This study considers the problem of testing the difference between treatment and control groups on m [greater than or equal to] 2 measures when it is assumed a priori that the treatment group will perform better than the control group on all measures. Two procedures are investigated that do not rest on the assumptions of covariance homogeneity or multivariate normality: a likelihood ratio test based on a bootstrap critical value and a composite step-down procedure based on trimmed means. Type I error rates of both procedures are insensitive to assumption violations. Procedures that test a directional alternative hypothesis can be substantially more powerful than a procedure that tests a nondirectional hypothesis for certain configurations of the population mean vectors. The differences in average power of the investigated procedures are a function of the configuration of the population means, the magnitude of correlation among the outcome measures, and the shape of the population distribution. (Contains 4 tables.)