When using Bayesian networks for modelling the behavior of man-made machinery, it usu­ally happens that a large part of the model is deterministic. For such Bayesian networks the deterministic part of the model can be represented as a Boolean function, and a cen­tral part of belief updating reduces to the task of calculating the number of satisfying configurations in a Boolean function. In this paper we explore how advances in the calculation of Boolean functions can be adopted for belief updating, in particular within the context of troubleshooting. We present ex­perimental results indicating a substantial speed-up compared to traditional junction tree propagation.