Four sets of compositional data with a departure z or epsilon from the stoichiometry of tenorite Cu1+/-zO or CuO1+/-epsilon are re-examined for possible point defects. Correlations z(p(O2)) at equilibrium solid double left right arrow pure di-oxygen - when they can be computed - indicate the presence of either oxygen vacancies or copper interstitials or clusters of them. Some recent data after quenching are in favor of copper interstitials. Few data concerning tenorite prepared by decomposition of a salt, by oxidation of copper and by CVT in sealed tubes have generally been interpreted in the literature as indicating copper deficiency. In those oxides a large departure from the stoichiometry indicates a complex behavior likely due to several point defects possibly ordering at short and/or long range, and including chemical impurities in the case of sealed tube preparation. It is, however, in fact likely that the defect structure of such samples involves the two sub-lattices. Cu3O2- or Cu4O3-like clusters can even be envisaged.