The binary Distortion Compensated Dither-Modulation (DCDM), which can be regarded to as a baseline for quantizationbased data-hiding methods, is rigorously analyzed. A novel and accurate procedure for computing the exact probability of bit error is given, as well as an approximation amenable to differentiation which allows to obtain the optimal weights in a newly proposed decoding structure, for significant improvements on performance. The results are particularized for a JPEG compression scenario which allows to show their usefulness. Experimental results validating the proposed theory are presented.