Delphinoids (Delphinidae, Odontoceti) produce tonal sounds and clicks by forcing pressurized air past phonic lips in the nasal complex. It has been proposed that homologous, hypertrophied nasal structures in the deep-diving sperm whale (Physeter macrocephalus) (Physeteridae, Odontoceti) are dedicated to the production of clicks. However, air volumes in diving mammals are reduced with increasing ambient pressure, which seems likely to influence pneumatic sound production at depth. To study sperm whale sound production at depth, we attached ultrasound time/depth-recording tags to sperm whales by means of a pole and suction cup. We demonstrate that sperm whale click production in terms of output and frequency content is unaffected by hydrostatic reduction in available air volume down to less than 2% of the initial air volume in the nasal complex. We present evidence suggesting that the sound-generating mechanism has a bimodal function, allowing for the production of clicks suited for biosonar and clicks more suited for communication. Shared click features suggest that sound production in sperm whales is based on the same fundamental biomechanics as in smaller odontocetes and that the nasal complexes are therefore not only anatomically but also functionally homologous in generating the initial sound pulse.