Listeners with cochlear implants (CIs) typically show poor sensitivity to the temporal-envelope pitch of high-rate pulse trains. Sensitivity to interaural time differences improves when adding pulses with short inter-pulse intervals (SIPIs) to high-rate pulse trains. In the current study, monaural temporal-pitch sensitivity with SIPI pulses was investigated for six CI listeners. Amplitude-modulated single-electrode stimuli, representing the coding of the fundamental frequency (F0) in the envelope of a high-rate carrier, were used. Two SIPI-insertion approaches, five modulation depths, two typical speech-F0s, and two carrier rates were tested. SIPI pulses were inserted either in every amplitude-modulation period (full-rate SIPI) to support the F0 cue or in every other amplitude-modulation period (half-rate SIPI) to circumvent a potential rate limitation at higher F0s. The results demonstrate that full-rate SIPI pulses improve temporal-pitch sensitivity across F0s and particularly at low modulation depths where envelope-pitch cues are weak. The half-rate SIPI pulses did not circumvent the limitation and further increased variability across listeners. Further, no effect of the carrier rate was found. Thus, the SIPI approach appears to be a promising approach to enhance CI listeners' access to temporal-envelope pitch cues at pulse rates used clinically.