Averaging single trial evoked potential data to produce an estimate of the underlying signal obscures trial-to-trial variation in the response. We describe a method for estimating slow changes in the evoked potential signal by smoothing the data over trials. We discuss the crucial issue of deciding how much to smooth and suggest that an appropriate smoothing parameter is one that minimizes the estimated mean average square error of the smoothed data. Equations to estimate the mean average square error for a one-dimensional local linear regression smoother are presented. Performance of the method is assessed using simulated evoked potential data with several different models of a changing signal and different values of the signal-to-noise ratio. We find that the method rarely imputes trial-to-trial variation to data sets that have an unchanging signal, while it almost always produces less error than averaging when estimating a varying signal. The ability of the method to reveal signal heterogeneity is hampered by very low signal-to-noise ratios. When applied to real auditory evoked potential data from a sample of elderly subjects, the method indicated a changing signal in 35% of all subjects and in 56% of subjects with signal-to-noise ratios above 0.6. Consistent patterns of variation in the auditory evoked potential were present in this sample.