Absolute thresholds were estimated for pure tones of 500, 1000, and 2000 Hz using both a maximum‐likelihood yes–no procedure and a traditional three‐down one‐up forced‐choice adaptive procedure. Threshold estimates obtained with the two procedures were highly correlated. In the maximum‐likelihood yes–no procedure, the false‐alarm probability was poorly estimated. A simple change in that procedure produced less‐biased estimates of the false‐alarm rate. In a second experiment, the influence of the false‐alarm rate on the threshold estimates was investigated. The listeners’ absolute thresholds were estimated when they adopted either a liberal or conservative criterion for detecting the signals. Data were collected using both a constant‐stimulus yes–no procedure and a maximum‐likelihood yes–no procedure. Threshold estimates are 5 to 6 dB higher for the low than for the high false‐alarm rates. Psychometric functions based on a stimulus‐power model provided the best fit to the data obtained with the constant‐stimulus method. This stimulus‐power model was used to produce the assumed psychometric function in the maximum‐likelihood yes–no procedure. Computer simulations were conducted to determine how threshold estimates were affected by the listener’s inattention or by mismatches between the slope parameter of the listener’s psychometric function and that assumed in the maximum‐likelihood procedure.