Stronger selection on males has the potential to lower the deleterious mutation load of females, reducing the cost of sex. However, few studies have directly quantified the strength of selection for both sexes. As the magnitude of inbreeding depression (ID) is related to the strength of selection, we measured the cost of inbreeding for both males and females in a laboratory population of Drosophila melanogaster. Using a novel technique for inbreeding, we found significant ID for both juvenile viability and adult fitness in both sexes. The genetic variation responsible for this depression in fitness appeared to be recessive for adult fitness (h ¼ 0.11) and partially additive for juvenile viability (h ¼ 0.29). ID was identical across the sexes in terms of juvenile viability but was significantly more deleterious for males than females as adults, even though female X-chromosome homogamety should predispose them to a higher inbreeding load. We estimated the strength of selection on adult males to be 1.24 greater than on adult females, and this appears to be a consequence of selection arising from competition for mates. Combined with the generally positive intersexual genetic correlation for inbred lines, our results suggest that the mutation load of sexual females could be meaningfully reduced by stronger selection acting on males.