An attempt was made to reconcile discrepant findings in the size constancy performance of poor premorbid, process, non-paranoid schizophrenic men. It was postulated that an impairment of basic cognitive skills, and particularly of conservation, differentiates schizophrenics and normals, and under-constant and over-constant non-paranoid schizophrenics, and that this and an associated primitive visual centration effect may lead to paradoxical over-constancy for some schizophrenics. The results confirm that schizophrenics may be both under- and over-constant, and that they exhibit significantly low levels in primitive cognitive operations. The latter abnormalities are particularly marked in over-constant schizophrenics, for whom there is strong evidence of centration with a distant standard. Contradictory findings of over- as well as under-constancy in non-paranoid schizophrenics may thus be a function, apart from other determinants, of differences in the availability of conserving operations, and differences in centration strategies, where the latter would be influenced by characteristics of the experimental display.