary and capricious. “Noncommercial broadcaster” appellants — including the Collegiate Broadcasters, Inc., Intercollegiate Broadcasting System, Inc., and the National Religious Broadcasters Noncommercial Music License Committee — argue that the Judges set unreasonable rates for noncommercial webcasters, that they established a $500 minimum fee per station without substantial evidence, and that they improperly deferred consideration of record-keeping requirements to a later proceeding. Appellant Royalty Logic, Inc., a contender to serve as the clearinghouse (or “collective”) for royalty payments, argues that the Judges exceeded their statutory authority by naming SoundExchange, Inc. the sole royalty collective.1 Respondent Copyright Royalty Board defends the Judges’ determination. (The Board is “the institutional entity in the Library of Congress that house[s]” the Judges. 37 C.F.R. § 301.1.) SoundExchange intervened to defend the Judges’ determination.
Months after the briefing schedule had been set, Royalty Logic moved to file supplementary briefs on the issue of whether the appointment of the Copyright Royalty Judges violated the Appointments Clause of the Constitution of the United States. A motions panel of this court granted the motion “without prejudice to the merits panel deciding whether or not to consider” the issue, and set a supplemental briefing schedule, soliciting briefs from Royalty Logic, the Board, and SoundExchange. Royalty Logic argued that the Judges’ appointment violated the Constitution. SoundExchange and the Board argued it did not, and argued further that Royalty Logic had forfeited consideration of the issue by not raising it in initial briefing before this court. We hold that Royalty *392Logic has forfeited the Appointments Clause issue. We vacate the $500 minimum fee for both noncommercials and commercials, and remand those portions of the determination for reconsideration by the Copyright Royalty Judges. In all other respects, we affirm the determination.
I. Background
A. Statutory Background
Recorded music may be protected by two copyrights. One copyright protects the “musical work” written by a composer and usually owned by a music publisher. The other protects the “sound recording” and is owned by the producer of the sound recording. See 17 U.S.C. § § 101-102. The copyright owners of musical works, but not those of sound recordings, have long enjoyed exclusive rights to public performances of their works. Id. § 106(4). The practical effect of this scheme is that when radio stations play a song, they must pay a royalty to the musical work owner but not the sound recording owner. See id. §§ 106(4), 114(a).
In 1995, Congress passed the Digital Performance Right in Sound Recordings Act, Pub.L. No. 104-39, granting the owners of sound recordings an exclusive right in performance “by means of a digital audio transmission.” 17 U.S.C. § 106(6); see Beethoven.com LLC v. Librarian of Cong., 394 F.3d 939, 942 (D.C.Cir.2005). The Digital Millennium Copyright Act of 1998, Pub.L. No. 105-304, “created a statutory license in performances by webcast,” to serve Internet broadcasters and to provide a means of paying copyright owners. Beethoven.com, 394 F.3d at 942; see 17 U.S.C. § 114(d)(2), (f)(2). To govern the broadcast of sound recordings, Congress also created a licensing scheme for so-called “ephemeral” recordings, “the temporary copies necessary to facilitate the transmission of sound recordings during internet broadcasting.” Beethoven. com, 394 F.3d at 942-43; see 17 U.S.C. § 112(e)(4).
Congress has delegated authority to set rates for these rights and licenses under several statutory schemes. The most recent, passed in 2005, directed the Librarian of Congress to appoint three Copyright Royalty Judges who serve staggered, six-year terms. See 17 U.S.C. § 801, et seq. These Judges conduct complex, adversarial proceedings, described in 17 U.S.C. § 803 and 37 C.F.R. § 351, et seq., and ultimately set “reasonable rates and terms” for royalty payments from digital performances. 17 U.S.C. § 114(f).
In delegating authority, Congress required the Judges to follow certain statutory guidelines. The schedule of rates and terms must “distinguish among the different types of eligible nonsubscription transmission services then in operation and shall include a minimum fee for each such type of service.” Id. § 114(f)(2)(B). Rates should “most clearly represent the rates and terms that would have been negotiated in the marketplace between a willing buyer and a willing seller.” Id. “In determining such rates and terms,”, the Judges must “base [their] decision on economic, competitive and programming information presented by the parties.” Id. Specifically, they must consider whether “the service may substitute for or may promote the sales of phonorecords” or otherwise affect the “copyright owner’s other streams of revenue.” Id. § 114(f)(2)(B)(i). The Judges must also consider “the relative roles of the copyright owner and the transmitting entity” with respect to “relative creative contribution, technological contribution, capital investment, cost, and risk.” Id. § 114(f)(2)(B)(ii). Finally, “[i]n establishing such rates and terms,” the Judges “may consider the rates and terms for comparable types of digital audio transmission services and comparable cir*393cumstances under voluntary license agreements described in subparagraph (A).” Id. § 114(f)(2)(B). Identical statutory language applies to “reasonable rates and terms” for ephemeral recordings. Id. § 112(e).
B. This Proceeding
The rates and terms for webcasting are established according to a webcasting statutory license. See 17 U.S.C. § 112(e)(4); id. § 114(d)(2), (f)(2). If parties can agree, rates and terms of a license may be set through voluntary negotiation. Id. § 114(f)(3). For all parties that do not agree, the Copyright Royalty Judges conduct adversarial proceedings and issue a determination. Id. § 803. The resulting rate changes are retroactive. Id. § 803(d)(2).
This case represents such an adversarial proceeding. The Judges received notices from 28 parties of them intention to submit written direct statements at the start of the process, and another five submitted written direct statements after a final attempt at negotiation failed. Order, 72 Fed.Reg. at 24,084. Following discovery, the participants presented testimony from a total of 39 witnesses. Id. at 24,084-85. Additional written rebuttal statements were then admitted, followed by more discovery. Id. at 24,085. At the end of this second discovery period, participants presented rebuttal testimony from 27 witnesses, and the record was closed. Id. In addition to the written statements, the Judges “heard 48 days of testimony, which filled 13,288 pages of transcript, and 192 exhibits were admitted.” Id. Following the evidentiary phase of the proceeding, the participants filed proposed findings of fact and conclusions of law with responses three days later. Id. A week passed before closing arguments, when the matter was submitted to the Judges. Id.
Following the initial determination, many of the participants filed motions for rehearing, along with written arguments and responses at the request of the Judges. Id. at 24,085 & n. 2. The Judges denied these motions, but modified the determination in one important respect: they added an option for commercial web-casters to pay based on ATH for 2006 and 2007 rather than per play. Id. at 24,086. Their final determination was published May 1, 2007. Id. at 24,084.
The Judges’ initial determination set rates and terms for digital performances and related ephemeral recordings, and determined other details of the statutory licenses for commercial and noncommercial webcasters. Specifically, it designated per play rates for commercial webcasters that will increase gradually over the covered period — from January 1, 2006 through December 31, 2010. Id. at 24,084, 24,096. It also charged all webcasters a $500 annual minimum fee to cover administrative costs, reeoupable against usage charges. Id. at 24,096. For noncommercial broadcasters, this minimum fee covers 159,140 aggregate tuning hours (“ATH,” which is the total number of hours of programming multiplied by the number of listeners per hour). For any month in which a noncommercial broadcaster’s ATH exceeds this threshold, it must pay the same per-performance rates as the commercial webcasters for the excess ATH. Id. at 24,100. The Judges’ initial determination set terms for the payment of royalties, including the method of aggregating payments through SoundExchange as a collective; set late payment fees; and provided for the form of account statements, audits, and payment verification. Id. at 24,102-09. Finally, the Judges decided to leave record-keeping regulations unchanged, but left open the possibility of their modification in a future rulemaking. Id. at 24,109-10.
