One of the fundamental questions involving the high-temperature copper oxide containing superconductors is to understand the relationship between hole concentration and the superconducting transition temperature, Tc. We help resolve this question by a study of Nd-, La-, Ga-, Ca-, and Zn-substituted YBa2Cu3Oy with controlled oxygen stoichiometry. The total hole concentration is determined by a chemical method and trends in the mobile hole concentration by Hall measurements. By considering Tc to be a function of the mobile sheet holes only, there is a maximum in Tc (92 K) at a sheet-hole concentration of about 0.20-0.25 per Cu site. © 1989 The American Physical Society.