  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 M{\o}ller-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 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. The RMSE of
DLPNO-CEPA/1 in the test set is only 0.147 kcal/mol 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.
