The widespread and locally massive introgression of Y chromosomes of the eastern house mouse (Mus musculus musculus) into the range of the western subspecies (M. m. domesticus) in Central Europe calls for an explanation of its underlying mechanisms. Given the paternal inheritance pattern, obvious candidates for traits mediating the introgression are characters associated with sperm quantity and quality. We can also expect traits such as size, aggression or the length of generation cycles to facilitate the spread. We have created two consomic strains carrying the non-recombining region of the Y chromosome of the opposite subspecies, allowing us to study introgression in both directions, something impossible in nature due to the unidirectionality of introgression. We analyzed several traits potentially related to male fitness. Transmission of the domesticus Y onto the musculus background had negative effects on all studied traits. Likewise, domesticus males possessing the musculus Y had, on average, smaller body and testes and lower sperm count than the parental strain. However, the same consomic males tended to produce less- dissociated sperm heads, to win more dyadic encounters, and to have shorter generation cycles than pure domesticus males. These data suggest that the domesticus Y is disadvantageous on the musculus background, while introgression in the opposite direction can confer a recognizable, though not always significant, selective advantage. Our results are thus congruent with the unidirectional musculus → domesticus Y chromosome introgression in Central Europe. In addition to some previous studies, they show this to be a multifaceted phenomenon demanding a multidisciplinary approach.