An experimental test of one of the central predictions of the theory of paramagnetic enhancement of NMR relaxation rates in solution (the NMR-PRE) for spins S > 1/2 is reported. For S greater than or equal to 1, zero-field splitting (zfs) interactions are present that, when larger than the electronic Zeeman interaction, act to align the spatial quantization of the electron spin motion along the molecule-fixed principal axis system of the zfs tensor. When the zfs energy is comparable to or greater than the Zeeman energy, the NMR-PRE has been predicted theoretically to be a function of the angular variables that specify the orientation of the electron-nuclear interspin vector in the molecular coordinate frame, such that the paramagnetic relaxation enhancement is larger for nuclear spins on the molecular z-axis than for nuclear spins in the x-y plane. The theoretically predicted range for rho, the ratio of axial/equatorial NMR T-1 relaxation rates, is 1 less than or equal to rho less than or equal to 4, the value of unity corresponding to the Zeeman limit (H-Zeem much greater than H-zfs); in the zfs limit, rho is predicted to reach its maximum value, which is significantly greater than unity. The ratio rho has been determined experimentally for the first time for the axial (H2O) and equatorial (CH3) protons of an S = 1 complex, Ni(II)(acac)(2)(H2O)(2), under conditions that approximate the zfs limit, as was demonstrated from a measurement of the magnetic field dispersion profile of the H2O proton T-1's. The measured axial/equatorial T-1(-1) ratio, rho(exp) = 2.2 +/- 0.3, was significantly greater than unity as expected theoretically. The measured T-1(-1) ratio was in agreement with the results of spin dynamics simulations carried out by the method of Abernathy and Sharp (J. Chem. Phys. 1997, 106, 9032).