To better understand the processing of complex high-frequency sounds, modulation-detection thresholds were measured for sinusoidal frequency modulation (SFM), quasi-frequency modulation (QFM), sinusoidal amplitude modulation (SAM), and random-phase FM (RPFM). At the lowest modulation frequency (5 Hz) modulation thresholds expressed as AM depth were similar for RPFM, SAM and QFM suggesting the predominance of envelope cues. At the higher modulation frequencies (20 and 40 Hz) thresholds expressed as total frequency excursions were similar for SFM and QFM suggesting a common mechanism, one perhaps based on single-channel FM-to-AM conversion or on a multi-channel place mechanism. The fact that the nominal envelopes of SFM and QFM are different (SFM has a flat envelope), seems to preclude processing based on the envelope of the external stimulus. Also, given the 4-kHz carrier and the similarity to previously published results obtained with a 1-kHz carrier, processing based on temporally-coded fine structure for all four types of modulation appears unlikely.