The detection of an increment in the intensity of the central component of a multi-component complex was measured as a function of the frequency spacing of the components and the duration of the presentation. The overall intensity of the complex was randomly varied on each presentation of the stimulus. Curiously, the increment becomes easier to hear as the range and density of the surrounding complex is increased. This increase in range and density is also effective in improving the detectability of the increment when there is no random variation in intensity, i.e., a conventional Weber fraction experiment. This is unlike the results obtained in many other critical-band experiments where energy remote from the signal frequency has little or no effect. Measurement of the effects of signal duration showed that when presentations were shorter than about 100 msec a greater increment in intensity was required than for longer durations. These results with duration are similar to those obtained in other intensity-discrimination tasks.