We present a new theory for rates of diffusion-controlled reactions on small electrodes in binary electrolytes. The theory reproduces the results of conventional theory for macroelectrodes and for microelectrodes with small electrode-ion interaction (as would apply for macroelectrodes) as compared to ion-ion interactions while allowing extension beyond this traditional macroelectrode regime. It predicts a new dependence of the limiting current on the parameters of the electrode and of the environment when the electrode-ion interaction is large.