Discontinuities in nanoindentation loading curves are frequently observed in ceramic materials. These normally occur at fairly random loads and displacements, probably due to the random distance of pre-existing defects from the indent location. Here we report the observation of reproducible, sudden indent-depth changes which occur over a very narrow distribution of depths and loads, for GaAs and a range of related epitaxial layer systems. The surface preparation and material defect density have a significant influence. Different tip geometries have been used to gain insights into the deformation processes which cause these discontinuities.