Understanding why some species thrive in captivity, while others struggle to adjust, can suggest new ways to improve animal care. Approximately half of all Psittaciformes, a highly threatened order, live in zoos, breeding centres and private homes. Here, some species are prone to behavioural and reproductive problems that raise conservation and ethical concerns. To identify risk factors, we analysed data on hatching rates in breeding centres (115 species, 10 255 pairs) and stereotypic behaviour (SB) in private homes (50 species, 1378 individuals), using phylogenetic comparative methods (PCMs). Small captive population sizes predicted low hatch rates, potentially due to genetic bottlenecks, inbreeding and low availability of compatible mates. Species naturally reliant on diets requiring substantial handling were most prone to feather-damaging behaviours (e.g. self-plucking), indicating inadequacies in the composition or presentation of feed (often highly processed). Parrot species with relatively large brains were most prone to oral and whole-body SB: the first empirical evidence that intelligence can confer poor captive welfare. Together, results suggest that more naturalistic diets would improve welfare, and that intelligent psittacines need increased cognitive stimulation. These findings should help improve captive parrot care and inspire further PCM research to understand species differences in responses to captivity.