Theory and evidence on political party competition in the U. S. Congress and its effect on the compositions of committees is considered. Parties compete over multiple policy dimensions by allocating party members to committees. The leadership of each party simultaneously and non-cooperatively selects its committees’ membership in order to maximize the joint utility of its members, taking into account how the committee membership affects the legislation adopted by the legislature. Parties are constrained both by institutional rules and by the heterogeneity of party members’ preferences in their allocation of members across committees. These restrictions mean that to gain an edge in one policy dimension, a party must give ground elsewhere. Interest group ratings from the U.S. House of Representatives provide evidence that the parties stack of committees in a manner consistent with the predictions of the theoretical model. Indeed, tests of alternative hypotheses reveal that these hypotheses explain at best only half of the committees in the U. S. Congress, while the party competition hypothesis is consistent with the overall structure of the committees.