Personality traits are becoming increasingly important in explaining adaptive individual differences in animal behaviour and probably represent a leading edge of the evolutionary process. Despite the new-found interest in animal personality among behavioural ecologists, few studies have investigated the link between personality traits and fitness measures. We examined this link using male rainbowfish, Melanotaenia duboulayi, as a model species and found that a range of personality traits (aggression, activity and boldness) covaried with a male’s position in a hierarchy, which is directly related to reproductive success in this and many other species. Dominant fish were more aggressive, active, bold and also significantly larger than subordinate fish. Moreover, we found strong correlations between activity levels and boldness suggesting that selection may act on a suite of traits in concert (sensu behavioural syndromes). When taken together with previous research, our results suggest that the activity–boldness syndrome is likely to be domain specific. We suggest that multiple trait correlations may be generated by high levels of competition (e.g. sexual selection) in addition to predation pressure as identified by previous studies.