The decision to provide parental care is often associated with trade-offs, because resources allocated to parental care typically cannot be invested in self-maintenance or mating. In most animals, females provide more parental care than males, but the reason for this pattern is still debated in evolutionary ecology. To better understand sex differences in parental care and its consequences, we need to study closely related species where the sexes differ in offspring care. We investigated parental care in relation to offspring growth in two closely related coucal species that fundamentally differ in sex roles and parental care, but live in the same food-rich habitat with a benign climate and have a similar breeding phenology. Incubation patterns differed and uniparental male black coucals fed their offspring two times more often than female and male white-browed coucals combined. Also, white-browed coucals had more ‘off-times’ than male black coucals, during which they perched and preened. However, these differences in parental care were not reflected in offspring growth, probably because white-browed coucals fed their nestlings a larger proportion of frogs than insects. A food-rich habitat with a benign climate may be a necessary, but—perhaps unsurprisingly—is not a sufficient factor for the evolution of uniparental care. In combination with previous results (Goymann et al. 2015 J. Evol. Biol. 28, 1335–1353 (doi:10.1111/jeb.1265710.1111/jeb.12657)), these data suggest that white-browed coucals may cooperate in parental care, because they lack opportunities to become polygamous rather than because both parents were needed to successfully raise all offspring. Our case study supports recent theory suggesting that permissive environmental conditions in combination with a particular life history may induce sexual selection in females. A positive feedback loop among sexual selection, body size and adult sex-ratio may then stabilize reversed sex roles in competition and parental care.