Winsorized regression is an alternative to least squares for estimating a simple regression model by altering data values based upon the magnitude of residuals. Three versions of Winsorization combined with two methods for estimating residuals are compared with least squares by means of relative efficiency measurements obtained from Monte Carlo samples. Winsorization showed improvement, over least. squares when the data are taken from a scale contaminated normal distribution. Some estimates resulted in a loss of no more than 7% efficiency when no contamination existed. Two of the Winsorization methods are applied to a numerical example of real data.