The reverse type of indentation size effect (ISE), where the apparent microhardness increases with increasing applied test load, was critically examined for the experimentally reported data for a number of single crystals differing in crystal structure and chemical bond, using the theoretical models reported in the literature. The analysis revealed that the indentation-induced cracking model, initially proposed to explain the reverse ISE, is not satisfactory. Examination of the data from the standpoint of the models of the normal ISE showed that, in the case of the reverse ISE, a specimen does not offer resistance or undergo elastic recovery, as postulated in some of the models, but undergoes relaxation involving a release of the indentation stress along the surface away from the indentation site. It was found that, for the comparison of microhardness of a face along different directions, of different planes or that of the same face of the crystals of the same substance subjected to different thermal treatment, the Meyer law and the Hays-Kendall approach are not reliable but that the proportional specimen resistance and elastic/plastic deformation response models give similar results. It was also found that the reverse ISE phenomenon occurs only in materials in which plastic deformation is predominant. The possible origins of the occurrence of reverse ISE are suggested.