NMR structure determination of nucleic acids presents an intrinsically difficult problem since the density of short interproton distance contacts is relatively low and limited to adjacent base pairs. Although residual dipolar couplings provide orientational information that is clearly helpful, they do not provide translational information of either a short-range (with the exception of proton-proton dipolar couplings) or long-range nature. As a consequence, the description of the nonbonded contacts has a major impact on the structures of nucleic acids generated from NMR data. In this paper, we describe the derivation of a potential of mean force derived from all high-resolution (2 A or better) DNA crystal structures available in the Nucleic Acid Database (NDB) as of May 2000 that provides a statistical description, in simple geometric terms, of the relative positions of pairs of neighboring bases (both intra- and interstrand) in Cartesian space. The purpose of this pseudopotential, which we term a DELPHIC base-base positioning potential, is to bias sampling during simulated annealing refinement to physically reasonable regions of conformational space within the range of possibilities that are consistent with the experimental NMR restraints. We illustrate the application of the DELPHIC base-base positioning potential to the structure refinement of a DNA dodecamer, d(CGCGAATTCGCG)(2), for which NOE and dipolar coupling data have been measured in solution and for which crystal structures have been determined. We demonstrate by cross-validation against independent NMR observables (that is, both residual dipolar couplings and NOE-derived intereproton distance restraints) that the DELPHIC base-base positioning potential results in a significant increase in accuracy and obviates artifactual distortions in the structures arising from the limitations of conventional descriptions of the nonbonded contacts in terms of either Lennard-Jones van der Waals and electrostatic potentials or a simple van der Waals repulsion potential. We also demonstrate, using experimental NMR data for a complex of the male sex determining factor SRY with a duplex DNA 14mer, which includes a region of highly unusual and distorted DNA, that the DELPHIC base-base positioning potential does not in any way hinder unusual interactions and conformations from being satisfactorily sampled and reproduced. We expect that the methodology described in this paper for DNA can be equally applied to RNA, as well as side chain-side chain interactions in proteins and protein-protein complexes, and side chain-nucleic acid interactions in protein-nucleic acid complexes. Further, this approach should be useful not only for NMR structure determination but also for refinement of low-resolution (3-3.5 A) X-ray data.