Thresholds for detection of sinusoidal amplitude modulation at a signal modulation frequency were measured in the presence of a masker modulation frequency, with broadband noise carriers. Broad tuning for modulation frequency was observed. For maskers half or twice the signal frequency, thresholds depended on the relative phases of the signal and masker. These results were used to determine what aspects of envelopes listeners might be using in making decisions. Simulations were performed using an envelope detector model, consisting of bandpass filtering, half-wave rectification, and low-pass filtering. Decisions were based on envelope statistics that have been used to predict other data. These statistics were (1) rms power, (2) ratio of maximum to minimum amplitude (max/min), (3) crest factor, (4) fourth moment, and (5) average slope. The max/min statistic was successful at predicting the major trends in the data, without requiring the presence of channels tuned to modulation frequency.