We propose an efficient and accurate non-iterative method, dubbed uESE, for calculating solvation free energies. Apart from a COSMO-like electrostatic term, the model takes into account non-electrostatic contributions, which depend on atomic surfaces, induced surface charge densities, and the molecular volume. uESE is tested on 35 polar and 57 non-polar solvents. The calculated and experimental solvation free energies are compared for 2892 systems. The method exhibits an excellent performance, which is superior to major solvation methods. The mean absolute error of predicted solvation energies is found below 1 kcal/mol for neutral solutes and below 3 kcal/mol for ions. The calculated data are almost independent of the quantum-chemical method or/and basis sets employed. © 2021 Wiley Periodicals LLC.