Cite as: 526 U. S. 473 (1999)
Opinion of the Court
dictional prohibition" barring the tribal court from determining its jurisdiction over Price-Anderson Act claims. Id., at 617-620. Judge Kleinfeld dissented, concluding that the unappealed partial injunctions against litigating Price-Anderson Act claims in tribal court should be treated as law of the case, that all of the tribal-law claims were actually Price-Anderson Act claims, and that exhaustion was not required. Id., at 620-622. We granted certiorari, 525 U. S. 928 (1998), and now vacate and remand.
II
There is one matter preliminary to the principal issue. Because respondents did not appeal those portions of the District Court's orders enjoining them from pursuing Price-Anderson Act claims in Tribal Court, those injunctions were not properly before the Court of Appeals, which consequently erred in addressing them. We have repeatedly affirmed two linked principles governing the consequences of an appellee's failure to cross-appeal. Absent a cross-appeal, an appellee may "urge in support of a decree any matter appearing in the record, although his argument may involve an attack upon the reasoning of the lower court," but may not "attack the decree with a view either to enlarging his own rights thereunder or of lessening the rights of his adversary." United States v. American Railway Express Co., 265 U. S. 425, 435 (1924); see also Union Tool Co. v. Wilson, 259 U. S. 107, 111 (1922). We recognized the latter limitation as early as 1796, see McDonough v. Dannery, 3 Dall. 188, 198, and more than 60 years ago we spoke of it as "inveterate and certain," Morley Constr. Co. v. Maryland Casualty Co., 300 U. S. 185, 191 (1937).
The Court of Appeals acknowledged the rule, but, in light of the natural temptation to dispose of the related questions of jurisdiction and exhaustion at one blow, still thought it could take up the unappealed portions of the District Court's orders sua sponte because "important comity considera-
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