Population genetic models have shown that female choice is a potential cause of the evolution of male display. In these models the display is assumed to be the immediate object of female choice. Here I present an explicit genetic model that shows that male display can evolve as a consequence of female choice even when the display is not the immediate object of choice. When females initially base their preferences on the existence of variance in a cue that is correlated with male viability, a rare display can evolve to fixation if it amplifies the previously recognized differences in males, (i.e. if it increases the resolution power of females with respect to the original cue). By definition, amplifying displays (or amplifiers) increase mating success of the more viable males and decrease mating success of the less viable males. Therefore, the higher the frequency of the preferred, more viable males, the more likely it is that amplifiers will evolve to fixation. The evolution of an amplifier is further facilitated by a genetic association that is built up between the amplifier allele and the more viable allele. If the expression of the amplifier is limited to the more viable males, the amplifier will evolve to fixation provided only that the change in total fitness to the more viable males (higher mating success, lower viability), is positive.