Subjects were presented with low‐frequency tonal signals, leading in time to one ear but more intense to the other. For differing values of interaural time (Δt) and intensity (ΔI), the listener's task was to detect the difference between the dichotic signals and diotic tones of the same frequency. The shapes of the psychometric functions demonstrate that time and intensity do trade but that the trade is incomplete—a result shown to be in accord with other experiments where listeners presented with such signals report the presence of two distinct “images.” A model of time‐intensity trading is presented in which it is assumed that differences of intensity are converted to time by two different trading mechanisms and that the two sums of Δtand converted ΔIact as different loci on a single interaural dimension. It is further suggested that the inner and outer hair cells may represent the site of the two trades.