It is often the case that a substantial number of torsion angles (both backbone and sidechain) in structures of proteins and nucleic acids determined by NMR are found in physically unlikely and energetically unfavorable conformations. We have previously proposed a database-derived potential of mean force comprising one-, two-, three-, and four-dimensional potential surfaces which describe the likelihood of various torsion angle combinations to bias conformational sampling during simulated annealing refinement toward those regions that are populated in very high resolution (< or =1.75 A) crystal structures. We now note a shortcoming of our original implementation of this approach: namely, the forces it places on atoms are very rough. When the density of experimental restraints is low, this roughness can both hinder convergence to commonly populated regions of torsion angle space and reduce overall conformational sampling. In this paper we describe a modification that completely eliminates these problems by replacing the original potential surfaces by a sum of multidimensional Gaussian functions. Structures refined with the new Gaussian implementation now simultaneously enjoy excellent global sampling and excellent local choices of torsion angles.