Positive static allometry is a scaling relationship where the relative size of traits covaries with adult body size. Traditionally, positive allometry is thought to result from either altered physiological requirements at larger body size or from strongly condition-dependent allocation under sexual selection. Yet, there are no theoretical reasons why positive allometry cannot evolve in fitness-related traits that are solely under the influence of natural selection. We investigated scaling and sexual dimorphism of a naturally selected trait, pectoral fin size, in comparison to a trait important in male–male combat, head width in natural populations of a fish, the desert goby Chlamydogobius eremius. Male desert gobies provide uniparental care and use their pectoral fins to fan the brood (often under hypoxic conditions); hence, larger fins are expected to be more efficient. Male pectoral fins do not appear to fulfil a signalling function in this species. We found that, for both pectoral fin size and head width, males exhibited positive allometric slopes and greater relative trait size (allometric elevation) than females. However, for head width, females also showed positive allometry, albeit to a lesser degree than males. Because fin locomotory function typically does not result in positive allometry, our findings indicate that other naturally selected uses, such as paternal care, can exaggerate trait scaling relationships.