Based on Bayes theory of hypothesis testing, a new DWT-domain decoder structure for image watermarking has been proposed in this work. The statistical distribution of wavelet coefficients is deliberately described with the Laplacian model so that the decoding algorithm could couple effectiveness and simplicity. Under the Neyman-Pearson criterion, the decision rule is optimized by minimizing the probability of missing the watermark for a given false detection rate. Compared with other domain decoders, the proposed DWT-domain decoder has more flexibility in constructing new watermarking algorithms by using visual models that have varying spatial support.