We design an optimum modulator for the Costa (dirty-paper) precoding problem under the constraint of a binary signaling alphabet, and assuming the interference symbols belong to a binary constellation. We evaluate the performance of our technique in terms of the mutual information between the channel input and output, and compare it to that of Tomlinson-Harashima precoding (THP) with optimized parameters. We show that our optimal modulator is always better than THP. In many relevant scenarios, the performance difference is significant.