Interaural time differences (ITDs) in the signal are important for sound localization in the lateral dimension. However, even under laboratory stimulus control, ITD sensitivity of cochlear-implant (CI) listeners is poor at pulse rates commonly used for encoding speech. Recently, improvements in ITD sensitivity were shown for unmodulated high-rate pulse trains with extra pulses at short interpulse intervals (SIPIs). In this study, we extended this approach to more realistic stimuli, i.e., high-rate (1000 pulses-per-second) pulse trains with vowel-like temporal envelopes. Using fixed SIPI parameters derived from the preceding study, we independently varied the timing of the extra pulses across the fundamental frequency (F0) period, the modulation depth (0.1, 0.3, 0.5, 0.7, and 0.9), and the F0 frequency (125 and 250 Hz). Our results show largest improvements in ITD sensitivity for SIPIs at the rising and peak portions of the F0 period and for larger modulation depths. These findings may be useful for enhancing sound localization cues with bilateral CI strategies.