It is widely recognized that steganography with sideinformation in the form of a precover at the sender enjoys significantly higher empirical security than other embedding schemes. Despite the success of side-informed steganography, current designs are purely heuristic and little has been done to develop the embedding rule from first principles. Building upon the recently proposed MiPOD steganography, in this paper we impose multivariate Gaussian model on acquisition noise and estimate its parameters from the available precover. The embedding is then designed to minimize the KL divergence between cover and stego distributions. In contrast to existing heuristic algorithms that modulate the embedding costs by 1–2| e |, where e is the rounding error, in our model-based approach the sender should modulate the steganographic Fisher information, which is a loose equivalent of embedding costs, by (1–2| e |)^2. Experiments with uncompressed and JPEG images show promise of this theoretically well-founded approach.