To explore the "Perturb and Combine" idea for estimating probability densities, we study mixtures of tree structured Markov networks derived by bagging combined with the Chow and Liu maximum weight spanning tree algorithm and we try to accelerate the research procedure by reducing its computation complexity below the quadratic and keepingg similar accuracy. We empirically assess the performances of these heuristics in terms of accuracy and computation complexity, with respect to mixtures of bagged Markov trees, and single Markov tree CL built using the Chow and Liu algorithm.