1. A method for fitting a cochlear implant for a recipient, comprising: receiving a user-specified current level; applying to a stimulation channel of the cochlear implant a stimulus signal comprising a substantially imperceptible neural response component based on the user-specified current level and configured to elicit an evoked compound action potential (ECAP) neural response, and a perceivable psychophysics component having the user-specified current level and configured to elicit a psychophysics response, wherein each of the neural response component and the psychophysics component are configured for determination of a common dynamic range parameter for the cochlear implant; automatically measuring the ECAP neural response; and concurrently displaying the ECAP neural response measurement and an indication of the user-specified current level.