The study of territorial polygyny in birds has been influential in the development of the theory of social mating systems. Alternative female mating options have been studied within the framework of the polygyny-threshold model and later as the outcome of conflicts of interest between individuals. However, little attention has been given to variations between individual females, and how this affects their mating behaviour. Here, we test the hypothesis that some females are better adapted to raise nestlings without male assistance, and thus to mate polygynously. Specifically, we investigate whether intraspecific variation in female bill morphology is related to mating behaviour. This hypothesis is derived from earlier studies showing that, in both intra- and interspecific comparisons, uniparental care by females is correlated with the catching of larger prey items than when both parents provision the young. Using the polygynous dusky warbler (Phylloscopus fuscatus) as a model species, we found that, in accordance with our prediction, females with deep bills were more likely to mate as a secondary female. Moreover, regardless of mating status, females with deep bills settled in territories with more food and they received less male assistance in feeding their offspring. We argue that females with stronger bills are better adapted to exploit the abundance of large food items in rich territories and thus to raise young on their own. Our results demonstrate the importance of studying variations between individual females, and provide evidence for an extended version of the 'constrained-female hypothesis'. As bill depth is a highly heritable trait, our study strongly suggests that variation in female mating behaviour is not only related to ecological factors and female condition (as shown elsewhere) but also to heritable morphological traits.