We report tests of new (2005) and established (1999-2003) multilevel methods against essentially converged benchmark results for nonbonded interactions in benzene dimers. We found that the newly developed multicoefficient extrapolated density functional theory (DFT) methods (which combine DFT with correlated wave function methods) give better performance than multilevel methods such as G3SX, G3SX(MP3), and CBS-QB3 that are based purely on wave function theory (WFT); furthermore, they have a lower computational cost. We conclude that our empirical approach for combining WFT methods with DFT methods is a very efficient and effective way for describing not only covalent interactions (as shown previously) but also nonbonded interactions.