The facts concerning the occurrence of superconductivity in R 2- z Ce z CuO 4 and in R 2- z Th z CuO 4 are studied using a combination of simple tools: a hard-sphere model, the self-consistent bond-valence-sum method and Madelung potential calculations. Doping by isolated substitutional Ce should produce Ce 3+ , and not Ce 4+ , causing us to conclude that the dopants are not isolated, but pairs, which make the material p type and not n type. The (...) L = 0 magnetic rare-earth ions Gd and Cm are unsplit pair breakers, unlike the other magnetic rare-earth ions which lead to superconductivity. As the rare-earth ions become smaller, the c -axis length shortens; then the O ions rotate after they come into contact with one another. Eu 1.85 Th 0.15 CuO 4 does not superconduct because quadrivalent Th is too large to fit at the dopant site, but Eu 1.85 Ce 0.15 CuO 4 does superconduct because Ce fits. (shrink)