*394Most of the parties appealed to this court, which has jurisdiction under 17 U.S.C. § 803(d)(1). We have power to modify, vacate, or remand any portion of the Judges’ determination. Id. § 803(d)(3). We vacate the $500 minimum fee for noncommercials and for commercials, remand those portions of the determination for reconsideration by the Judges, and otherwise affirm the determination.
II. Analysis
We review determinations of the Judges under the familiar standard of the Administrative Procedure Act (“APA”). 17 U.S.C. § 803(d)(3); see 5 U.S.C. § 706. Under the APA, we uphold the results of adversarial agency proceedings unless they are arbitrary, capricious, contrary to law, or not supported by substantial evidence. See 5 U.S.C. § 706(2). Review of administratively determined rates is “particularly deferential” because of their “highly technical” nature. E. Ky. Power Coop. v. FERC, 489 F.3d 1299, 1306 (D.C.Cir.2007) (quotation omitted).
A. Appointments Clause Challenge
Before reviewing the substance of the Judges’ determination, we must address a question raised about the tribunal itself. Nearly a year after appealing the Judges’ order, and almost three months after filing its opening brief, Royalty Logic submitted a supplemental brief in which it argued for the first time that the manner in which the Copyright Royalty Judges are appointed violates the Appointments Clause of the United States Constitution. This court allowed the filing “without prejudice to the merits panel deciding whether or not to consider the Appointments Clause issue” and directed the Board and SoundExehange to file responsive supplemental briefs. Supp. Briefing Order (D.C.Cir. May 30, 2008).
“[T]he Congress may by Law vest the Appointment of ... inferior Officers” — a category that all parties agree includes the Judges — “in the President alone, in the Courts of Law, or in the Heads of Departments.” U.S. CONST. art. II, § 2, cl. 2. Congress has entrusted the appointment of the Judges to the Librarian of Congress. See 17 U.S.C. § 801(a) (“The Librarian shall appoint 3 full-time Copyright Royalty Judges ... after consultation with the Register of Copyrights.”). The Librarian, of course, is neither the President nor a court of law. Royalty Logic argues that he is also not a “Head of Department,” maintaining that under Freytag v. Commissioner, 501 U.S. 868, 111 S.Ct. 2631, 115 L.Ed.2d 764 (1991), only the heads of cabinet-level departments within the executive branch qualify. According to Royalty Logic, the Library of Congress is within the legislative branch. The government and SoundExehange dispute both points. They note that the Library serves several executive functions and that the Librarian is subject to appointment and removal by the President. They also reject the reading of Freytag that limits “Departments” to those at the cabinet level.
We need not resolve the dispute. As appellees point out, Royalty Logic has forfeited its argument by failing to raise it in its opening brief. See Sw. Airlines Co. v. Transp. Sec. Admin., 554 F.3d 1065, 1072 (D.C.Cir.2009). It is certainly within our power to consider Royalty Logic’s challenge. The Freytag petitioners failed to object to the special trial judge’s appointment, raising their constitutional argument for the first time on appeal. But the Court emphasized that its consideration of the untimely objection was an exercise of discretion, and that only in “rare cases” is it proper to do so. Freytag, 501 U.S. at 879, 111 S.Ct. 2631; see also id. at 893, 111 S.Ct. 2631 (Scalia, J., concurring) (noting *395that the majority did not accept petitioners’ argument that Appointments Clause challenges cannot be forfeited).
This is not the rare case that compels us to exercise our discretion to consider an untimely argument. An Appointments Clause challenge is “nonjurisdietional,” id. at 878, 111 S.Ct. 2631 (majority opinion), and thus not subject to the axiom that jurisdiction may not be waived, see NetworkIP, LLC v. FCC, 548 F.3d 116, 120 (D.C.Cir.2008). And Royalty Logic has not given us any reason to depart from our normal forfeiture rule. It offers no justification for its delay. At oral argument, Royalty Logic’s counsel explained that the issue simply had not occurred to him until, several months after filing his opening brief, he was “reading the cases ... and particularly Frey tag,” and concluded that “this was a foundational and structural issue.” Oral Arg. Rec. at 1:35-55. But these cases were not new. Freytag was decided over eighteen years ago, and the most recent case cited in Royalty Logic’s supplemental brief dates from 2003. See Royalty Logic Supp. Br. ii-iii. We have cautioned litigants that “[sjupplemental briefs do not provide an opportunity to convert review of an agency order into a broadbased ... constitutional attack,” and that we will not consider a supplemental brief that is “nothing more than a poorly disguised attempt to file' a second main brief to advance arguments overlooked in [the party’s] first main brief.” Plaquemines Port, Harbor & Terminal Dist. v. Fed. Mar. Comm’n, 838 F.2d 536, 551 (D.C.Cir.1988).
Nothing in the supplemental briefing (which was allowed without prejudice to the decision we have now made to hold Royalty Logic to its forfeiture) persuades us otherwise. To the contrary, the briefs’ incomplete treatment of the Appointments Clause issue underscores our decision. For example, the parties failed to cite or discuss the effect of our statements, in other contexts, that the Library of Congress is not part of the executive branch. See, e.g., Wash. Legal Found. v. U.S. Sentencing Comm’n, 17 F.3d 1446, 1449 (D.C.Cir.1994) (noting that the Library “is exempt from the APA because its provisions do not apply to ‘the Congress’ — that is, the legislative branch”); Judd v. Billington, 863 F.2d 103, 105 (D.C.Cir.1988) (former Library employee could not bring claim under Rehabilitation Act because that statute “applies only to employees in the executive branch”). The absence of the webcasters’ views compounds the problem. Were we to decide the constitutional question without thorough, considered briefing from all interested parties, we would run “the risk of an improvident or ill-advised opinion on the legal issues tendered,” McBride v. Merrell Dow & Pharm., Inc., 800 F.2d 1208, 1211 (D.C.Cir.1986) (refusing to decide issue not raised until reply brief).
Finally, the potential for far-reaching consequences counsels against resolving the Appointments Clause question on this record. The Librarian of Congress appoints not only the Copyright Royalty Judges but also the Register of Copyrights. See 17 U.S.C. § 701(a). To hold that the Librarian is not the head of a department within the meaning of the Appointments Clause would invalidate the Judges’ determinations and call into question the status of every registered American copyright. We decline to resolve this “important question[] of far-reaching significance,” Carducci v. Regan, 714 F.2d 171, 177 (D.C.Cir.1983), on the basis of hasty, inadequate, and untimely briefing.
B. Commercial Webcasters’ Challenges
1. Competitive Market Requirement
The Judges are required to determine royalty rates that “most clearly rep-
*396resent the rates and terms that would have been negotiated in the marketplace between a willing buyer and a willing seller.” 17 U.S.C. § 114(f)(2)(B). The commercial webeasters argue that an earlier decision by the Librarian, “affirmed” by this court, requires the Judges to base rates on a perfectly competitive market. See Determination of Reasonable Rates and Terms for the Digital Performance of Sound Recordings. and Ephemeral Recordings (“Webcaster P), 67 Fed.Reg. 45, 240, 45, 244-45 (July 8, 2002) (“Because of the diversity among the buyers and the sellers, the [Copyright Arbitration Royalty Panel] noted that one would expect ‘a range of negotiated rates,’ and so interpreted the statutory standard as ‘the rates to which, absent special circumstances, most willing buyers and willing sellers would agree’ in a competitive marketplace.”). This claim fails for two reasons. First, the dictum from the prior decision calling for a competitive benchmark does not require rates to be based on a perfectly competitive market. Second, our having “affirmed” Webcaster I in Beethoven, com lends no additional weight to the commercial webeasters’ argument. Far from endorsing a competitive (or perfectly competitive) standard, we specifically refused to “examine the correctness of the Librarian’s decision” regarding competitiveness. Beethoven.com, 894 F.3d at 952 (emphasis added). Because of the “exceptionally deferential” review undertaken in that case, our having affirmed the decision of the Librarian cannot be taken to bind the Judges today. Id. The statute speaks only of a “willing buyer and a willing seller.” This is the standard the Judges were to apply in evaluating whether a market benchmark was an appropriate model on which to base their own rate determinations.
