Ultrathin ReBa2Cu3O7-δ (ReBCO) (Re = Y, Nd) films in the form of trilayer sandwiches between (PrxY1-x)Ba2Cu3O 7-δ((PrxY1-x)BCO) (1 ≥ x ≥ 0) and YBCO/(Pr xY1-x)BCO superlattices with nominal YBCO layer thickness as thin as 1 unit- cell were grown by pulsed laser deposition. It was found that although the 1-unit-cell thick YBCO films were superconducting, the Tc value depends strongly on the doping level x in the adjacent layers. The Tc value increases when x is reduced. A number of effects, either extrinsic or intrinsic in origin, have been examined by various experiments. The results indicate that the lattice mismatch, interdiffusion between Y and Pr atoms, and oxygen deficiency are unlikely to be the primary reason. Charge redistribution and the possibility of K-T transition were suggested by Raman and transport measurement, but the effects observed may not be sufficient to explain the change of zero resistance temperature and the broadening of the transition in these sample structures.