Core correlation and scalar relativistic contributions to the atomization energy of 120 first- and second-row molecules have been determined using coupled cluster and averaged coupled-pair functional methods and the MTsmall core correlation basis set. These results are used to parametrize an improved version of a previously proposed bond order scheme for estimating contributions to atomization energies. The resulting model, which requires negligible computational effort, reproduces the computed core correlation contributions with 88%-94% average accuracy (depending on the type of molecule), and the scalar relativistic contribution with 82%-89% accuracy. This permits high-accuracy thermochemical calculations at greatly reduced computational cost.