Behavioural lateralization is widespread across animal taxa. Consistent with the idea that lateralization indicates advantageous specialization of the brain hemispheres, individuals with more lateralized behaviour are often found to have better cognition. Among-individual differences in behavioural lateralization nevertheless exist, sometimes associated with differences in other phenotypic traits. Knowing which phenotypes are associated with behavioural lateralization gives cues as to why differences in lateralization exist within populations, but past research has often focused on one or a few phenotypes, and found different, sometimes opposed, correlations with lateralization. Here, we assayed behavioural lateralization of common waxbills, Estrilda astrild, in a feeding task, to test for associations with phenotypic differences, using a broad set of traits that might influence or be influenced by lateralization: a cognitive trait (inhibitory control), size, personality, social dominance, cues of stress and sex. Most individuals consistently fed with the right side towards the food, resulting in a population level right-side lateralization. However, evaluating photographs from waxbills feeding in the wild worldwide, we found no evidence of a preferred feeding side, contrasting with results in our population. There were also differences between individuals in our population in the direction and strength of lateralization. Females were, on average, more right-side lateralized than males, and there were larger among-individual differences in lateralization among males. None of the phenotypes studied predicted differences in the strength of lateralization. However, individual differences in the direction of lateralization were related to inhibitory control, an aspect of cognition, more strongly so in males than in females. These are among the few results indicating that the direction of behavioural lateralization, rather than its strength, is associated with cognitive differences among individuals. It is also the first time that a sex-dependent association between behavioural lateralization and cognitive performance has been found, suggesting that sex-specific functions are implicated in maintaining differences in behavioural lateralization.