In DNA or RNA duplexes, the six-bond C3'-O3'-P-O5'-C5'-C4-C3' backbone linkage connecting adjacent residues contains six torsion angles (epsilon, zeta, alpha, beta, gamma, delta) but only four protons. This seriously limits the ability to define the backbone conformation by NMR using purely H-1-H-1 distance geometry (DG) methods. The problem is further compounded by the inability to assign two of the four backbone protons, namely, the poorly resolved H5' and H5" protons, and invariably leads to DG structures with poorly defined backbone conformations. We have developed and tested a reliable method to constrain the beta, gamma, and epsilon (and indirectly alpha and zeta) backbone torsion angles by lower-bound NOE distances to unassigned H5'/H5" resonances combined with either H-1 line widths or the conservative use of SIGMA-J measurements; the method relies only on H-1 2-D NMR data, does not involve any structural assumptions, and leads to much improved backbone convergence among DG structures. The C4'-C5' torsion angle-gamma is constrained by lower-bound NOE distances from H2' and from H6/H8 to any H5'/H5", as well as by SIGMA-J(H4') coupling measurements in the 3.9-4.4 ppm region; delta is constrained by H1'-H4' NOE distances and by H3'-H4' and H3'-H2" J couplings in COSY data; epsilon is partially constrained by H3' line width and/or further constrained by subtracting the minimum possible SIGMA-J(H3'-H) from the observed SIGMA-J(H3') (COSY) to arrive at the maximum possible J(H3'-P), which is then converted to H3'-P distance bounds. The angle-beta is partially constrained via H5'-P and H5"-P distance bounds consistent with the maximum H5'-P and H5"-P J couplings derived from the observed H5' and H5" line widths, while alpha and zeta are indirectly constrained by lower distance bounds on the observed (n)H1' to (n + 1)H5'/H5" NOEs combined with the prior partial constraints on beta, gamma, delta, and epsilon. The combined effects of these additional constraints in determining distance geometry structures have been demonstrated using a 12-base duplex, [d(GCCGTTAACGGC)]2. Coordinate RMSDs per atom between structures refined with these constraints from random-embedded DG structures, from ideal A-DNA, and from B-DNA starting structures were less than 0.4 angstrom for the central 8 base pairs indicating good convergence. All backbone angles for the central 8 base pairs are very well constrained with less than 10-degrees variation in any of the 48 torsion angles.