Monogamous female razorbills Alca torda actively sought extra-pair copulations (EPCs) in mating arenas outside their nesting colony. Females showed marked variation in promiscuity, defined as the number of EPCs they accepted (0-7), and in receptivity, defined as the percentage of EPC opportunities accepted (0%-100%). The opportunity of females to encounter males for EPCs was measured by (a) the time spent in the mating arena, and (b) the guarding effectiveness of their mates. Females appeared to encounter males and accept EPCs independently of opportunity, which suggests that variation in promiscuity and receptivity is caused by differences in the degree to which individual females might benefit from EPCs. I tested predictions of four hypotheses which propose benefits which females could obtain from EPCs: "good genes", genetic diversity of offspring, insurance against infertility of mate, and acquisition of a new mate. No evidence was found to support two predictions made exclusively by the good genes hypothesis: (a) paired males did not achieve greater EPC success than unpaired males, and (b) males who were cuckolded did not obtain fewer EPCs than males whose mates avoided EPCs, suggesting that a male's attractiveness to other females does not ensure his own mate's fidelity. A prediction of both the insurance and good genes hypotheses was supported: females (who in this species retain their mates between years) showed similar receptivity to EPCs between years. This finding contradicts the genetic diversity hypothesis which predicts that in species that lay one egg per year, females who refuse EPCs in one year will accept them in the next. The good genes and genetic diversity hypotheses both predict that females who accept EPCs will behave as if to maximize their chances of being fertilized by extra-pair males. Results contradicted this prediction: females who accepted EPCs were more, rather than less receptive to their mates' copulation attempts than were females who did not accept EPCs. This finding is compatible with the insurance hypothesis which only requires females to store the sperm of extra-pair males, without necessarily being fertilized by it. Insurance against male infertility was the only hypothesis whose predictions were not contradicted by any of the results.