We examine the effect on the superconducting transition temperature (Tc) of chemical inhomogeneities in Bi2Sr2CuO 6+δ and Bi2Sr2CaCu2O 8+δ single crystals. Cation disorder at the Sr crystallographic site is inherent in these materials and strongly affects the value of Tc. Partial substitution of Sr by Ln (Ln = La, Pr, Nd, Sm, Eu, Gd, and Bi) in Bi2Sr1.6Ln0.4CuO 6+δ results in a monotonic decrease of Tc with increasing ionic radius mismatch. By minimizing Sr site disorder at the expense of Ca site disorder, we demonstrate that the Tc of Bi2Sr2CaCu2O 8+δ can be increased to 96 K. Based on these results we discuss the effects of chemical inhomogeneity in other bulk high-temperature superconductors.