Single-crystal Mo-95 NMR spectra for a crystal of Mo(CO)(6) have been acquired for the central and satellite transitions at a high magnetic field (14.1 T). The spectra are analyzed in terms of the quadrupole coupling and chemical shielding tensors. Parameters of high precision for the magnitudes, relative, and absolute orientations of these tensors are determined. The orientations of the two tensors are obtained without any a priori knowledge on the crystal symmetry of the Mo(CO)(6) octahedron. The optimized Euler angles, describing the relative orientation of the two tensors, are in accordance with the location of the Mo atom in a crystallographic mirror plane as also seen from the crystal structure of Mo(CO)(6) (orthorhombic, Pnma). The data from single-crystal NMR fully confirm the magnitudes and relative orientation of the quadrupole coupling and chemical shielding tensors determined in a recent Mo-95 static-powder NMR study of Mo(CO)(6). Thus, uncertainties about the reliablility of particularly the three Euler angles, describing the relative orientation of the tensor for the very small chemical shielding anisotropy and the quadrupole coupling tensor, have been clarified. Finally, it is shown that slow-speed spinning Mo-95 MAS NMR at a high magnetic field (14.1 T) allows determination of the NMR parameters with good precision for the two tensorial interactions, despite the small chemical shielding anisotropy.