In this paper we study the problem of optimizing the distortion compensation parameter for the scalar Costa scheme, which is a practical version of the class of distortion compensated dither modulation schemes. In the literature, a number of results are known for finding the value of the distortion compensation parameter that maximizes the capacity of the watermarking channel. Instead, in this paper, we look at minimization of the bit error probability as the criterion for determining the optimal value of the distortion compensation parameter. To this end, we derive a model for the bit error probability, which is subsequently approximated and minimized. This is done both for the cases of Gaussian noise and uniform noise. The results match very well with earlier results by Eggers.