In confirmatory randomized clinical trials that are designed to compare multiple doses of a test treatment with a control group and with one another, there are often statistical issues regarding compound hypotheses and multiple comparisons which need to be considered. In most cases the analysis plan needs a clear specification for the proposed order for conducting statistical tests (or for managing the overall significance level), which statistical methods will be used, and whether adjustment for covariates will be performed. There are several benefits of specifying non-parametric analysis of covariance (ANCOVA) for performing the primary confirmatory analyses. Only minimal assumptions are needed beyond randomization in the study design, whereas regression model based methods have assumptions about model fit for which departures may require modifications that are incompatible with a fully prespecified analysis plan. Non-parametric methods provide traditionally expected results of ANCOVA; namely, a typically small adjustment to the estimate for a treatment comparison (so as to account for random imbalance of covariates between treatment groups) and variance reduction for this estimate when covariates are strongly correlated with the response of interest. The application of non-parametric ANCOVA is illustrated for two randomized clinical trials. The first has a (3 x 4) factorial response surface design for the comparison of 12 treatments (that is, combinations of three doses of one drug and four doses of a second drug) for change in blood pressure; and the second example addresses the comparison of three doses of test treatment and placebo for time-to-disease progression. This clinical trial has comparisons among treatments made for a dichotomous criterion, Wilcoxon rank scores and averages of cumulative survival rates. In each example, the non-parametric covariance method provides variance reduction relative to its unadjusted counterpart.