Female-limited intraspecific colour variation is a widely distributed trait within damselflies. Typically, one morph resembles the male (the andromorph) whereas one, or sometimes more, do not [the heteromorph(s)]. While several selective explanations have been offered, such as decreased harassment by males balanced by predation or lack of mating success, field data indicate that andromorphs and heteromorphs mate at equal frequencies in the field, and survive equally well. In this paper, I use a signal detection model to characterize the properties of a new male-mimicry hypothesis, in which andromorphs are not only more similar to males, but are also encountered more by males. I show that this combination of frequency-dependent and frequency-independent factors readily combine to generate a balanced polymorphism. The model explains why morphs have similar mean mating frequencies, why the experimentally observed mating preferences of males vary between ponds, and why the frequency of andromorphs tends to rise with sex ratio.