Two EEG experiments measured the sustained neural response to amplitude-modulated (AM) high-rate pulse trains presented to a single cochlear-implant (CI) electrode. Stimuli consisted of two interleaved pulse trains with AM rates F1 and F2 close to 80 and 120Hz respectively, and where F2 = 1.5F1. Following Carlyon et al. (J Assoc Res Otolaryngol, 2021), we assume that such stimuli can produce a neural distortion response (NDR) at F0 = F2-F1 Hz if temporal dependencies ("smoothing") in the auditory system are followed by one or more neural nonlinearities. In experiment 1, the rate of each pulse train was 480 pps and the gap between pulses in the F1 and F2 pulse trains ranged from 0 to 984µs. The NDR had a roughly constant amplitude for gaps between 0 and about 200-400µs, and decreased for longer gaps. We argue that this result is consistent with a temporal dependency, such as facilitation, operating at the level of the auditory nerve and/or with co-incidence detection by cochlear-nucleus neurons. Experiment 2 first measured the NDR for stimuli at each listener's most comfortable level ("MCL") and for F0 = 37, 40, and 43Hz. This revealed a group delay of about 42ms, consistent with a thalamic/cortical source. We then showed that the NDR grew steeply with stimulus amplitude and, for most listeners, decreased by more than 12dB between MCL and 75% of the listener's dynamic range. We argue that the NDR is a potentially useful objective estimate of MCL.