The statute does not require that the market assumed by the Judges achieve metaphysical perfection in competitiveness. The Judges, not this court, bear the initial responsibility for interpreting the statute. Applying the lessons of Chevron U.S.A. Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), we can only assess the reasonableness of the Judges’ interpretation of the inherent ambiguity in the statute’s mandate. Appellants have pointed to nothing in the Judges’ interpretation to establish unreasonableness.
2. Royalty Rates
The Judges set a per play royalty rate to be paid by commercial webeasters. This rate will increase, once a year, from $0.0008 per play in 2006 to $0.0019 per play in 2010. See Order, 72 Fed.Reg. at 24,096. The rate schedule was based on the testimony of SoundExchange’s expert economist Michael Pelcovits, who modeled his estimates on “the market for interactive webcasting covering the digital performance of sound recordings.” Id. at 24,-092. Interactive webcasting — which is not within the scope of the statutory license— allows a listener to access “particular sound recording[s]” on request or a program of sound recordings “specifically created for the recipient.” 17 U.S.C. § 114(j)(7). By contrast, the non-interactive webcasting at issue in this determination does not allow the same degree of user customization. Therefore Dr. Pelcovits proposed, and the Judges adopted, an “interactivity adjustment” by which to decrease the interactive rates. See Order, 72 Fed.Reg. at 24,092-94. Dr. Pelcovits calculated the adjustment through a process called hedonic regression, a statistical method that tries to isolate the value of a particular variable in a complex set of data. In this case, Dr. Pelcovits tried to isolate the value of interactive service, which he used to reduce his final estimates.
The commercial webeasters argue that the market for interactive music services— *397used by Dr. Pelcovits in his model, which was generally adopted by the Judges — was insufficiently competitive. They claim that the market for interactive music is different than the market for “passive,” non-interactive webcasting because an interactive music service is not viable unless it can provide music from each of the four major record labels. The commercial web-casters argue that subscribers to interactive webcasting services “expect” access to recordings from all four major labels “in exchange for [the] significant monthly payment” that is a condition of their subscription. Commercial Op. Br. 26. Assuming this asymmetry of consumer demand, they conclude that the Judges should not have produced webcasting rates by looking to interactive music rates. To provide music from each major record label, an interactive music service must reach agreement with each major record label independently. According to the commercial webcasters, this competitive dynamic gives record labels disproportionate bargaining power. Any one record label could block an entire service, so each in turn can negotiate higher rates. By looking to this market, they argue, the Judges provided better terms to the copyright owners than they would have earned in the marketplace.
Commercial webeasters presented this argument to the Judges, supported by the testimony of their expert witness, economist Adam Jaffe. The Judges considered the argument and found it to be “largely unsubstantiated.” Id. at 24,093. They further noted that “there was testimony that directly contradicted] any suggested generalization that the repertoires of all four major[ record labels] are necessary as a prerequisite prior to undertaking the operation of a consumer music service in the various digital music service markets.” Id. at 24,093 n. 24. The Judges cited evidence that “Yahoo! was able to operate its custom radio channels without” one of those record labels “for two years,” even though the record label accounted for “nearly one-third of the market in terms of repertoire.” Id. They summarized their assessment of Dr. Jaffe’s testimony by calling his “concerns that the benchmark market [wa]s not sufficiently competitive ... little more than the theoretical speculations of an academic offering a quick outline of possible criticisms without carefully considering the applicable facts or alternative explanations.” Id. at 24,093. The Judges assessed Dr. Jaffe’s testimony and pointed to contrary evidence in the record. Having evaluated the arguments on both sides, we hold that it was not unreasonable for the Judges to base their webcasting rates in part on the market for interactive music.2
*398The standard of review applicable in ratemaking eases is highly deferential. See E. Ky. Power Coop., 489 F.3d at 1306. The deferential standard of review extends to our consideration of arguments by the commercial webcasters about whether a voluntary agreement could be considered “comparable” to the ratesetting the Judges were undertaking. See 17 U.S.C. § 114(f)(2)(B). When setting rates and terms, “the Copyright Royalty Judges may consider the rates and terms for comparable types of digital audio transmission services and comparable circumstances under voluntary license agreements.” 17 U.S.C. § 114(f)(2)(B) (emphasis added). The commercial webcasters argue that the Judges committed reversible error by failing to consider a 2003 voluntary agreement between record companies and satellite digital audio services. Nothing in the statute requires the Judges to consider any comparable agreements, let alone particular agreements. It is generally within the discretion of the Judges to assess evidence of an agreement’s comparability and to decide whether to look to its rates and terms for guidance. We therefore affirm the Judges’ decision not to consider the 2003 agreement when setting rates for webcasting.
Apart from the objections to the Judges’ assessment of the market and voluntary agreements, the commercial web-casters also dispute the hedonic regression analysis used by Dr. Pelcovits to reduce the rates. In a later determination, setting rates and terms for satellite radio subscription services, the Judges credited a study with an interactivity adjustment much greater than the interactivity adjustment Dr. Pelcovits used in this determination. See Determination of Rates and Terms for Preexisting Subscription Services and Satellite Digital Audio Radio Services (“SDARS”), 73 Fed.Reg. 4080 (Jan. 24, 2008). If the Judges had used the SDARS adjustment, the final rates would have been two-thirds smaller. Commercial webcasters contend that this was arbitrary. This argument fails for two reasons. First and most obviously, the Judges are not bound by future agency action. The suggestion defies logic. The Judges must “act ... on the basis of a written record [and] prior determinations and interpretations of ... the Copyright Royalty Judges.” 17 U.S.C. § 803(a)(1). They are not required to act on the basis of future determinations of the Copyright Royalty Judges. Failure to conform with subsequent agency action cannot be a basis for a finding of arbitrariness. See Tesoro Ref. & Mktg. Co. v. FERC, 552 F.3d 868, 873-74 (D.C.Cir.2009) (rejecting futility argument based on subsequent agency action). Second, even if the Judges were so bound, their determination in SDARS specifically criticized the interactivity adjustment, saying it “might well be improved through a hedonic regression analysis.” See 73 Fed.Reg. at 4093. The Judges’ “failure” to use a similarly inexact *399adjustment for webcasting was not arbitrary or otherwise contrary to law.
Finally, the commercial webcasters argue for setting aside the Judges’ proposed rates because they are “crushing and disproportionate.” Commercial Op. Br. 38. The APA permits us to set aside agency action that is “arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law.” 5 U.S.C. § 706(2)(A). This they have not shown.
3. Percentage-of-Revenue Rates
The Judges adopted a per-performance usage fee structure for all commercial webcasters. Small commercial webcasters object to this uniform solution, seeking instead to pay a percentage of their revenues. The Judges rejected such an argument because they found “no evidence in the record about how [to] delineate between small webcasters and large webcasters” and noted that “none of the small commercial webcasters ... provided helpful evidence about what demarcates a ‘small’ commercial webcaster from other webcasters at any given point in time.” Order; 72 Fed.Reg. at 24,089 & n. 9. The small commercial webcasters now argue that the definition of “small commercial webcaster” is irrelevant because the percentage-of-revenue approach would apply only to those webcasters that elected to pay a percentage of total gross revenue. The Board and SoundExchange say that this revised argument, which they claim was first raised at rehearing, is waived. See 37 C.F.R. § 351.14(b) (“A party waives any objection to a provision in the determination unless the provision conflicts with a proposed finding of fact or conclusion of law filed by the party.”). We assume without deciding that the small commercial webcasters’ initial proposal, combined with the references to “gross revenue” they made during the proceedings, are sufficient to avoid waiver.
