The interfacial curvature free energy is shown to cause a significant barrier height correction to the classical nucleation rate. This correction is found to be temperature dependent, bur independent of nucleus size. Density functional (DF) calculations are presented for a nonuniform spherical droplet model of the nucleus, Calculations for the surface tension, as a function of nucleus size, and for the interfacial curvature free energy support theoretical predictions and provide an explanation for systematic discrepancies between classical and DF nucleation theories and between the classical theory and experiment.