In an important subset of surgical procedures, the procedure itself poses a significant threat to the patient's nervous system. In order to reduce this threat, neurophysiological function of the structures at risk may be monitored during surgery using time-locked sensory or motor-evoked responses. A simple but powerful extension of the segmented and sliding average techniques currently in wide use is described and demonstrated. By fitting polynomial functions of time to capture time variations in the evoked response, signal/noise enhancement comparable with that of averaging is obtained. More importantly, a considerable improvement in time resolution is gained. In the demonstration data set presented in the figures, clinically significant changes were identifiable in one-sixth of the time required using signal averaging.