In previous models of parasite-driven sexual selection, the signals that reveal parasite resistances and that are used in mate choice should be costly to be reliable ("Handicap Principle"). However, sometimes parameter constellations could exist that allow for cheap signals directly revealing the identity of resistance genes. Despite the general conflict of interests between the sexes, sexual selection may, in these cases, have led males to focus on improving their offspring's survival chances instead of trying to get a maximum number of offspring. Males may achieve this by allowing choosy females to optimize costs and benefits of each resistance in the progeny. Multiple signals (such as odours) may serve to encode the necessary information about the identity of resistance genes. As an example, the connection between the major histocompatibility complex and odour-based mate choice in mice could be explained by this hypothesis.