The correlation-attenuating effects of arbitrary and fortuitous metrics in multivariate analysis procedures, together with previous attempts to circumvent these, are discussed. A new procedure utilizes side conditions imposed on reduced rank models and proposes the use of maximum covariance matrices in formulating these conditions. Approximations to the side conditions are developed and the procedures are applied to the binary simplex matrix. Expressions for maximum covariances as functions of relative frequency distributions are developed and special cases are considered.
