Thresholds for the discrimination of the depth of sinusoidal amplitude modulation with a broadband noise carrier were measured for three listeners in a two-alternative, forced-choice task for modulation frequencies of 8, 32, and 128 Hz. Thresholds were measured with the spectrum level of the carrier fixed at 20 dB across all trials and, separately, with the carrier spectrum level roved randomly over a 20‐dB range (10–30 dB) in each interval. Mean thresholds were equal or slightly lower (but not significantly so) for the fixed conditions relative to the roved conditions, and the differences between thresholds were too small to be explained by assuming that listeners compared instantaneous intensity at corresponding phases of the modulation cycle (for example, in the troughs). Rather, it appears that listeners discriminated modulation depth by extracting an estimate of the modulation depth within each interval that was independent of the overall level. Consequently, models of envelope extraction must include normalization of the envelope fluctuations to the envelope dc.