Density-dependent S-33 magnetic shielding has been measured for the first time. For pure gaseous SF6 and its binary mixtures with Xe, CO2 and NH3 at 298 K, an increase in density linearly decreases the 33S shielding constant of SF6. This permits one to separate quantitatively the shielding contributions due to intermolecular interactions and the shielding parameter of an isolated SF6 molecule. Spin-spin coupling in SF6 ((1)J(SF)) has also been measured but only for gaseous samples of high densities. It was observed that the (1)J(SF) coupling constant increases for more dense samples and that the increase is even more pronounced in liquid solutions. All of the new results can be used for an improved verification of ab initio calculations of sulfur shielding and spin-spin coupling in the SF6 molecule because the new S-33 NMR measurements reveal the magnitudes of appropriate intermolecular effects.