Cochlear implant (CI) listeners have difficulty understanding speech in complex listening environments. This deficit is thought to be largely due to peripheral encoding problems arising from current spread, which results in wide peripheral filters. In normal hearing (NH) listeners, central processing contributes to segregation of speech from competing sounds. We tested the hypothesis that basic central processing abilities are retained in post-lingually deaf CI listeners, but processing is hampered by degraded input from the periphery. In eight CI listeners, we measured auditory nerve compound action potentials to characterize peripheral filters. Then, we measured psychophysical detection thresholds in the presence of multi-electrode maskers placed either inside (peripheral masking) or outside (central masking) the peripheral filter. This was intended to distinguish peripheral from central contributions to signal detection. Introduction of temporal asynchrony between the signal and masker improved signal detection in both peripheral and central masking conditions for all CI listeners. Randomly varying components of the masker created spectral-variance cues, which seemed to benefit only two out of eight CI listeners. Contrastingly, the spectral-variance cues improved signal detection in all five NH listeners who listened to our CI simulation. Together these results indicate that widened peripheral filters significantly hamper central processing of spectral-variance cues but not of temporal cues in post-lingually deaf CI listeners. As indicated by two CI listeners in our study, however, post-lingually deaf CI listeners may retain some central processing abilities similar to NH listeners.