Most spatial models of competing species assume symmetries in the spatial scales of dispersal and interactions. This makes analysis tractable, and has led to the conclusion that segregation of species in space does not promote coexistence. However, these symmetries leave parts of the parameter space uninvestigated. Using a moment-approximation method, we present a spatial version of the Lotka–Volterra competition equations to investigate effects of removing symmetries in the distances over which individuals disperse and interact. Some spatial segregation of the species always comes about due to competition, and such segregation does not necessarily lead to coexistence. But, if interspecific competition occurs over shorter distances than intraspecific competition (heteromyopia), spatial segregation becomes strong enough to promote coexistence. Such coexistence is most likely when the species have similar dynamics, in contrast to the competition–colonization trade-off that requires large competitive differences between species.