The sexy-sperm hypothesis predicts that females obtain indirect benefits for their offspring via polyandy, in the form of increased fertilization success for their sons. I use a quantitative genetic approach to test the sexy-sperm hypothesis using the field cricket Teleogryllus oceanicus . Previous studies of this species have shown considerable phenotypic variation in fertilization success when two or more males compete. There were high broad-sense heritabilities for both paternity and polyandry. Patterns of genotypic variance were consistent with X-linked inheritance and/or maternal effects on these traits. The genetic architecture therefore precludes the evolution of polyandry via a sexy-sperm process. Thus the positive genetic correlation between paternity in sons and polyandry in daughters predicted by the sexy-sperm hypothesis was absent. There was significant heritable variation in the investment by females in ovaries and by males in the accessory gland. Surprisingly there was a very strong genetic correlation between these two traits. The significance of this genetic correlation for the coevolution of male seminal products and polyandry is discussed.