Sexual selection should produce sexual size dimorphism in species where larger members of one sex obtain disproportionately more matings. Recent theory suggests that the degree of sexual size dimorphism depends on physical and temporal constraints involving the operational sex ratio, the potential reproductive rate and the trade-off between current reproductive effort and residual reproductive value. As part of a large-scale experiment on dispersal, we investigated the mating system of common brushtail possums inhabiting old-growth Eucalyptus forest in Australia. Paternity was assigned to 20 of 28 pouch-young (maternity known) genotyped at six microsatellite loci. Male mating success was strongly related to body size and age; male body weight and age being highly correlated. Despite disproportionate mating success favouring larger males, sexual size dimorphism was only apparent among older animals. Trapping and telemetry indicated that the operational sex ratio was effectively 1 : 1 and the potential reproductive rate of males was at most four times that of females. Being larger appeared to entail significant survival costs because males ‘died-off’ at the age at which sexual size dimorphism became apparent (8–9 years). Male and female home ranges were the same size and males appeared to be as sedentary as females. Moreover, longevity appears to be only slightly less important to male reproductive success than it is to females. It is suggested that a sedentary lifestyle and longevity are the key elements constraining selection for greater sexual size dimorphism in this ‘model’ medium-sized Australian marsupial herbivore.