Much debate surrounds the exact rules that influence mating behaviour, and in particular the selective forces that explain the evolution of female preferences. A key example is the lek paradox, in which female choice is expected rapidly to become ineffective owing to loss of additive genetic variability for the preferred traits1-3. Here we exploit a remarkable system in which female fur seals exert choice by moving across a crowded breeding colony to visit largely static males. We show that females move further to maximize the balance between male high multilocus heterozygosity and low relatedness. Such a system shows that female choice can be important even in a strongly polygynous species, and at the same time may help to resolve the lek paradox because heterozygosity has low heritability and inbreeding avoidance means there is no single 'best' male for all females.