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The efficacy of the optimal detector of a known vanishingly small signal in additive nonwhite transformation noise is compared with that of some eleven structurally simpler suboptimal detectors. Simulation is done under various signal choices, marginal densities, and correlation functions. The block g lo and the block combination g followed by R v -1 in the optimal detector structure are found to be important for good performance in constant and oscillating signals, respectively. Two suboptimal detectors with these block structures, D 8 and D 10, are found to perform well consistently in all situations considered. A structurally simple suboptimal detector D 2 is found to be good in the cases with less correlated noise.