Differences in voice pitch (F0) and vocal tract length (VTL) improve intelligibility of speech masked by a background talker (speech-on-speech; SoS) for normal-hearing (NH) listeners. Cochlear implant (CI) users, who are less sensitive to these two voice cues compared to NH listeners, experience difficulties in SoS perception. Three research questions were addressed: (1) whether increasing the F0 and VTL difference (ΔF0; ΔVTL) between two competing talkers benefits CI users in SoS intelligibility and comprehension, (2) whether this benefit is related to their F0 and VTL sensitivity, and (3) whether their overall SoS intelligibility and comprehension are related to their F0 and VTL sensitivity. Results showed: (1) CI users did not benefit in SoS perception from increasing ΔF0 and ΔVTL; increasing ΔVTL had a slightly detrimental effect on SoS intelligibility and comprehension. Results also showed: (2) the effect from increasing ΔF0 on SoS intelligibility was correlated with F0 sensitivity, while the effect from increasing ΔVTL on SoS comprehension was correlated with VTL sensitivity. Finally, (3) the sensitivity to both F0 and VTL, and not only one of them, was found to be correlated with overall SoS performance, elucidating important aspects of voice perception that should be optimized through future coding strategies.