A proper understanding of nucleation is crucial in several natural and industrial processes. However, accurate quantitative predictions of this phenomenon have not been possible. The most popular tool for calculating nucleation rates, classical nucleation theory (CNT), deviates by orders of magnitude from experiments for most substances. We investigate whether part of this discrepancy can be accounted for by the curvature-dependence of the surface tension. To that end, we evaluate the eading order corrections for water, the Tolman length and the rigidity constants, using square gradient theory coupled with the accurate cubic plus association equation of state. The Helfrich expansion is then used to incorporate them into the CNT-framework. For water condensation, the modified framework successfully corrects the erroneous temperature dependence of the nucleation rates given by the classical theory and reproduces experimental nucleation rates.