In many cooperatively-breeding species females mate extra-group, the adaptive value of which remains poorly understood. One hypothesis posits that females employ extra-group mating to access mates whose genotypes are more dissimilar to their own than their social mates’, so as to increase offspring heterozygosity. We test this hypothesis using life-history and genetic data from 36 cooperatively-breeding white-browed sparrow weaver (Plocepasser mahali) groups. Contrary to prediction, a dominant female’s relatedness to her social mate did not drive extra-group mating decisions and, moreover, extra-group mating females were significantly more related to their extra-group sires than their social mates. Instead, dominant females were substantially more likely to mate extra-group when paired to a dominant male of low heterozygosity, and their extra-group mates (typically dominants themselves) were significantly more heterozygous than the males they cuckolded. The combined effects of mating with extra-group males of closer relatedness but higher heterozygosity resulted in extra-group-sired offspring that were no more heterozygous than their within-group-sired half-siblings. Our findings are consistent with a role for male-male competition in driving extra-group mating and suggest that the local kin structure typical of cooperative breeders could counter potential benefits to females of mating extra-group by exposing them to a risk of inbreeding.