This report is concerned with the estimation of noisy signals which are time-locked to the occurrence of a reference event (usually a stimulus). By employing a simple additive model for the signal and noise processes involved, it is shown that the signal may be estimated using polarity measurements taken from the noisy signal. This estimation method, called "polarity estimation", is compared with the more traditional method of estimation by signal averaging by both analytical means and by computer simulation experiments. Both the mathematical analysis and the computer simulation experiments indicate that the polarity estimation method works for small signal-to-noise ratios, but fails when the signal-to-noise ratio of the measurement data greatly exceeds unity; by contrast, this is when signal averaging works best. In addition, signal averaging is shown analytically and emperically to work better than polarity estimation from a mean-square error viewpoint.