Regardless, their objection fails on the merits. The Judges’ determination spelled out five reasons they favored payments based on performances rather than web-caster revenue: (1) performances are more “directly tied to the nature of the right being licensed”; (2) it is difficult to calculate revenue; (3) it is difficult to define revenue unambiguously; (4) “auditing and enforcement” would be more difficult; and (5) payments might not increase with increased usage of copyrights. Id. at 24,-089-90.
An opt-in regime charging a fraction of total gross revenue would address only two of the Judges’ five concerns. It might remove some of the difficulty in calculating and defining revenue, because total gross revenue includes all money received by a webcaster. But it would not address the other problems raised by the Judges: that total gross revenue is not directly tied to the right being licensed; that auditing and enforcement would be difficult; and that usage might increase without a corresponding increase in royalty payments. In an attempt to address these problems, the small commercial webcasters point to the Judges’ subsequent adoption of a “percentage-of-revenue royalty in the SDARS [(i.e., satellite radio)] proceeding.” Commercial Op. Br. 47. Because the Judges adopted it for satellite radio, they argue, the Judges should have adopted it for webcasting. Beyond the ordinary problem of trying to hold an agency to action it takes in a subsequent proceeding, see supra Part II. B.2, the Judges were explicitly reluctant to adopt that approach in the satellite radio proceeding:
Because we have no true per performance fee proposal before us nor sufficient information from evidence of record to accurately transform any of the parties’ proposals into a true per performance fee proposal, the Copyright Royalty Judges conclude that a revenue-*400based fee structure for the SDARS is the most appropriate fee structure applicable to these licensees.
SDARS, 73 Fed.Reg. at 4085. The Judges therefore appear committed to applying per-perfoi'mance royalties for commercial services, and deviated from that preference for satellite-radio licensing only because the parties presented them with no better options.
Finally, it was not error for the Judges to reject the small commercial webcasters’ pleas that paying per performance would wreck their inefficient business models. The Judges made clear they could not “guarantee a profitable business to every market entrant.” Order, 72 Fed.Reg. at 24,088 n. 8. The Judges are not required to preserve the business of every participant in a market. They are required to set rates and terms that “most clearly represent the rates and terms that would have been negotiated in the marketplace between a willing buyer and a willing seller.” 17 U.S.C. § 114(f)(2)(B). If small commercial webcasters cannot pay the same rate as other willing buyers and still earn a profit, then the Judges are not required to accommodate them.
J. Minimum Annual Fee
In addition to setting royalty rates—to be paid by webcasters to the owners of sound recording copyrights—the statute requires there to be “a minimum fee for each ... type of service” provided. 17 U.S.C. § 114(f)(2)(B). These fees are paid by licensees, like the webcasters, to the collective, to cover “administrative costs of the copyright owners in administering the license.” Webcaster I, 67 Fed. Reg. at 45,262. The Judges found “reasonable” “a minimum fee of an annual nonrefundable, but recoupable $500 minimum per channel or station payable in advance.” Order, 72 Fed.Reg. at 24,097.
Commercial webcasters object to the “per channel or station” phraseology for its failure to set a cap on the number of minimum fees a licensee could be required to pay. In particular, they fear that some of their business models might be deemed to contain thousands or tens of thousands of “channels,” making the combined fees prohibitively expensive. Anticipating such an interpretation, DiMA and SoundExchange agreed to cap minimum fees at $50,000 per year per licensee in 2007. (Voluntary negotiation by affected parties is “given effect in lieu of any ... determination by” the Judges. 17 U.S.C. § 114(f)(3).) Because some parties have not contracted around this provision, the issue is not moot and we have power to reach it.
The Board argues that the commercial webcasters waived their right to make any objection to the minimum fees because they did not raise it before the Judges. See 37 C.F.R. § 351.14(b). But even if the commercial webcasters failed to specifically object to the omission of a fee cap, they objected to SoundExchange’s proposal, which included no fee cap. See DiMA and Radio Broadcasters Proposed Findings of Fact and Conclusions of Law ¶¶' 257-258. They also endorsed a 2003 agreement between SoundExchange and DiMA that contained a fee cap (the “2003 Voluntary Agreement”). See DiMA, America Online, Inc., and Yahoo!, Inc. Proposed Findings of Fact and Conclusions of Law ¶¶ 35-38. These proposals “conflictf ]” with the Judges’ determination, which lacks any provision relating to a cap on the number of minimum fees that any licensee may be required to pay. 37 C.F.R. § 351.14(b). Therefore, the arguments were not waived.
On the merits, commercial webcasters raise several objections. They argue the determination was an arbitrary departure *401from Webcaster I, which contained a flat minimum fee of $500 per licensee, without any possibility of raising it for additional channels or stations. 67 Fed.Reg. at 45,-262. They also argue it was arbitrary for the Judges to fail to limit the number of minimum fees that might be paid by a single licensee, when they relied in part on the 2003 Voluntary Agreement, which had such a limit. That agreement charged licensees “a minimum fee of $2,500, or $500 per channel or station ..., whichever is less,” per year. 37 C.F.R. § 262.3(d)(2). Finally, they argue that without a cap, the accumulation of minimum fees could become excessively burdensome.
The Judges are free to depart from precedent if they provide reasoned explanations for their departures, and they discussed minimum fees in their determination. See Order, 72 Fed.Reg. at 24,096-97. But in only two footnotes do they appear aware of the possibility of individual licensees paying more than $500. See id. at 24,097 nn. 38-39. Even in the Judges’ discussion of “side channels”— which included an example of one licensee being charged $1000, id. at 24,097 n. 39—■ they do not seem to anticipate the possibility of a webcaster paying hundreds of thousands of dollars or more. The 2003 Voluntary Agreement the Judges quoted, see id. at 24,097 n. 38, capped minimum fees at $2500 per licensee. Depending on future interpretations of “channel or station,” the Judges’ determination might impose enormous fees on some business models and tiny fees on others, based on regulations that have not yet been defined. Such a regime is arbitrary and does not appear to represent what “would have been negotiated in the marketplace between a willing buyer and a willing seller.” See 17 U.S.C. § 114(f)(2)(B).
Therefore we vacate the minimum fee provision for commercial webcasters, and remand for the Judges to reconsider this portion of their determination.
5. Late Fees
The Judges set a late fee of 1.5% of the royalty payment due for that period, accruing monthly. See Order, 72 Fed.Reg. at 24,107. The commercial webcasters object, arguing that the Judges should have considered “course of dealing” evidence showing that “in practice, rates of such magnitude are very rarely, if ever, imposed.” Commercial Op. Br. 41. The Judges did, however, consider course of dealing evidence. See Order, 72 Fed.Reg. at 24,107. They considered it and were “not persuaded that contracting parties’ ability to waive late fees require[d] rejection of a higher late fee.” Id. They noted that some contracts lacked discretion to grant waiver and observed that “[w]hile waiving a late fee can promote good feelings in a private agreement ..., it has no bearing for a statutory license where copyright owners and performers cannot ... terminate access to their works under the license.” Id. Therefore we affirm the Judges’ determination with respect to late fees.
