Female mate choice influences the maintenance of genetic variation by altering the mating success of males with different genotypes. The evolution of preferences themselves, on the other hand, depends on genetic variation present in the population. Few models have tracked this feedback between a choice gene and its effects on genetic variation, in particular when genes that determine offspring viability and attractiveness have dominance effects. Here we build a population genetic model that allows comparing the evolution of various choice rules in a single framework. We first consider preferences for good genes and show that focused preferences for homozygotes evolve more easily than broad preferences, which allow heterozygous males high mating success too. This occurs despite better maintenance of genetic diversity in the latter scenario, and we discuss why empirical findings of superior mating success of heterozygous males consequently do not immediately lead to a better understanding of the lek paradox. Our results thus suggest that the mechanisms that help maintain genetic diversity also have a flipside of making female choice an inaccurate means of producing the desired kind of offspring. We then consider preferences for heterozygosity per se, and show that these evolve only under very special conditions. Choice for compatible genotypes can evolve but its selective advantage diminishes quickly due to frequency-dependent selection. Finally, we show that our model reproduces earlier results on selfing, when the female choice strategy produces assortative mating. Overall, our model indicates that various forms of heterozygote-favouring (or variable) female choice pose a problem for the theory of sexual ornamentation based on indirect benefits, rather than a solution.