We provide a set of new models of three different processes by which political parties nominate candidates for a general election: nominations by party leaders, nominations by a vote of party members, and nominations by a spending competition among potential candidates. We show that more extreme outcomes can emerge from spending competition than from nominations by votes or by party leaders, and that non-median outcomes can result via any of these processes. When voters (and potential nominees) are free to switch political parties, then median outcomes ensue when nominations are decided by a vote but not when nominations are decided by spending competition.