NMR deuteron and oxygen-17 relaxation rates of water in a mixture of 68 mol % water and 32 mol % dimethyl sulfoxide (DMSO) were measured for temperatures between 308 and 183 K. Using these data and the rotational correlation times obtained from the oxygen-17-induced proton relaxation rate in a former study, the quadrupole coupling constants for deuterium and oxygen-17 were derived. Both quadrupole coupling constants show a slight temperture dependence. Comparison of deuteron and oxygen-17 correlation times indicates that the reorientation of the water molecule in the H2O/DMSO mixture is anisotropic.