The penetrating power of neutrons means that neutron diffraction may be employed to determine the lattice parameters of mineral phases within samples over 1 cm in size. We have exploited this fact to obtain high-resolution measurements of the elastic strains experienced by olivine and orthopyroxene during room temperature, uniaxial deformation experiments performed in a neutron beam-line, on a mylonite from the Oman ophiolite. Specimens were loaded in three orthogonal directions with respect to the macroscopic fabric of the rock. In each case the average olivine and orthopyroxene strains were the same, even though the elastic stiffnesses of the two phases were different. In comparison with the strains expected from the single-crystal elastic stiffness tensors, the average strains in the different lattice directions for each phase were found to be greater in the stiffer directions, and lesser in the more compliant directions. The overall effect of this tendency toward strain homogenization was for the measured elastic anisotropy of the rock to be significantly lesser than that given by Voigt/Reuss averaging of the single-crystal elastic properties according to the lattice preferred orientations of each phase. The technique used to derive these conclusions potentially provides an important experimental method for the quantitative examination of nonfracture-related controls on the elastic anisotropy of geological materials.