Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the nn,1 2 atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tight bounds on all the nn,1 2 pairwise distances. This process is referred to as bound-smoothing. The initial lower and upper bounds for the pairwise distances not measured are usually assumed to