The hypothesis that female extra-pair reproduction in socially monogamous animals reflects indirect genetic benefits requires that there be additive and/or nonadditive genetic variance in fitness. However, the specific hypotheses that male extra-pair reproductive success (EPRS) shows additive genetic variance (V(A)), heritability (h2), or inbreeding depression, and hence that females could acquire indirect genetic benefits through increased EPRS of sons, have not been explicitly tested. We used comprehensive genetic pedigree data from song sparrows (Melospiza melodia) to estimate V(A), h2, and inbreeding depression in the number of extra-pair offspring a male sired per year and the probability that a male would sire any extra-pair offspring per year. Inbreeding depression was substantial: more inbred males sired fewer extra-pair offspring and were less likely to sire any extra-pair offspring. In contrast, estimates of V(A) and h2 were close to 0, although 95% credible intervals were relatively wide. These data suggest that females could accrue indirect genetic benefits, in terms of increased EPRS of outbred sons, by mating with unrelated social or extra-pair mates. In contrast, any indirect benefit of extra-pair reproduction in terms of producing sons with high additive genetic value for EPRS is most likely to be small.