Empirical data indicate that sexual preferences are critical for maintaining species boundaries(1-4), yet theoretical work has suggested that, on their own, they can have only a minimal role in maintaining biodiversity(5-9). This is because long-term coexistence within overlapping ranges is thought to be unlikely in the absence of ecological differentiation(9). Here we challenge this widely held view by generalizing a standard model of sexual selection to include two ubiquitous features of populations with sexual selection: spatial variation in local carrying capacity, and mate-search costs in females. We show that, when these two features are combined, sexual preferences can single-handedly maintain coexistence, even when spatial variation in local carrying capacity is so slight that it might go unnoticed empirically. This theoretical study demonstrates that sexual selection alone can promote the long-term coexistence of ecologically equivalent species with overlapping ranges, and it thus provides a novel explanation for the maintenance of species diversity.