The dispute in this case is among three television broadcasters: Cosmos of Montgomery, Alabama (a VHF broadcaster); Eagle of Columbus, Georgia (a UHF broadcaster); and WTVY of Dothan, Alabama (a VHF broadcaster). The first of these, Cosmos, has been granted FCC permission to move its transmission facilities some twelve miles east-southeast of their former site, and to increase the height of its antenna to roughly double its former size. The latter two, having opposed the grant, now seek direct review of the issuance of the construction permit.
Cosmos’s application was initially denied by the Hearing Examiner on the ground that the plan would have an adverse impact on UHF broadcasters, particularly Eagle.1 The Review Board disagreed with the Examiner in this respect, concluding that there would be only minimal impact on UHF competitors, and that this was outweighed by the substantial improvement in VHF service that the new facilities would *18achieve. The denial of approval for the plan was, however, affirmed by the Board on a different ground, namely, that Cosmos had not adequately shown that its expanded service would be responsive to community interests and needs, as required by Suburban Broadcasters, 30 FCC 1021 (1961), aff’d sub nom., Henry v. FCC, 112 U.S.App.D.C. 247, 302 F.2d 191 (1962).
After granting review of only this part of the Board’s decision, the Commission remanded the case to the Board in order to allow Cosmos to amend its Suburban showing in the light of the Commission’s newly-issued Primer on Ascertainment of Community Problems by Broadcast Applicants. 27 FCC 2d 650 (1971). Petitioners requested that on remand they also be allowed to update the record by adducing new evidence relevant to the UHF impact issue,2 but this request was denied and the Board’s adverse resolution of that issue was allowed to stand. After further evidentiary hearings on the Suburban issue, the Board resolved it in Cosmos’s favor and approved construction of the new antenna. The Commission this time upheld the Board, and this appeal followed. For the reasons stated below, we affirm.
Petitioners first attack the merits of the adverse finding with respect to the UHF impact of the proposed construction. As we have said before, the protection of UHF broadcasting is the Commission’s policy, not ours; and it is free to apply it in any way that is not arbitrary or capricious. WCOV, Inc. v. FCC, 150 U.S.App.D.C. 303, 464 F.2d 812, 815 (1972). We see no arbitrariness here. Petitioners claim that the Review Board, misinterpreting the Commission’s then-recent Mount Vernon decision,3 imposed “a new and higher standard of proof” that the Commission, so it is alleged, later disavowed. In fact the Mount Vernon decision was upheld upon reconsideration, 22 FCC 2d 222 (1970), and we find no subsequent repudiation by the Commission of the language in it which was relied on by the Review Board, i. e., that requiring “some substantial specific impact on UHF.” See 17 RR 2d at 1630. In any event, it is not clear that the Review Board held petitioners even to that standard, since it found that in this case “only minimal impact on UHF ha[d] been shown.” J.A. 54.
Petitioners’ second contention is that when it remanded the case for further proceedings on the Suburban issue, the Commission should have allowed the UHF impact issue to be reopened as well. It is true that a rehearing of particular issues may be made necessary by new and relevant evidence. See, e. g:, WMOZ, Inc. v. FCC, 120 U.S.App.D.C. 103, 344 F.2d 197 (1965). But this is true only where the new evidence “might have gone far toward undermining the basis for the Commission’s conclusion.” Id. at 198. See also WEBR, Inc. v. FCC, 136 U.S.App.D.C. 316, 420 F.2d 158, 166 (1969). No description has been offered of any new evidence that would “undermine” the Board’s UHF impact finding in this case; petitioners simply assert that the new evidence would be “harder” and therefore might undermine that finding. This is not enough to establish an abuse of the Commission’s discretion to consider the matter closed.4 Nor does the Commission appear to us to have been unfaithful to its own decision in Daily Telegraph Printing Co., 40 FCC 2d 109 (1973). It there remanded a construction permit proceeding for further *19evidence on UHF impact, but such a remand of the UHF issue (as opposed to some other issue in the case) was already required for other and stronger reasons.5
Petitioners also claim that a remand of the UHF impact issue was required by the fact that Cosmos was given a second chance on an issue on which it had previously failed, i. e., the Suburban issue. They insist that the reopening of one issue made it expedient to reopen the other, and unfair not to do so. The short answer is that, to a busy agency, limited further proceedings are preferable to more extensive further proceedings, and that the agency is free to follow that preference where the claims for a second chance vary in strength as much as do those of Cosmos and petitioners in this case. Cosmos was permitted to supplement its showing of community needs because the question of what precisely was required of it in this respect had been a matter of some confusion that the issuance of the Commission’s Primer had only later dispelled. Petitioners have no claim of comparable merit.6
Petitioners’ strongest claim is that the Commission has never given sufficient reasons for its denial of their request for a remand on the UHF impact issue. That request was first made in a “Petition for Reconsideration” of the Commission’s initial decision remanding on the Suburban issue but denying review on the UHF impact issue. This petition was denied on the ground that a Commission rule bars reconsideration of any denial of review for which reasons were not given, as they were not in this case. See 47 C.F.R. § 1.115(g) (1973). Petitioners then filed a request for waiver of the rule barring reconsideration. The Commission denied the request for waiver because petitioners had “not shown good cause for their request, [nor] made any significant showing affecting the merits of the actions taken in this proceeding.” (Emphasis added.)7 Charging that this response by the Commission is inadequate, petitioners point to the requirement of 47 U.S.C. § 405 (1970) that a denial by the Commission of a petition for rehearing be accompanied by “a concise statement of the reasons therefor.” See also 5 U.S.C. § 555(e) (1970); 47 C.F.R. § 1.106(j)(1973).
Reliance by the Commission on its own rule against reconsideration would in itself be a clearly inadequate reason for the refusal to rehear. The rule may have some justification where the summary denial of review reflects a Commission judgment that the appeal was frivolous, and where the request for rehearing is only a rehash of the same, frivolous arguments. But the fact that no reasons were thought necessary when the Commission first heard the case is no basis for rejecting a proffer of new evidence.8
*20In this case, however, the Commission did not stand solely on its procedural rule. It added, albeit in an exiguous manner, that it saw nothing in what petitioners offered to unsettle its initial decision to deny review. In view of the weakness of the case for remand, but only for this reason, we think that what the Commission said here was enough.9
Petitioners’ final claim is that the Commission erred in remanding to allow Cosmos to bring its Suburban showing into compliance with the Commission’s Primer. In so doing the Commission was extending to Cosmos a privilege generally available to applicants in pending cases.10 Petitioners object on the ground that Cosmos had put in only a “desultory” performance on the Suburban issue, and that this “stemmed from its indifference to the Commission’s requirements in this area — rather than from any uncertainty or confusion.”
The opinion of the Review Board reports, ' however, that Cosmos personally interviewed some thirty-seven community leaders and followed these up with a questionnaire mailed to some ninety-two. That there was no gross delinquency on Cosmos’s part is suggested by the fact that the Hearing Examiner resolved the issue in Cosmos’s favor. Cosmos’s principal difficulty seems to have been that it assumed that, since it was merely extending its coverage to an area larger than but encompassing the area it already served, it need not propose any programming changes, but could rest on the appropriateness of its existing service to its old constituency. The Hearing Examiner agreed; the Review Board did not.11