In this chapter Bayes decision rules are developed for optimizing the detection of multiple targets. We show that the strategy consists of an independent threshold test at each expected time of arrival for all targets in the radar field of view. This separable test strategy is shown to be optimum for the limiting cases of large and small signal-to-noise ratios; however, a different threshold level is required, in general, for large signal detection and for small signal detection. The separable test strategy is compared to the averaging solution, which is obtained from a Bayes strategy with cost assignments that are independent of parameters. The averaging approach is shown to be unsuitable for most radars when echo arrival times are unknown.