This paper presents an any-time scheme for computing lower and upper bounds on posterior marginals in Bayesian networks. The scheme draws from two previ- ously proposed methods, bounded conditioning (Horvitz et al., 1989) and bounds propagation algorithm (Leisink and Kappen, 2003). Following the principles of cut- set conditioning (Pearl, 1988), our method enumerates a subset of cutset tuples and applies exact reasoning in the network instances conditioned on those tuples. The probability mass of the remaining tuples is bounded using a variant of bound propagation. We show that our new scheme improves on the earlier schemes.