Summary: I study a directed search model of oligopolistic competition, extended to incorporate general capacity constraints, congestion effects, and pricing based on ex post demand. In the presence of any one of these ingredients, the Bertrand paradox fails to hold. Hence, despite the emphasis that has been placed by the literature on sellers' capacity constraints as a resolution to the paradox, the existence of such constraints is only a subcase of a general class of environments where the paradox fails. Specifically, Bertrand's paradox will not arise whenever the buyers' expected utility from visiting a seller is decreasing in that seller's realized demand.