The local structures of the new phosphorus chalcogenide-copper iodide coordination compounds (CuI)P4Se4, (CuI)(2)P8Se3, (CuI)(3)P4Se4, and (CuI)(3)P4S4 are investigated using comprehensive Cu-63, Cu-65, and P-31 magic angle spinning NMR techniques. Peak assignments are proposed on the basis of homo- and heteronuclear indirect spin-spin interactions, available from lineshape analysis and/or two-dimensional correlation spectroscopy. In particular, the P-31-Cu-63,Cu-65 scalar coupling constants have been extracted from detailed lineshape simulations of the P-31 resonances associated with the Cu-bonded P atoms. In addition, the RNnnu pulse symmetry concept of Levitt and coworkers has been utilized for total through-bond correlation spectroscopy (TOBSY) of directly-bonded phosphorus species. The resonance assignments obtained facilitate a discussion of the P-31 and Cu-63,Cu-65 NMR Hamiltonian parameters in terms of the detailed local atomic environments. Analysis of the limited data set available for this group of closely related compounds offers the following conclusions: (1) bonding of a special phosphorus site in a given P4Xn (X = S, Se) molecule to Cu+ ions shifts the corresponding P-31 NMR signal upfield by about 50 ppm relative to the uncomplexed molecule, (2) the magnitude of the corresponding scalar P-31-Cu-63,Cu-65 spin-spin coupling constant tends to decrease with increasing Cu-P distance, and (3) the Cu-63,Cu-65 nuclear electric quadrupolar coupling constants appear to be weakly correlated with the shear strain parameter specifying the degree of local distortion present in the four-coordinated [CuI2P2] and [CuI3P] environments. Overall, the results illustrate the power and potential of advanced solid state NMR methodology to provide useful structural information in this class of materials.