The quadratic configuration interaction calculation in the Gaussian-2 second-order Moller-Plesset perturbation theory approach, G2(MP2), is replaced by a coupled-cluster (CC) singles and doubles calculation including a perturbational estimate of the triples excitations. In addition, the self-consistent-held (SCF) and MP2 geometry optimizations and SCF frequency calculation in the G2(MP2) approach are replaced by a density functional theory geometry optimization and frequency calculation [using the Becke three parameter hybrid functional with the Lee-Yang-Parr non-local correlation functional (B3LYP)] in the proposed G2(B3LYP/MP2/CC) approach. This simplification does not affect the average absolute deviation from experiment, but decreases the maximum error compared with the G2(MP2) approach. The G2(B3LYP/MP2/CC) atomization energies are compared with those obtained using the B3LYP approach, and the G2(B3LYP/MP2/CC) model is found to be more reliable, even if the B3LYP calculations are performed using a large basis set.