An attempt was made to assess the effect of an imposed amplitude envelope on the binaural fusion of dichotic tone signals and noise signals. The envelope was imposed by an electronic switch at three rise/decay rates—10 msec, 25 msec, and 50 msec. The duration of the signals was such that there was no constant amplitude portion for any signal. The tonal signals covered a range from 250 to 2000 Hz. The noise was either high passed or low passed at 1000 Hz. Only the imposed envelope was delayed at one ear—not the microstructure of the signal. For tonal signals, the maximum envelope delay time for which the signal still yields a single stationary image is definitely a function of the envelope slope, being approximately 5–7 msec for the 10‐msec slope; 10–12 msec for the 25‐msec slope; and 15–20 msec for the 50‐msec slope. For the two lesser slopes, there is also an envelope delay range for which the image moves across the head from leading ear to lagging ear. For the signals with noise microstructure, behavior of the image is more complex than for tones, but a number of tentative principles emerge, most of them amenable to further testing: (1) The position of the signal is predominantly determined by the interaural envelope delay. (2) Correlated microstructure (noise from the same noise generator) definitely increases the likelihood that a signal with large interaural envelope delay will fuse into a single image, even though the delay and the microstructure should yield different positions for the image. (3) Signals presented at higher sensation level tend to split into two at smaller envelope delays when microstructure information indicates the signals are different. (4) For the type of signal used here, maximum single‐image envelope delays are greater for low‐frequency microstructure than for high‐frequency microstructure. For these signals, singleness of image and position of image appear to be analyzed separately, the information being combined later into a single perceptual impression.