The detection of sinusoidal amplitude modulation (SAM) provides a lower bound on the degree to which temporal information in the envelope of complex waveforms is encoded by the auditory system. The extent to which changes in the amount of modulation are discriminable provides additional information on the ability of the auditory system to utilize envelope fluctuations. Results from an experiment on the discrimination of modulation depth of broadband noise are presented. Discrimination thresholds, expressed as differences in modulation power, increase monotonically with the modulation depth of the standard, but do not obey Weber’s Law. The effects of carrier level and of modulation frequency are consistent with those observed in modulation detection: Changes in carrier level have little effect on modulation discrimination; changes in modulation frequency also have little effect except for standards near the modulation detection threshold. The discrimination of modulation depth is consistent with the leaky‐integrator model of modulation detection for standards below −10 dB (20 log ms); for standards greater than −10 dB, the leaky integrator predicts better performance than that observed behaviorally.