Most of our everyday listening happens under adverse conditions largely because natural auditory scenes often comprise a multitude of sounds heard at once. These “cocktail-party”-like situations pose a difficult problem for normal-hearing (NH) listeners and are particularly challenging for cochlear-implant (CI) users. We have previously shown (Kreitewolf et al., 2018, doi:10.1121/1.5058684) that NH listeners are better at comprehending target speech when they can group sounds based on continuity in two prominent voice features: glottal-pulse rate (GPR) and vocal-tract length (VTL). Unlike NH listeners, CI users do not seem to benefit from voice cues. For example, recent work (El Boghdady et al., 2019, doi:10.1121/1.5087693) suggests that CI users do not exploit differences in GPR and VTL to segregate target from masker speech. Here, we took a different approach to investigate the use of GPR and VTL for cocktail-party listening in N = 20 NH listeners and N = 20 CI users. In this experiment, participants heard a stream of spoken digits embedded in multi-talker babble noise and were asked to report each digit immediately after its presentation. To explore the contributions of GPR and VTL to cocktail-party listening, we manipulated continuity in GPR and VTL across consecutive digits. Overall performance was fixed at approximately 67%-correct. Our results showed that both NH listeners and CI users benefited from voice-feature continuity. Both NH and CI showed the greatest benefits when both voice features were continuous across consecutive target digits. When only one voice feature was continuous, both listener groups benefited from VTL but not GPR continuity. Once listeners successfully tracked the target stream, they were more likely to correctly report the subsequent digit. The magnitude of this so-called previous-digit-correct benefit (PDCB), however, differed across conditions and listener groups. Interestingly, CI showed greater PDCBs when they could rely on VTL versus GPR continuity. NH listeners seemed to benefit equally from GPR and VTL continuity. Sensitivity to differences in GPR and VTL was not correlated with benefits from voice-feature continuity. These findings provide evidence that CI users exploit continuity in voice features to improve listening at the cocktail party. Unlike NH listeners, CI users seem to rely exclusively on VTL continuity for perceptual grouping of target sounds, which may be due to their impaired processing of pitch cues. VTL is effectively fixed within natural talkers. Stronger reliance on VTL continuity may thus explain CI users’ residual abilities to solve the cocktail-party problem in natural settings.