Accurate measurements of the magnitudes and relative orientations of chemical shielding, J coupling and dipolar coupling tensors for isolated homonuclear P-31-P-31 spin pairs, using standard P-31 MAS NMR experiments in conjunction with efficient numerical simulation and iterative fitting procedures are described. For a series of transition-metal phosphine complexes (R3P)(2)MX2, containing pairs of crystallographically equivalent phosphorus atoms such that they constitute isolated magnetically nonequivalent P-31-P-31 spin-pair systems, it is demonstrated that the combined effects from MAS averaging, n = 0 rotational resonance dipolar recoupling, and J recoupling lead to P-31 MAS NMR spectra with detailed structural features. These features are highly dependent on the tensorial interactions as well as on the applied external magnetic field strength and MAS frequency. The experimental observations are reproduced by numerically exact computer simulations. Iterative fitting of P-31 MAS spectra, recorded under various experimental conditions, allows for determination of accurate parameters for the isotropic and anisotropic interactions characterizing the P-31-P-31 spin pair. In particular, we demonstrate that the orientation of the chemical shielding tensors relative to each other and relative to the internuclear axis can be determined with high accuracy.