Morphology, habitat and various selective pressures (e.g., social and sexual selection) can influence the evolution of acoustic signals, but the relative importance of their effects is not well understood. The order Psittaciformes (parrots, sensu lato) is a large clade of very vocal and often gregarious species for which large-scale comparative studies of vocalizations are lacking. We measured acoustic traits (duration, sound frequency, frequency bandwidth and sound entropy) of the predominant call type for >200 parrot species to test: (1) for associations with body size; (2) the acoustic adaptation hypothesis (predicting differences between forest and open-habitat species); (3) the social complexity hypothesis (predicting more complex calls in gregarious species); and (4) influences of sexual selection (predicting correlated evolution with colour ornamentation). Larger species had on average longer calls, lower sound frequency and wider frequency bandwidth. These associations with body size are all predicted by physical principles of sound production. We found no evidence for the acoustic adaptation and social complexity hypotheses, but perhaps social complexity is associated with vocal traits not studied here, such as call repertoire sizes. More sexually dichromatic species had on average simpler calls (shorter, with lower entropy and narrower frequency bandwidth) indicating an influence of sexual selection, namely an evolutionary negative correlation between colour ornamentation and elaborate acoustic signals, as predicted by the transference hypothesis. Our study is the first large-scale attempt at understanding acoustic diversity across the Psittaciformes, and indicates that body size and sexual selection influenced the evolution of species differences in vocal signals.