Summary: ``Aggregating a set of Bayesian Networks (BNs), also known as BN fusion, has been studied in the literature, providing a precise theoretical framework for the structural phase. This phase depends on a total ordering of the variables, but both the problem of searching for the optimal consensus structure (according to standard problem definition), as well as the one of looking for the optimal ordering are NP-hard. \par ``In this paper we start from this theoretical framework and extend it from a practical point of view. We propose a heuristic method to identify a suitable order of the variables, which allows us to obtain consensus BNs having (by far) less edges than those obtained by using random orderings. Furthermore, we apply an optimization method based on the GES algorithm to remove the extra edges. As GES is a data-driven method and we have not data but a set of incoming networks, we propose to use the independences codified in the incoming networks to determine a score in order to evaluate the goodness of removing a given edge. From the experiments carried out, we observe that our heuristic is very competitive, driving the fusion process to solutions close to the optimal one.''