Summary: This paper analyzes duopolistic price-leadership games in which firms have capacity constraints. We provide a complete characterization of price leader equilibria under quite general assumptions on demand and for arbitrary capacities. We show that when capacities are in the range where the simultaneous-move price-setting game (with efficiently rationed demand) yields a mixed-strategy solution the large firm is indifferent between being a leader, a follower, or moving simultaneously. The small firm, while indifferent between being a leader and moving simultaneously, strictly prefers to be a follower. This motivates the discussion of games of timing with ex-post inflexible prices in which the large firm becomes an endogenously determined price leader. We thus provide a game-theoretic model of dominant-firm price leadership.