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Recent studies suggest that normal-hearing listeners maintain robust speech intelligibility despite severe degradations of amplitude-modulation (AM) cues, by using temporal-envelope information recovered from broadband frequency-modulation (FM) speech cues at the output of cochlear filters. This study aimed to assess whether cochlear damage affects this capacity to reconstruct temporal-envelope information from FM. This was achieved by measuring the ability of 40 normal-hearing listeners and 41 listeners with mild-to-moderate hearing loss to identify syllables processed to degrade AM cues while leaving FM cues intact within three broad frequency bands spanning the range 65–3,645 Hz. Stimuli were presented at 65 dB SPL for both normal-hearing listeners and hearing-impaired listeners. They were presented as such or amplified using a modified half-gain rule for hearing-impaired listeners. Hearing-impaired listeners showed significantly poorer identification scores than normal-hearing listeners at both presentation levels. However, the deficit shown by hearing-impaired listeners for amplified stimuli was relatively modest. Overall, hearing-impaired data and the results of a simulation study were consistent with a poorer-than-normal ability to reconstruct temporal-envelope information resulting from a broadening of cochlear filters by a factor ranging from 2 to 4. These results suggest that mild-to-moderate cochlear hearing loss has only a modest detrimental effect on peripheral, temporal-envelope reconstruction mechanisms.