Body size is a key determinant of mortality risk. In natural populations, a broad range of relationships are observed between body size and mortality, including positive and negative correlations. Previous evolutionary modelling has shown that negatively size-dependent mortality can result in life-history bistability, with early maturation at small size and late maturation at large size representing alternative fitness optima. Here we present a general analysis of conditions under which such life-history bistabilities can occur, reporting the following findings. First, alternative fitness optima can be found for any arbitrarily chosen forms of mortality functions, including functions according to which mortality smoothly declines with size. Second, while bistabilities occur more readily under negatively size-dependent mortality, our analysis reveals that they can also emerge under positively size-dependent mortality, a feature missed in earlier work. Third, any sharp drop of mortality with size facilitates bistability. Fourth, if the mortality regime involves more than one such sharp drop, multistable life histories can occur, with alternative fitness optima straddling each of the drops. Paradoxically, our findings imply that, fifth, a species-poor predator community capable of creating a 'rugged' mortality regime is conducive to evolutionary multistability, which could act as a stepping stone toward prey life-history diversification, whereas a species-rich predator community that results in a smoothly varying mortality regime may prevent diversification through this pathway.