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.