6. Confidential Information
Webcaster I, 67 Fed.Reg. at 45,-275, codified at 37 C.F.R. § 261, entitled copyright owners to view certain confidential information of the webcasters, but only as part of their “statements of account ... in aggregated form.” 37 C.F.R. § 261.5(c). The collective, which held the information, was prohibited from using it for “any purpose other than royalty collection and distribution and activities directly related thereto.” Id. In the determination under review, the Judges chose to expand access to non-aggregated statements of account, though “limit[ing]” this right “to copyright owners and performers, and *402their agents and representatives.” Order, 72 Fed.Reg. at 24,109.
The commercial webcasters object to this change, saying the information is sensitive and pointing to several marketplace agreeinents with confidentiality agreements similar to the prior regime. The Judges reasonably rejected these arguments. As they made clear in their determination, there was “no finding that [disclosure of] the types of information contained in the statements of account ... would harm the business interests of the reporting Services.” Id. at 24,108. The commercial webcasters’ witness “did not articulate how the information contained in the statements ... could injure the competitiveness of a Service, or otherwise negatively affect its operation.” Id. The Judges also found that the existing confidentiality arrangement negatively “impactfed]” the copyright owners’ “substantive rights under the section 112 and 114 licenses.” Id. Because we ask only whether the Judges acted reasonably based on record evidence, we are easily satisfied that the Judges met their burden on this point.
C. Noncommercial Broadcasters’ Challenges
The Judges set an annual noncommercial rate of $500 per channel or station up to a monthly cap of 159,140 ATH. Beyond this cap, the Judges ordered noncommercial broadcasters (“noncommercials”) to pay the usage rate applicable to the commercial webcasters. The Judges refused to modify an interim order establishing record-keeping requirements for all services, instead deferring a decision on this issue to a future rulemaking.
Noncommercials contend this rate and cap constituted reversible error because noncommercial broadcasting constitutes a different type of service than commercial webcasting and the Act required the Judges to treat different types of services differently, see 17 U.S.C. § 114(f)(2)(B). Specifically, noncommercials contend that the Judges arbitrarily: (1) rejected a flat fee non-interactive non-subscription benchmark for noneommercials in favor of a commercial interactive subscription benchmark; (2) adopted an annual $500 per channel or station minimum fee as necessary to cover SoundExehange’s administrative costs; (3) adopted a use-based fee above a listenership threshold, contrary to their mandate and without evidentiary support; and (4) set the noncommercial usage fee equal to the commercial usage fee without evidentiary support. Noncommercials also contend the Judges erred in refusing to adopt new record-keeping requirements. Although the Judges’ adoption of the $500 fee was unsupported by record evidence, and we remand that issue, we conclude noncommercials’ other contentions are unpersuasive.
1. Rejection of Noncommercials’ Proposed Benchmarks
In determining the noncommercial rates, the Judges rejected, as benchmarks, two proposals offered by noncommercials: (1) rates loosely based on an NPRSoundExchange Agreement covering licenses under Sections 112 and 114 of the Copyright Act for the term October 28,1998 to December 31, 2004 (“NPR Agreement”) and (2) rates for musical works paid by noncommercial radio stations for over-the-air musical work performances under Section 118 of the Act. At the outset, we note that the Judges did not, as noncommercials contend, adopt SoundExchange’s commercial interactive subscription benchmark for noncommercial broadcasting. The Judges in fact rejected the proposed benchmarks of both noncommercials and SoundExchange. Order, 72 Fed.Reg. at 24,099. Although the Judges derived rates above a listenership threshold from the rates appli*403cable to commercial webcasters, the Judges offered noncommercials a huge discount over these rates in the form of a monthly 159,140 ATH allowance that would be covered by a minimum fee.
a. Rejection of the NPR Agreement as a Benchmark
Executed in 2001, the NPR Agreement provided that NPR would pay SoundExchange a flat-fee lump sum for licenses over a six-year period but did not specify the parties’ valuations of any given year of the contract. At the time the agreement was executed, NPR had 410 stations providing streaming content. By the end of the NPR agreement period, NPR had 798 such stations. The agreement was silent as to how stations beyond the original 410 were to be handled.
The Judges rejected the NPR Agreement as a benchmark, finding that it “[did] not provide clear evidence of a per station rate that could be viewed as a proxy for one that a willing buyer and a willing-seller would negotiate today.” Order, 72 Fed.Reg. at 24,098. The Judges gave four reasons. First, the agreement provided for a “lump sum amount to cover the entire 74-month term of the contract with no amount specified for different years.” Id. The Judges noted that there was nothing in the agreement or the record to indicate “the proper attribution of payments for any given year.” The Judges declined noncommercials’ invitation to arrive at this annual per station rate by simply dividing the lump sum amount by the number of years and number of stations covered, because such a proposal accounted for neither the “time value of money in the latter years of the [agreement]” nor “the erosion in the purchasing power of the dollar since 2004.” Id. at 24,098-99. Second, the proposal sought to divide the average yearly rate by 798 stations (the number of NPR stations covered by the agreement in 2004), but the Judges noted that the agreement covered only 410 stations when it was executed and that neither the contract nor the record indicated “how additional stations beyond the 410 covered by the agreement were to be handled.” Id. at 24,098. Depending on which figure was used, the two possible fees would have been approximately one-half or double the amount of the other. Id. Third, the Judges took issue with the fact that nothing in the agreement or the record “indicate^] the parties’ expectations as to levels of streaming.” Id. Fourth, the Judges stated that “none of the final rate proposals of the Noncommercial Webcasters would cover the minimum annual fee determined for Commercial Webcasters.” Id. at 24,099.
In maintaining that this determination was arbitrary, noncommercials object not simply to the Judges’ rejection of the agreement as evidence of the appropriate rate, but to their failure to adopt the agreement as the appropriate benchmark. See, e.g., Noncommercials Op. Br. 20. Congress invited the Judges to consider voluntary marketplace agreements for comparable types of digital audio transmission services and comparable circumstances. 17 U.S.C. § 114(f)(2)(B). Noncommercials contend that the NPR agreement was exactly the type of agreement suggested by Congress, as it covered (1) “the same rights at issue here,” (2) “the same activity: noninteractive Internet simulcast streaming of radio broadcasts,” (3) “the same seller: SoundExchange and its members,” and (4) “the same buyer: NPR, one of the noncommercial broadcasters who brought this appeal.” Noncommercials Op. Br. 17-18. For the reasons that follow, however, the Judges’ decision to reject the agreement as a benchmark was not arbitrary.
*404First, the Judges noted that the number of NPR stations covered by the agreement seemed to have nearly doubled over the course of the agreement, making it unclear which figure it ought to use in calculating a benchmark. Second, given the Judges’ dual concerns that flat fee structures “permit increasing usage without increasing payment,” Order, 72 Fed.Reg. at 24,091, and that this benchmark was proposed to cover all noncommercials, “irrespective of whether they were part of a submarket in the marketplace for non-interactive web-casting that was distinctly different from commercial non-interactive webcasting,” id. at 24,098, the Judges could reasonably conclude the agreement’s silence as to “the parties’ expectations as to levels of streaming,” id., was relevant to their decision to reject the agreement as a benchmark. Finally, the Judges’ statement that the agreement did not serve as a “proxy for one that a willing buyer and a willing seller would negotiate today,” id., evinces concern with the age of the agreement, especially in light of them further emphasis that the lump sum payment covered the period between 1998 and 2004. In addition to the Judges’ concern that the proposal failed to account for the “time value of money,” reference to the agreement’s 1998-2004 coverage dates highlights how outmoded the agreement was. This time period began a little over seven years prior to the Order’s January 1, 2006 applicability date and just a few months short of nine years prior to the Order’s May 1, 2007 effective date. The Judges might have been able to compensate for some of these mathematical deficiencies in calculating a fee. But another shortcoming — the lack of evidence that SoundExchange valued each year of the agreement equally — prevented them from making those adjustments in a rational way.
