Mating preferences for genetic compatibility strictly depend on the interplay of the genotypes of potential partners and are therein fundamentally different from directional preferences for ornamental secondary sexual traits. Thus, the most compatible partner is on average not the one with most pronounced ornaments and vice versa. Hence, mating preferences may often conflict. Here, we present a solution to this problem while investigating the interplay of mating preferences for relatedness (a compatibility criterion) and large body size (an ornamental or quality trait). In previous experiments, both sexes of Pelvicachromis taeniatus, a cichlid fish with mutual mate choice, showed preferences for kin and large partners when these criteria were tested separately. In the present study, test fish were given a conflicting choice between two potential mating partners differing in relatedness as well as in body size in such a way that preferences for both criteria could not simultaneously be satisfied. We show that a sex-specific trade-off occurs between mating preferences for body size and relatedness. For females, relatedness gained greater importance than body size, whereas the opposite was true for males. We discuss the potential role of the interplay between mating preferences for relatedness and body size for the evolution of inbreeding preference.