(1) This study investigated the maintenance of variation in the black throat patch or 'badge' of the male house sparrow. This sexually dimorphic trait is thought to be a sexually selected ornament, with previous workers providing evidence of a role in both mate choice of males by females and male-male competition. The study was conducted in 1995 and 1996 in a closed population of approximately 40 breeding pairs on Lundy Island, in the Bristol Channel, England. (2) Genetic analysis of paternity using PCR-based microsatellite genotyping revealed a very low level of extra-pair paternity in both years and no intra-specific brood parasitism. Just three extra-pair chicks (1.0% offspring in 2.5% of broods) were discovered among 305 chicks in 112 broods. This low frequency of extra-pair paternity is significantly lower than the rates reported in three other populations of house sparrows and provides further evidence for a low level of extra-pair paternity occurring in isolated populations. (3) The very low frequency of extra-pair paternity in this population allowed an examination of the costs and benefits that may be gained by a female exhibiting a preference for a large-badged male, unconfounded by the effects of extra-pair behaviour. (4) The direct benefits models of sexual selection were tested by assessing male help in provisioning chicks at the nest. Counter to the predictions of these models, large-badged males contributed relatively fewer feeds than males with smaller badges. Similarly, large-badged males, and the females that chose them as maters, had lower annual fecundity and were predicted to recruit significantly less offspring into the breeding population. 5) A female preference might be driven by the indirect benefits of obtaining genes for either viability or attractiveness for the female's offspring. A cross-fostering experiment revealed that variation in badge size had a large environmental component with a strong correlation between offspring badge size and that of their foster father, with no discernible additive genetic variation. This mechanism for the determination of badge size cannot support a process of Fisherian 'runaway' selection and is consistent with those models which require a sexual ornament to be phenotypically plastic and therefore provide an honest signal.