A simple multiplicative approach is presented for approximating the full configuration interaction (FCI) limit at the complete basis set limit from the small basis set FCI and coupled cluster [most notably CCSD(T) and CCSDT] calculations. The proposed scaled higher-order correlation (SHOC) correction scheme is demonstrated to extrapolate CCSD(T) and CCSDT correlation energies for BH and AlH to the FCI limit with remarkable accuracy, and to correct the dissociation energies of [CN,C-2,N-2] computed at the CCSD(T) and CCSDT levels by [+1.4, +2.3, +1.5] kcal/mol, respectively, bringing them in much closer agreement with the best experimental values. The approach is also well suited for the generation of accurate potential energy hypersurfaces. (C) 2001 American Institute of Physics.