Abstract. Given several Dempster-Shafer belief functions, the framework of valuation networks describes an efficient method for computing the marginal of the combined belief function. The computation is based on a message passing scheme in a Markov tree where after the selection of a root node an inward and an outward propagation can be distinguished. In this paper it will be shown that outward propagation can be replaced by another partial inward propagation. In addition it will also be shown how the efficiency of inward propagation can be improved.