For Gaussian Assumed Density Filtering based on moment matching, a framework for the efficient calculation of posterior moments is proposed that exploits the structure of the given nonlinear system. The key idea is a careful discretization of some dimensions of the state space only in order to decompose the system into a set of nonlinear subsystems that are conditionally integrable in closed form. This approach is more efficient than full discretization approaches. In addition, the new decomposition is far more general than known Rao-Blackwellization approaches relying on conditionally linear subsystems. As a result, the new framework is applicable to a much larger class of nonlinear systems.