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Minimization of the error probability to determine optimum signals is often difficult to carry out. Consequently, several suboptimum performance measures that are easier than the error probability to evaluate and manipulate have been studied. In this partly tutorial paper, we compare the properties of an often used measure, the divergence, with a new measure that we have called the Bhattacharyya distance. This new distance measure is often easier to evaluate than the divergence. In the problems we have worked, it gives results that are at least as good as, and are often better, than those given by the divergence.