The rapid divergence of genitalia is a pervasive trend in animal evolution, thought to be due to the action of sexual selection. To test predictions from the sexual selection hypothesis, we here report data on the allometry, variation, plasticity and condition dependence of baculum morphology in the house mouse (Mus musculus domesticus). We find that that baculum size: (a) exhibits no consistent pattern of allometric scaling (baculum size being in most cases unrelated to body size), (b) exhibits low to moderate levels of phenotypic variation, (c) does not exhibit phenotypic plasticity in response to differences in perceived levels of sexual competition and (d) exhibits limited evidence of condition dependence. These patterns provide only limited evidence in support of the sexual selection hypothesis, and no consistent support for any particular sexual selection mechanism; however, more direct measures of how genital morphology influences male fertilization success are required.