Cochlear-implant (CI) users have difficulty understanding speech in the presence of interfering sounds. This study was designed to determine if binaural unmasking of speech is limited by peripheral or central encoding. Speech was presented to bilateral CI listeners using their clinical processors; unprocessed or vocoded speech was presented to normal-hearing (NH) listeners. Performance was worst for all listener groups in conditions where both the target and interferer were presented monaurally or diotically (i.e., no spatial differences). Listeners demonstrated improved performance compared to the monaural and diotic conditions when the target and interferer were presented to opposite ears. However, only some CI listeners demonstrated improved performance if the target was in one ear and the interferer was presented diotically, and there was no change for the group on average. This is unlike the 12-dB benefit observed in the NH group when presented the CI simulation. The results suggest that CI users can direct attention to a target talker if the target and interferer are presented to opposite ears; however, larger binaural benefits are limited for more realistic listening configurations, likely due to the imprecise peripheral encoding of the two sounds.