Noncommercials point out that the Judges adopted rates for commercial web-casting that were based on an interactive commercial subscription benchmark that required mathematical adjustments to deduct the value added by interactivity even though the benchmark was concededly “not ... without any warts.” Id. at 24,-094. Consequently, noncommercials contend that the Judges’ rejection of the NPR agreement as the benchmark was arbitrary because “[ajgencies cannot ‘treat[] type A cases differently from similarly situated type B cases.’ ” Noncommercials Reply Br. 9 (quoting Indep. Petroleum Ass’n v. Babbitt, 92 F.3d 1248, 1260 (D.C.Cir. 1996)). This contention might have merit if the NPR Agreement and the interactive subscriptions benchmark suffered from the same shortcomings. However, the Judges rejected the NPR Agreement for reasons independent of the mathematical adjustments it required. Nevertheless, even if the required mathematical adjustments were the only shortcomings of the agreement, the Judges adopted the benchmark for commercial webcasters based on the testimony of Dr. Michael Pelcovits, SoundExchange’s expert, regarding the hedonic regression analysis that he performed to quantify and deduct the value of interactivity from the interactive commercial subscription benchmark. By contrast, noncommercials presented no evidence quantifying SoundExchange’s yearly valuation of the NPR agreement, the time value of money, or the declining purchasing power of the dollar. Because the Judges had no duty to compensate for these shortcomings, the situations were not “similarly situated” and any purported differences in treatment were not arbitrary. Moreover, even if the Judges erred in rejecting the NPR Agreement because the proposed fee would not cover “the minimum annual fee determined for Commercial Webcasters,” Order, 72 Fed.Reg. at 24,099, see infra Part II.C. l.b, this was harmless error in light of the Judges’ other independent reasons for rejecting the *405agreement. See PDK Labs., Inc. v. U.S. Drug Enforcement Admin., 362 F.3d 786, 799 (D.C.Cir.2004).
b. Rejection of the Musical Works Benchmark
In rejecting the rates paid by noncommercial radio stations for over-the-air musical works performances under Section 118 of the Copyright Act as a benchmark, the Judges explained that “the musical works benchmark proposed by [noncommercials] is based on a very different marketplace characterized by different sellers who are selling different rights.” Order, 72 Fed.Reg. at 24,098. Further, the Judges found “ample evidence in the record ... to controvert the underlying premise of this proposed benchmark that the market for sound recordings and the market for musical works are necessarily equivalent.” Id.; see SoundExchange Pi*oposed Findings of Fact ¶¶ 486-495 (discussing evidence that in comparable markets musical works publishers receive lower royalty rates than do owners of sound recording rights).
Noncommercials do not dispute the Judges’ rationale for rejecting this benchmark, but instead insist it was arbitrary for the Judges not to justify rejecting reliance on the fee structure of these agreements as evidence that a flat-fee structure, regardless of usage, was appropriate for noncommercials. However, because the Judges noted that these agreements were so different from the rights at issue, representing “different sellers who are selling different rights” of different value, the Judges did not act arbitrarily by rejecting these agreements even for this limited purpose. Moreover, the rates set by the Judges did establish a flat-fee structure for the vast majority of noncommercial broadcasters then before them. Order, 72 Fed.Reg. at 24,099-100. The Judges estimated that the monthly 159,140 ATH allowance would create, effectively, a flat-fee structure covering approximately 80% of the NPR stations that streamed over the web. Id. at 24,099-100. While this appeal was pending, NPR was dismissed voluntarily from the case. Order No. 07-1123 (D.C.Cir. Mar. 18, 2009). Because NPR appears to have represented the largest of the noncommercial broadcasters, see Order, 72 Fed.Reg. at 24,099, the allowance may cover all the broadcasting needs of the remaining noncommercials. For instance, the National Religious Broadcasters Noncommercial Music License Committee (“Noncommercial Religious Broadcaster Committee”) stated that “listenership on [Committee-represented stations] is typically small. CDR, [a Committee-represented station], is representative of other [Committee-represented] stations and averages a concurrent online audience of just under 14 listeners.” Noncommercial Religious Broadcasters Committee Proposed Findings of Fact ¶ 6. Assuming thirty-one days in a month, this listenership level would result in 10,416 ATH of streaming content, or only 6.5% of the monthly ATH allowance.
2. Minimum Annual Fee
The Judges adopted an annual $500 per channel or station minimum fee on the rationale that “certainly the bare minimum that such services should have to pay is the administrative cost of administering the license.” Order, 72 Fed.Reg. at 24,099. The Judges set $500 as the fee amount based on their previous conclusion that $500 was the appropriate minimum fee for commercial webeasters and on the lack of record evidence “to suggest that the submarket in which a Noncommercial Webcaster may reside would yield a different administrative cost to SoundExchange as compared to the administrative costs associated with Commercial Webeasters.” Id. Furthermore, the Judges stated that SoundExchange had made no distinction *406between webcasters with regards to the $500 fee and relied on Webeaster I for the notion that all webcasters should pay the same minimum fee for the same license. Order, 72 Fed.Reg. at 24,099. Because there is no record evidence that $500 represented SoundExchange’s administrative cost per channel or station, the Judges’ determination in this regard cannot be sustained.
In discussing the appropriate minimum fee for commercial webcasters, the Judges observed that they had “little evidence of the administrative cost per licensee.” Id. They nevertheless set $500 as the minimum fee for commercial webcasters because SoundExchange proposed the amount, the amount was “substantially lower” than the minimum fees proposed by the various webcasters, id. at 24,096, and “SoundExchange must [have] anticipate^] that [$500] [would] cover its administrative costs even in the absence of royalties,” id. Whatever merit this approach may have for commercial webcasters, the Judges could hardly apply it rationally to noncommercial broadcasters, some of which proposed arrangements with minimum fees well below $500. See, e.g., Noncommercial Religious Broadcasters Proposed Findings of Fact ¶ 30. This is especially so given the lack of evidence supporting SoundExchange’s administrative costs. The most that can be inferred from SoundExchange’s proposal is that its annual per channel or station administrative costs do not exceed $500, not that they equal $500. Additionally, noncommercials suggest there was record evidence refuting the level of SoundExchange’s administrative costs: the NPR Agreement, viewed most favorably to SoundExchange, averages out to a per-year inflation-adjusted rate significantly less than $500 and so undercuts the Judges’ view that a $500 minimum fee represented the lower bound of SoundExchange’s administrative costs. The Judges offered no reason for rejecting the agreement as evidence of SoundExchange’s administrative costs.
The Board’s response on appeal misses the mark. It offers that if there was a lack of evidence of SoundExchange’s administrative costs, the fault lies with noncommercials, which did not obtain discovery and introduce evidence to establish that fact. But this approach is inconsistent with rational decisionmaking, which requires more than an absence' of contrary evidence; it requires substantial evidence to support a decision, see Natural Res. Def. Council, Inc. v. Herrington, 768 F.2d 1355, 1421 n. 63 (D.C.Cir.1985). Furthermore, because SoundExchange did not base its minimum-fee proposal on administrative costs, noncommercials could hardly challenge a theory first presented in the Judges’ determination and not advanced by any participant. In effect, noncommercials cannot be faulted for failing to present “contrary” evidence of administrative costs, because no evidence existed yet to counter.
In sum, it was arbitrary for the Judges, in the absence of record evidence, to apply the $500 fee to noncommercials on the theory that “the bai-e minimum” noncommercials should have to pay is the “administrative cost of administering the license,” and we remand the issue of the appropriate minimum fee for noncommercials.
