Won et al. (J Acoust Soc Am 132:1113-1119, 2012 reported that cochlear implant (CI) speech processors generate amplitude-modulation (AM) cues recovered from broadband speech frequency modulation (FM) and that CI users can use these cues for speech identification in quiet. The present study was designed to extend this finding for a wide range of listening conditions, where the original speech cues were severely degraded by manipulating either the acoustic signals or the speech processor. The manipulation of the acoustic signals included the presentation of background noise, simulation of reverberation, and amplitude compression. The manipulation of the speech processor included changing the input dynamic range and the number of channels. For each of these conditions, multiple levels of speech degradation were tested. Speech identification was measured for CI users and compared for stimuli having both AM and FM information (intact condition) or FM information only (FM condition). Each manipulation degraded speech identification performance for both intact and FM conditions. Performance for the intact and FM conditions became similar for stimuli having the most severe degradations. Identification performance generally overlapped for the intact and FM conditions. Moreover, identification performance for the FM condition was better than chance performance even at the maximum level of distortion. Finally, significant correlations were found between speech identification scores for the intact and FM conditions. Altogether, these results suggest that despite poor frequency selectivity, CI users can make efficient use of AM cues recovered from speech FM in difficult listening situations.