Scholars of congressional elections have argued that an increase in constituent diversity increases the level of electoral competition. Following models of boundedly rational candidates, we argue that there is strong reason to believe that the opposite is true. As the complexity of the electoral landscape increases, challengers will have a more difficult time locating an optimal platform when facing an experienced incumbent. Using data from the 2000 National Annenberg Election Study, we construct a novel 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, which stands in contrast to most of the existing literature on diversity and incumbent performance.