The role of surface energy anisotropy during grain growth is investigated using both physical experiments on octachloropropane and numerical experiments using the Elle microstructural modeling system. In particular the effects of anisotropy on growth rates, grain shapes, and lattice-preferred orientations are analyzed. Anisotropic growth in thin polycrystalline sheets of octachloropropane is found to systematically remove certain c-axis orientations from the sample, without obviously modifying the grain shapes. By comparison with equivalent numerical experiments, we can explain these observations with a simple boundary-layer model that treats each side of each grainboundary as an independent system. The observed growth exponent in the physical experiment of 0.35 is significantly below the theoretical level of 1, and although the numerical experiments have growth rates as low as 0.68, apparently some other factor that suppresses the growth rate in the octachloropropane was also active. The anisotropy of surface energies also leads to an increase in the grain-size distribution, and when it occurs in rocks with a strong preexisting crystallographic preferred orientation, may even lead to the development of a shape-preferred orientation that is completely unrelated to the shape of the finite strain ellipsoid.