Bayesian networks are efficient tools for probabilistic reasoning over large sets of variables, due to the fact that the joint distribution factorises according to the structure of the network, which captures conditional independence relations among the variables. Beyond conditional independence, the concept of asymmetric (or context specific) independence makes possible the definition of even more efficient reasoning schemes, based on the representation of probability functions through probability trees. In this paper we investigate how it is possible to achieve a finer factorisation by decomposing the original factors for which some conditions hold. We also introduce the concept of approximate factorisation and apply this methodology to the Lazy-Penniless propagation algorithm.