In field and laboratory studies of birds, positive associations between male phenotype and success at obtaining extra-pair copulations or extra-pair fertilizations are often interpreted as providing evidence that females are using extra-pair copulations to obtain indirect benefits for their offspring, either through genes for increased viability, or for a fisherian mating advantage. I describe a simple model, in which functional fertility (the success of ejaculates in fertilizing eggs) covaries with male phenotype, which can explain the observed associations equally well. Under such a model, females pursue extra-pair copulations as insurance against the functional infertility of their mate, and obtain only direct benefits for themselves in their current reproductive event. Several studies of birds suggest that a relation between male phenotype and functional fertility is often likely to exist and that there are many potential causes of functional infertility. Non-manipulative field studies are unlikely to produce results which distinguish between the two hypotheses, and I discuss several alternative approaches which may allow their resolution.