Current schemes in steganography relying on synchronization are all based on a general heuristic to take into account interactions between embedding changes. However these approaches, while often competitive, lack a clear model for the relationship between pixels/DCT coefficient and the distortion function, and, as such, do not give any guarantees in terms of detectabilty. To solve this problem, we herein propose a synchronized side-informed scheme in the JPEG domain based on minimizing statistical detectability which achieves state-of-the-art performances. This is done by exploiting a statistical model that takes into account correlations between DCT coefficients and adding an optimal steganographic-signal with covariance which is a scaled version of the cover noise covariance. This method allows a clear understanding of the reasons why, depending on the processing pipeline, synchronization using both intra and inter-block dependencies allows such gains in performance.