We propose an information–theoretic approach to the watermark embedding and detection under limited detector resources. First, we present asymptotically optimal decision regions in the Neyman–Pearson sense. We expand these results to the case of zero-mean i.i.d. Gaussian covertext distribution with unknown variance. For this case, we propose a lower bound on the exponential decay rate of the false–negative probability and prove that the optimal embedding and detecting strategy is superior to the customary linear, additive embedding strategy in the exponential sense.