3. Adoption of a Use-Based Fee Above a Listenership Threshold
Acknowledging that commercial and certain noncommercial webcasters represent “two different segments of the marketplace,” the Judges noted that “agreements produced by the parties in this proceeding covering noncommercial services typically structured payments as flat fees.” Order, 72 Fed.Reg. at 24,091 (citing the NPR Agreement). The Judges also noted “the myriad of characteristics *407that [noncommercials] claim set them apart from commercial broadcasters,” such as non-profit status, different noncommercial mission, and different sources of funding. Id. at 24,098. Nevertheless, the Judges expressed concern that “flat fees do permit increasing usage without increasing payment.” Id. Therefore, to account for these competing considerations, the Judges adopted a flat, per-station rate structure up to a specified cap coupled with a per performance rate for usage exceeding the cap. Id. In imposing the cap, the Judges relied on testimony from SoundExchange’s economic expert, Dr. Erik Brynjolfsson, that as noncommercial stations grow, they begin to compete with commercial stations for listeners. Dr. Brynjolfsson opined that, beyond a certain size, a cap is necessary in order “to reduce ‘the chance that small noncommercial stations mil cannibalize the webcasting market more generally’ and thereby adversely affect the value of the digital performance right in sound recordings.” Id. at 24,097 (quoting Brynjolfsson Written Rebuttal Testimony at 42). The Judges agreed, concluding as a matter of “pure economic rationale based on the willing buyer/willing seller standard,” that the proliferation of a different price for noncommercials “must include safeguards to assure that, as the submarket for noncommercial webcasters that can be distinguished from commercial webcasters evolves, it does not simply converge or overlap with the submarket for commercial webcasters.” Id. at 24,097-98. The Judges explained that this “convergence” theory approximates the circumstances “in which willing buyers and willing sellers would have a meeting of the minds that would result in a lower rate than the rate applicable to the general commercial webcasting market.” Id. at 24,100.
Noncommercials contend that the record evidence and the Judges’ reasoning demonstrate that the only appropriate fee structure for noncommercials is a flat fee. However, Dr. Brynjolfsson’s testimony provided evidence against a plain flat-fee structure beyond a certain listenership threshold, and the Judges’ decision to adopt a listenership threshold was rationally based on Dr. Brynjolfsson’s testimony of how the willing buyer/wdlling seller calculation would change as a noncommercial broadcaster grew' and competed with a commercial webcaster for listeners. Also, the Judges did set a flat fee structure for the vast majority of noncommercials, most of which were not expected to exceed the specified cap.
Noncommercials also contend that the Judges legally erred by substituting a theory of convergence for the willing buyer/willing seller standard. As the Judges stated, however, it relied on convergence as a proxy for what a willing buyer and willing seller would negotiate in the marketplace. Id. at 24,100. To the extent noncommercials suggest that this statement constituted “lip service” to the statutory standard, as “competition was the beginning and end of the Board’s inquiry,” Noncommercials Op. Br. 26 n. 8, this criticism is no criticism at all because competition certainly would affect the actions of a willing seller, as the Judges noted. Even assuming the Judges should have “recognized noncommercial services’ unwillingness to accept a commercial rate in a marketplace transaction,” id. 26, the Judges did not set a “commercial rate” for the noncommercials. It set a per-performance rate only above a listenership threshold. Noncommercials are given a monthly discount of 159,140 ATH on the commercial rate. Moreover, that assertion, as do many others made by noncommercials, speaks only to the willingness of the buyer to enter the transaction and says nothing of the seller. The Judges, taking both buyers and sellers into account, came to a *408reasonable compromise between the two positions.
Noncommercials further contend the Judges arbitrarily selected listener-ship levels as the measure of alleged convergence. They maintain “[f]ocusing on listenership rather than the standard Congress set is, by definition, arbitrary” because “agency action is arbitrary if it ‘relied on factors which Congress has not intended it to consider.’ ” Noncommercials Op. Br. 28 (quoting Motor Vehicle Mfrs. Ass’n v. State Farm Mut. Auto. Ins. Co., 463 U.S. 29, 43, 103 S.Ct. 2856, 77 L.Ed.2d 443 (1983)). As the Judges could rationally conclude that competition for listeners would be a major factor affecting convergence, however, it was also rational for them to conclude that competition could be assessed by looking to listener-ship. The Judges did not “reify] on factors which Congress has not intended it to consider,” State Farm, 463 U.S. at 43, 103 S.Ct. 2856, for competition is relevant to the willing buyer/willing seller standard. Still, noncommercials maintain that the arbitrariness of setting 159,140 ATH as the convergence point underscores the arbitrariness of using listenership to assess convergence. Even assuming the Judges’ decision to set the convergence point at 159,140 ATH was arbitrary, it would not undermine their approach of using listenership to assess convergence: miscalculating a convergence point does not undermine the validity of a convergence approach any more than an economics student who miscalculates the equilibrium point on a demand curve undermines the notion that such a point exists.
Finally, noncommercials contend the evidence upon which the Judges relied to support convergence does not demonstrate convergence. While noncommercials make several challenges on this score, their “most fundamental ]” objection is that this evidence “related to a few of the largest NPR stations.” Noncommercials Op. Br. 29. The Judges explained, however, that the “evidence of convergence in the record appears to apply more clearly to the stations at the larger end of the range of NPR station size,” Order, 72 Fed.Reg. at 24,099. Under these circumstances, the Judges reasonably looked to evidence of the largest NPR stations for evidence of convergence. Although noncommercials protest that the Judges cited very little non-NPR evidence in support of convergence, the Judges need not have cited any non-NPR evidence to reach a rational result; basing their determination on NPR evidence from large NPR stations made logical sense because “without evidence relating to the largest NPR stations, there would be very little evidence of convergence at all,” Noncommercials Op. Br. 29. In other words, this evidence constituted the most, if not only, relevant evidence. To show this determination was arbitrary, noncommercials had to demonstrate that the Judges misconstrued the evidence of convergence or else failed to consider important evidence that undermined their understanding of the convergent effect. The most noncommercials did, however, was to assert that the NPR Agreement undermined the theory of convergence because the agreement made no distinctions based on listenership. As noted, however, the Judges rejected the NPR Agreement’s flat-fee structure in favor of a structure that prohibited, beyond a threshold, increasing usage without increasing payment. Also, the ATH threshold imposed as a result of the adopted convergence theory would appear to apply only to large NPR stations, lending further support to the Judges’ use of and reliance on evidence from the larger NPR stations. Noncommercials thus fail to show the Judges’ determination in this regard was arbitrary.
*409 k. Adoption of a Noncommercial Usage Rate Above a Listenership Threshold Equal to the Commercial Rate
Noneommercials contend that setting the noncommercial usage fee equal to the commercial usage rate was arbitrary, capricious, and without record support. But the rate structures are not equal. While the prevailing rates for noncommercials that exceed a listenership threshold are equal to those of commercial webcasters, noneommercials’ contention attempts to obfuscate the fact that they are given a 159,140 ATH discount over the prevailing commercial rate. Because noncommercials have made no objection that such an allowance is trivial, this contention is unpersuasive. To the extent that noncommercials’ position is that the commercial rate itself is arbitrary, it lacks merit. See stipra Part II.B.2.
