The problem of determing how many significant discriminant functions are present in a given data set for a one-way, fixed-effects multivariate analysis of variance design is studied using a Monte Carlo procedure. A variety of procedures, including the popular partitioned-U procedure, are compared with respect to their Type I error rates and power to detect true population differences. Results of the study lead to the recommendation of the cautious use of the partitioned-U procedure. (JKS)