Given fixed numbers of labeled objects on which training data can be obtained, how many variables should be used for a particular discriminant algorithm? This, of course, cannot be answeredin general since it depends on the characteristics of the populations, the sample sizes, and the algorithm. Some insight is gained in this article by studying Gaussian populations and five algorithms: linear discrimination with urlknown means and known covariance, linear discrimination with unknown means and unknown covariances, quadratic discrimination with unknown covariances and two nonparametric Bayes-type algorithms having density estimates using different, kernels (Gaussian and Cauchy).