The use of two low-cost methods for the prediction of the inner-shells contribution to the correlation energy is analyzed. The Spin-Component-Scaled second-order Møller-Plesset perturbation theory (SCS-MP2) was reparameterized for the prediction of such contributions. The best results are found when only the same spin term is considered (SSS-MP2). The Coupled Electron Pair Approximation (CEPA) using the Domain-based Local Pair Natural Orbital approximation (DLPNO) was also studied for the same purpose. The methods were tested for atomization energies on the W4-11 test set using basis sets up to quadruple zeta quality. The SSS-MP2 proved to be a marked improvement upon MP2 decreasing the root-mean-square-error (RMSE) from 0.443 to 0.302 kcal mol-1 . The RMSE of DLPNO-CEPA/1 in the test set is only 0.147 kcal mol-1 and its computational cost is very low considering the intended applications. Furthermore, a linear combination of both methods decreased the RMSE to 0.118 kcal mol-1 . © 2020 Wiley Periodicals, Inc.