Recent theory has predicted that rhombicity in the zero-field splitting (zfs) tensor of transition metal ions with integer spin S greater than or equal to 1 exerts a strong influence on the NMR- paramagnetic relaxation enhancements (NMR-PRE) of resonances of nuclear spins in solution. ZFS rhombicity induces rapid oscillation in the z-component of the electron spin vector, which in the absence of rhombicity, is static with respect to precession or oscillation. Rapid oscillation of S; acts to decouple the nuclear spin magnetic moment from the local field produced by the electron spin, and in this way profoundly depresses the NMR-PRE. The influence of zfs-rhombicity on the solvent H-1 NMR-PRE produced by the complex ion trans-bis(2,4-pentanedione)diaquanickel(II) in dioxane solution has been studied by variable field (0.14-8.5 T) T-1 and T-2 measurements. It is shown that the functional form of the T-1 field dispersion profile can be fit by the mathematical expressions of the Zeeman-limit Solomon-Bloembergen-Morgan theory, although the parameters of such a fit are physically meaningless. Spin dynamics simulation methods which account quantitatively for the effects of zfs interactions lead to a very different physical picture of the spin relaxation process, one in which zfs rhombicity is of central importance in determining the functional form of the field dispersion profile.