We present a new approach to computer modeling of solvation free energies of oil in water. In Semi-Explicit Assembly, we first precompute structural and thermal properties of TIP3P waters around different Lennard-Jones spheres. This tabulated information is then used to compute the nonpolar solvation properties of arbitrary solutes. By accumulating interactions from whole regions of the solute molecule, Semi-Explicit Assembly more properly accounts for effects of solute shape and solves problems that appear as nonadditivities in traditional gamma A approaches. Semi-Explicit Assembly involves little parameter fitting because the solute and water properties are taken from existing force fields. We tested the predictions on alkanes, alkynes, linear and planar polyaromatic hydrocarbons, and on a diverse set of 504 molecules previously explored by explicit solvent simulations. We found that not all hydrocarbons are the same. Hydrocarbons have "hot spots", places where first-shell waters interact more strongly with the molecule than at other locations. For example, waters are more attracted to hover over hydrocarbon rings than at the edges. By accounting for these collective regional effects, Semi-Explicit Assembly approaches the physical accuracies of explicit solvent models in computing nonpolar solvation free energies, but because of the precomputations and the regional additivities, it is nearly as fast to compute as gamma A methods.