Female mate choice is thought to be responsible for the evolution of many extravagant male ornaments and displays, but the costs of being too selective may hinder the evolution of choosiness. Selection against choosiness may be particularly strong in socially monogamous mating systems, because females may end up without a partner and forego reproduction, especially when many females prefer the same few partners (frequency-dependent selection). Here, we quantify the fitness costs of having mating preferences that are difficult to satisfy, by manipulating the availability of preferred males. We capitalize on the recent discovery that female zebra finches (Taeniopygia guttata) prefer males of familiar song dialect. We measured female fitness in captive breeding colonies in which one-third of females were given ample opportunity to choose a mate of their preferred dialect (two-thirds of all males; "relaxed competition"), while two-thirds of the females had to compete over a limited pool of mates they preferred (one-third of all males; "high competition"). As expected, social pairings were strongly assortative with regard to song dialect. In the high-competition group, 26% of the females remained unpaired, yet they still obtained relatively high fitness by using brood parasitism as an alternative reproductive tactic. Another 31% of high-competition females paired disassortatively for song dialect. These females showed increased levels of extra-pair paternity, mostly with same-dialect males as sires, suggesting that preferences were not abolished after social pairing. However, females that paired disassortatively for song dialect did not have lower reproductive success. Overall, females in the high-competition group reached equal fitness to those that experienced relaxed competition. Our study suggests that alternative reproductive tactics such as egg dumping can help overcome the frequency-dependent costs of being selective in a monogamous mating system, thereby facilitating the evolution of female choosiness.