5. Record-Keeping Requirements
Although the parties introduced evidence as to record-keeping requirements, the Judges deferred a determination to a later rulemaking and left in place an interim rule. Order, 72 Fed.Reg. at 24,109-10. Although noncommercials challenge this action as arbitrary and capricious, as they recognize, the Judges have control of their docket. See 17 U.S.C. § 803(c)(3). In declining to resolve the question in the current proceeding, the Judges observed that the evidence presented “was vague and unsubstantiated and went little beyond the assertion that there are some costs associated with recordkeeping.” Order, 72 Fed.Reg. at 24,109. The Judges noted there “would be ample opportunity to again address the Services’ costs in a future rulemaking. The ability to influence and adjust the costs of recordkeeping is far more direct in that context than this rate determination proceeding and is more properly handled there.” Id. at 24,110. The Judges have statutory discretion to make this determination and administrative discretion to control their own docket. See Telecomms. Resellers Ass’n v. FCC, 141 F.3d 1193, 1196 (D.C.Cir.1998) (citing GTE Serv. Corp. v. FCC, 782 F.2d 263, 273-74 (D.C.Cir.1986)). Their exercise of this discretion here was not arbitrary.
D. Royalty Logic’s Challenges
Finally, we address Royalty Logic’s challenges to the substance of the Judges’ determination.
1. Designation of a Single Collective
As discussed above, the Judges designated a single organization—known as the “collective”—to receive royalties from licensees and distribute payments to copyright owners, performers, and any agents designated on their behalf to receive such payments. The Judges selected SoundExchange, rather than Royalty Logic, to serve this function. Royalty Logic argues that the Judges’ designation of only one collective was contrary to the statute.3 We disagree.
Royalty Logic relies principally on 17 U.S.C. § 114(e)(1), which allows copyright owners and licensees, “in negotiating statutory licenses,” to “designate common agents on a nonexclusive basis to negotiate, agree to, pay, or receive payments.” Royalty Logic contends that the statute confers on copyright owners or their designated agents the right to receive royalty payments directly from licensees. It also argues that Congress’s *410use of the word “nonexclusive” to describe the designated agents means that the Judges could not give a single entity the exclusive ability to receive payments. But this statute does not speak to the Judges’ authority. By its terms, it simply exempts copyright owners and licensees from “any provision of the antitrust laws” to allow them to designate common agents to negotiate rates and terms under the statutory license that will apply in lieu of the Judges’ decision. Id. Moreover, the statute merely authorizes copyright owners to designate agents to “receive” royalty payments; it does not mandate that those payments come directly from licensees rather than an intermediary collective. Id.
Royalty Logic also argues that, by giving the Judges the authority to set “terms of royalty payments,” id. § 114(f)(2)(A), Congress meant them to determine only how and when payments are made. But other provisions of the statutory licensing scheme make clear that Congress contemplated a role for the Judges in deciding who would actually receive royalty payments. For example, in providing for the continuity of royalty rates and terms while a motion for reconsideration is pending before the Judges, the statute requires “the entity designated by the Copyright Royalty Judges to which such royalties are paid” to return any excess payments once the motion is resolved. Id. § 803(c)(2)(E)(iii). Likewise, payments to “the entity designated by the Copyright Royalty Judges” must continue during the pendency of an appeal to this court, and that entity must return excess payments following the conclusion of the appeal. Id. § 803(d)(2)(C)(ii). Both provisions presuppose that, in setting the rates and terms of the statutory license, the Judges will “designate” a single “entity” to receive royalty payments. Following the “fundamental canon of statutory construction that the words of a statute must be read in them context and with a view to their place in the overall statutory scheme,” Davis v. Mich. Dep’t of Treasury, 489 U.S. 803, 809, 109 S.Ct. 1500, 103 L.Ed.2d 891 (1989), we cannot accept Royalty Logic’s unduly narrow reading of the word “terms” in Section 114(f)(2)(A).
Thus, in selecting SoundExchange as the sole collective, the Judges fulfilled Congress’s expectation that they would designate a single entity to receive royalty payments from licensees. And contrary to Royalty Logic’s argument, the Judges have not deprived copyright owners of the right to select their own receiving agents. Any copyright owner is free to negotiate, on its own or through an agent, for a method of payment that bypasses SoundExchange. But in the absence of a privately negotiated agreement, the Judges may designate a single entity to receive, process, and distribute royalty payments under the statutory license.
2. Account Statements
Royalty Logic also challenges the Judges’ decision — made in a separate proceeding — to limit it to inspecting licensees’ account statements at SoundExchange’s offices rather than receiving the statements directly. See Notice and Record-keeping for Use of Sound Recordings Under Statutony License, 71 Fed.Reg. 59,010, 59,019 (Oct. 6, 2006). That decision is not within the scope of this appeal, and we have no authority to review it. Royalty Logic could have asked the Judges to reconsider the record-keeping rules during the proceeding on review. See 17 U.S.C. § 803(c)(3) (Judges, as part of any determination, “may specify notice and record-keeping requirements ... that apply in lieu of those that would otherwise apply”). But Royalty Logic did not raise the record-keeping issue in this proceeding and may not challenge it as part of this appeal.
*411III. Conclusion
For the reasons given above we vacate the $500 minimum fee as arbitrary, capricious, and not supported by record evidence, and remand that portion of the determination to the Copyright Royalty Judges for further proceedings not inconsistent with this opinion. All other portions of the determination are affirmed.
So ordered.
. Another group of appellants, including Bonneville International Corp. and National Religious Broadcaster Music License Committee, joined by intervenor National Association of Broadcasters, also filed briefs in this case. Before oral argument, this court granted the appellants’ motion for voluntary dismissal and granted the intervenor's request to be dismissed as a party. Order Dismissing Case No. 07-1179 (D.C.Cir. Feb. 27, 2009).
. Appellants also contend that rejection of the NPR Agreement was inappropriate because § 114(f)(2)(B) prohibits the Judges from considering agreements for interactive services. Noncommercials Reply Br. 4-5; Bonneville Reply Br. 7-8. Section 114(f)(2)(B) invites the Judges to consider comparable "voluntary license agreements described in subparagraph (A).” 17 U.S.C. § 114(f)(2)(B). Sub-paragraph (A) in turn identifies "public performances of sound recordings by means of eligible nonsubscription transmission services and new subscription services specified by subsection (d)(2).” Id. § 114(f)(2)(A). Subsection (d)(2) stales that "performancefsj of a sound recording ... shall be subject to statutory licensing, in accordance with subsection (0 if [among other things] the transmission is not part of an interactive service.” Id. § 114(d)(2)(A)(l). Therefore, the argument goes, Section 114(f)(2)(B) prohibited consideration of the interactive benchmark that the Judges ultimately adopted.
This argument comes too late. Appearing for the first time in the reply briefs to this court, see Students Against Genocide v. Dep’t of State, 257 F.3d 828, 835 (D.C.Cir.2001), this argument was not presented to the Judges by any party involved in this litigation and may not be presented for the first time on appeal, 37 C.F.R. § 351.14(b); see also United Transp. Union v. Surface Transp. Bd., 114 *398F.3d 1242, 1244-45 (D.C.Cir. 1997). The Bonneville appellants (who were dismissed •voluntarily from this appeal) maintained that this argument was presented to the Judges in the DiMA and Member Companies Joint Proposed Findings of Fact 11¶ 88, 90, 115 n. 23. However, although the three cited paragraphs referred to the interactive benchmark and argued that it was "not comparable” to the licenses at issue because it covered "rights beyond those granted by the statutory license,” id. ¶ 90, none suggested that the Act bars the Judges from considering the interactive benchmarks as a matter of law, much less for the complex statutory construction arguments outlined in the reply briefs to this court. The paragraphs instead stated that the interactive benchmark was irrelevant because it was too dissimilar from the statutory license at issue, not because the statute precluded the Judges from considering it at all.
. In its reply brief, Royalty Logic argues that even if a single collective is permissible, the Judges erred by selecting SoundExchange to fill that role. Again, Royalty Logic has forfeited this argument by failing to raise it in its opening brief. See Sw. Airlines, 554 F.3d at 1072.