Previous studies have shown that normal-hearing (NH) listeners' spatial perception of non-stationary interaural time differences (ITDs) is dominated by the carrier ITD during rising amplitude segments. Here, ITD sensitivity throughout the amplitude-modulation cycle in NH listeners and bilateral cochlear implant (CI) subjects is compared, the latter by means of direct stimulation of a single electrode pair. The data indicate that, while NH listeners are most sensitive to ITDs applied toward the beginning of a modulation cycle at 600 Hz, NH listeners at 200 Hz and especially bilateral CI subjects at 200 pulses per second (pps) are more sensitive to ITDs applied to the modulation maximum. This has implications for spatial-hearing in complex environments: NH listeners' dominant 600-Hz ITD information from the rising amplitude segments comprises direct sound information. The 200-pps low rate required to get ITD sensitivity in CI users results in a higher weight of pulses later in the modulation cycle where the source ITDs are more likely corrupted by reflections. This indirectly indicates that even if future binaural CI processors are able to provide perceptually exploitable ITD information, CI users will likely not get the full benefit from such pulse-based ITD cues in reverberant and other complex environments.