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Many scholars of congressional elections have argued that an increase in the diversity of preferences in a district increases the level of electoral competition. We argue that there is strong reason to believe that the opposite is true. As the diversity of preferences increases, and thus as the complexity of the electoral landscape increases, challengers will have a more difficult time locating an optimal platform when facing an incumbent. Using data form the 2000 National Annenberg Election Study, we construct a measure of district complexity for U.S. House districts and test whether the entry of quality challengers and the incumbent‟s share of the two-party vote are affected by the complexity of the electoral landscape. We find strong support for the hypothesis that complexity benefits incumbents for both indicators of electoral competition. 2 Many studies of congressional elections characterize district preferences along a single partisan or ideological dimension. One implication of this perspective is that competition between candidates is reduced to a simple problem: locate at the position o