Magic-angle spinning (MAS) solid-state NMR (SSNMR) techniques have emerged in recent years for solving complete structures of uniformly labeled proteins lacking macroscopic order. Strategies used thus far have relied primarily on semiquantitative distance restraints, analogous to the nuclear Overhauser effect (NOE) routinely used in solution NMR. Here, we present a complementary approach for using relative orientations of molecular fragments, determined from dipolar line shapes. Whereas SSNMR distance restraints typically have an uncertainty of approximately 1 A, the tensor-based experiments report on relative vector (pseudobond) angles with precision of a few degrees. By using 3D techniques of this type, vector angle (VEAN) restraints were determined for the majority of the 56-residue B1 immunoglobulin binding domain of protein G [protein GB1 (a total of 47 HN-HN, 49 HN-HC, and 12 HA-HB restraints)]. By using distance restraints alone in the structure calculations, the overall backbone root-mean-square deviation (bbRMSD) was 1.01 +/- 0.13 A (1.52 +/- 0.12 A for all heavy atoms), which improved to 0.49 +/- 0.05 A (1.19 +/- 0.07 A) on the addition of empirical chemical shift [torsion angle likelihood obtained from shift and sequence similarity (TALOS)] restraints. VEAN restraints further improved the ensemble to 0.31 +/- 0.06 A bbRMSD (1.06 +/- 0.07 A); relative to the structure with distances alone, most of the improvement remained (bbRMSD 0.64 +/- 0.09 A; 1.29 +/- 0.07 A) when TALOS restraints were removed before refinement. These results represent significant progress toward atomic-resolution protein structure determination by SSNMR, capabilities that can be applied to a large range of membrane proteins and fibrils, which are often not amenable to solution NMR or x-ray crystallography.