Cochlear implants (CIs) convey the amplitude envelope of speech by modulating high-rate pulse trains. However, not all of the envelope may be necessary to perceive amplitude modulations (AMs); the effective envelope depth may be limited by forward and backward masking from the envelope peaks. Three experiments used modulated pulse trains to measure which portions of the envelope can be effectively processed by CI users as a function of AM frequency. Experiment 1 used a three-interval forced-choice task to test the ability of CI users to discriminate less-modulated pulse trains from a fully modulated standard, without controlling for loudness. The stimuli in experiment 2 were identical, but a two-interval task was used in which participants were required to choose the less-modulated interval, ignoring loudness. Catch trials, in which judgements based on level or modulation depth would give opposing answers, were included. Experiment 3 employed novel stimuli whose modulation envelope could be modified below a variable point in the dynamic range, without changing the loudness of the stimulus. Overall, results showed that substantial portions of the envelope are not accurately encoded by CI users. In experiment 1, where loudness cues were available, participants on average were insensitive to changes in the bottom 30% of their dynamic range. In experiment 2, where loudness was controlled, participants appeared insensitive to changes in the bottom 50% of the dynamic range. In experiment 3, participants were insensitive to changes in the bottom 80% of the dynamic range. We discuss potential reasons for this insensitivity and implications for CI speech-processing strategies.