15N shielding tensors were determined for the central peptide groups in GGV, AGG, and APG by single-crystal NMR. We find that the angle between the downfield component (delta11) and the N-H or the N-C(delta) (pro) bonds is in the range of 20-23 degrees and in accord with previous solid-state NMR measurements. However, AGG, unlike APG or GGV, has a distorted peptide plane, and delta11 lies approximately in the plane of N, C(alpha), and H rather than in the peptide plane defined by heavy atoms. Accurate orientations of delta22 and delta33 were determined, and the usual assumption that delta22 is along the peptide normal was found only in APG which has a highly nonaxial tensor. More generally, delta22 and delta33 are rotated about the delta11 axis (36 degrees in GGV). These results are compared with DFT calculations to gain a structural understanding of the effects of intermolecular interactions on shielding tensor principal components and orientations. Trimeric clusters containing H-bonded neighbors predict the orientations of the principal components within 2-3 degrees, but calculated principal components are less quantitative. Possible reasons for this disagreement are explored.