We present a new approach for predicting solvation free energies in nonaqueous solvents. Utilizing the corresponding states principle, we estimate solvent Lennard-Jones parameters directly from their critical points. Combined with atomic solutes and the pressure corrected three-dimensional reference interaction site model (3D-RISM/PC+), the model gives accurate predictions for a wide range of nonpolar solvents, including olive oil. The results, obtained without electrostatic interactions and with a very coarse-grained solvent, provide an interesting alternative to widely used and heavily parametrized models.