When females mate with multiple males both pre- and post-copulatory sexual selections occur. It has been suggested that females benefit from polyandry when better-quality males are successful in sperm competition and sire high-quality offspring. Indeed, studies of experimental evolution have confirmed that sperm competition selects for both increased ejaculate quality and elevated offspring viability. Fewer investigations have explored whether these fitness benefits are evident beyond early life-history stages. Here, I used house mice (Mus domesticus) from selection lines that had been evolving for 25 generations under either polygamy or monogamy to test whether females preferred males from lines that had evolved with sperm competition. Males from the polygamous lines had previously been shown to achieve a fitness advantage under semi-natural conditions, deeming them to be of high genetic quality and leading to the a priori expectation that females would prefer males that had evolved with sperm competition compared with males that had not. Contrary to expectation, the data showed that sexually receptive females spent more time associating with males from the monogamous lines. This unexpected but interesting result is discussed in relation to sperm competition theory that predicts a trade-off between male investment in pre- and post-copulatory sexually selected traits.