The results of a study of find alternative techniques for testing distributional normality are presented. A group of statistical techniques--some established and some new--were compared using empirical techniques. One new technique which appears to have higher power than the Lilliefors test was subjected to a better definition. Distributions under the null hypothesis are presented for small sample sizes. Modelled relationships from these to the chi-square distributions for similar degrees-of-freedom are discussed. A final comparison to the Lilliefors test using the theoretical distributions indicated that the original findings were not supported. The Lilliefors test has the higher power. The new test is proposed as a potential alternative to the Kolmogorov-Smirnov test for general distributions. (Author)