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Previous literature on detector design has presented many tractable results using efficacy as a performance functional, which is a small signal or local approach. Some nonlocal issues of memoryless detection are considered. We argue that the asymptotic exponential rate of decrease of error probabilities, or Bayes risk, provides the appropriate asymptotic measure of performance. A main contribution is the development of an approximation for nonlocal design that retains the tractability of the efficacy approach. We have proved the local consistency of our approximation. Also, as a consequence of the analysis, new proofs for Pitman-Noether-like theorems have been obtained.