Power and Type I error control were compared in a Monte Carlo simulation of the combinations of 2 methods of assignment to groups and 2 methods of analysis. Assignment to treatment groups was either random or systematic on the basis of alternating ranks on a concomitant variable. Analysis was either with a randomized block or analysis of covariance using the concomitant variable. The correlation between the concomitant and outcome variables was set at .2, .5, and .8. The skew of the concomitant and outcome were separately set at γ1 values of 0.0, 0.75, 1.25, and 1.75. Overall the most powerful design was an analysis of covariance with systematic assignment of subjects. This superiority was particularly noticeable when the correlation was large and the distribution of the outcome variable was exponentially skewed.