The automatic measurement of evoked compound action potential (ECAP) thresholds of the auditory nerve; that is, a neural response, concurrently with the performance of psychophysics measurements of a prosthetic hearing implant recipient. During the fitting process, a stimulus signal comprising two components is applied to each stimulation channel. One signal component is configured to elicit an ECAP neural response, referred to herein as a neural response signal component. The other component is configured to elicit a response to a psychophysics stimulation, referred to herein as a psychophysics signal component. Indications of the psychophysics measurement and the concurrently obtained neural response measurements are provided to the user. For the psychophysics measurement, this includes the selected characteristics of the psychophysics signal component since the results of the applied stimulation is a recipient behavioral or auditory response.