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Two approaches have been proposed to reduce the synchrony of the neural response to electrical stimuli in cochlear implants. One approach involves adding noise to the pulse-train stimulus, and the other is based on using a high-rate pulse-train carrier. Hypotheses regarding the efficacy of the two approaches can be tested using computational models of neural responsiveness prior to time-intensive psychophysical studies. In our previous work, we have used such models to examine the effects of noise on several psychophysical measures important to speech recognition. However, to date there has been no parallel analytic solution investigating the neural response to the high-rate pulse-train stimuli and their effect on psychophysical measures. This work investigates the properties of the neural response to high-rate pulse-train stimuli with amplitude modulated envelopes using a stochastic auditory nerve model. The statistics governing the neural response to each pulse are derived using a recursive method. The agreement between the theoretical predictions and model simulations is demonstrated for sinusoidal amplitude modulated (SAM) high rate pulse-train stimuli. With our approach, predicting the neural response in modern implant devices becomes tractable. Psychophysical measurements are also predicted using the stochastic auditory nerve model for SAM high-rate pulse-train stimuli. Changes in dynamic range (DR) and intensity discrimination are compared with that observed for noise-modulated pulse-train stimuli. Modulation frequency discrimination is also studied as a function of stimulus level and pulse rate. Results suggest that high rate carriers may positively impact such psychophysical measures.