Precision studies of the inelastic scattering of alpha particles from selected rare earth nuclei have been interpreted to yield quantitative determinations of the hexadecapole term in the mass distributions of these nuclei in addition to the now familiar, and dominant, quadrupole term. Cross sections for scattering to the 0 +, 2 + and 4 + states of the ground state rotational bands of 154Sm, 166Er and 176Yb were measured at 27.5, 30.0 and 32.5 MeV incident α-particle energy, and over the angular range from 20° to 140°. These data were analyzed with a theory which models the nucleus as a rigid rotor, and the interaction as a deformed, complex optical potential. The parameters of the undeformed potential were determined from an optical-model analysis of elastic scattering from the essentially spherical nucleide 148Sm, measured over the same α-particle angle and energy ranges. The analysis of the data has as its foundation the utilization of the interferences among Coulomb excitation, nuclear quadrupole and nuclear hexadecapole inelastic scattering amplitudes leading to the lower members of the ground state band. The characteristically different energy dependence of the interfering amplitudes has led to a determination of deformation parameters of these nuclei. The parameters so determined simultaneously fit the data obtained at all three incident energies. They are, moreover, in complete accord with parameters previously extracted from 50 MeV inelastic α-particle scattering data. Additional credence is therefore given to the interpretation of the parameterization as a physical representation of the nuclear shape.