This Monte Carlo investigation provides some possible solutions to problems related to choosing multiple-comparison methods that maximize true rejections and minimize false ones. It has been argued that the traditional Bonferroni approach to multiple comparisons, which satisfies the statistician's family-wise Type I error concerns, could be improved to satisfy the researcher's power concerns by converting it from a simultaneous procedure to a sequential (or stepwise) procedure. In this study, the algorithm proposed by W. H. Press et. al. (1986) was implemented to obtain random normal deviates. This technique generates random uniformly distributed values and applies the Box-Muller transformation to them. The problem of all-possible pairwise comparisons in a set of "K" independent means was addressed to: (1) assess the Type I error and power characteristics of the sequential Bonferroni approaches on the basis of an empirical study; and (2) compare those approaches with both the traditional Bonferroni and Tukey multiple-comparison procedures. Seven multiple-comparison procedures were used for testing the pairwise comparisons among means. Focus was on the increase in power that can be obtained by sequential tests when the Type I error is to be controlled for a family of comparisons. To provide a broad comparison of both Type I error rates and power among the various procedures, several parameters were varied. Each test was performed using the algorithm prescribed by the particular multiple-comparison procedure based on a family-wise alpha of 0.05. Results suggest that there are valid reasons for replacing the traditional (simultaneous) Bonferroni and Tukey procedures with improved sequential tests. (TJH)