  We explore the effect of higher order operators in the non-relativistic
formulation of QCD (NRQCD). We calculated masses in the b \bar b spectrum using
quenched gauge configurations at beta = 6.0 and two different NRQCD actions
which have been corrected to order mv^4 and mv^6. The two-point functions are
calculated in a gauge invariant fashion. We find the general structure of the
spectrum to be the same in the two cases. Using the P - 3S1 splitting we
determine the inverse lattice spacings to be 2.44(4) GeV and 2.44(5) GeV for
the mv^4 and mv^6 actions, respectively. We do observe shifts in the spin
splittings. The hyperfine splitting is reduced by approximately 4 MeV, while
the fine splitting is down by up to 10 MeV, albeit with large statistical
errors.
