SummaryAssume that a number of individuals are to be classified into one of two populations and that, at the same time, the proportion of members of each population needs to be estimated. The allocated proportions given by the Bayes classification rule are not consistent estimates of the true proportions, so a different classification rule is proposed; this rule yields consistent estimates with only a small increase in the probability of misclassification. As an illustration, the case of two normal distributions with equal covariance matrices is dealt with in detail.