Atomization energies were computed for 73 molecules, many of them chosen from the GAUSSIAN-2 and G2/97 test sets. A composite theoretical approach was adopted which incorporated estimated complete basis set binding energies based on frozen core coupled cluster theory with a quasiperturbative treatment of triple excitations and three corrections: (1) a coupled cluster core/ valence correction; (2) a configuration interaction scalar relativistic correction; and (3) an atomic spin-orbital correction. A fourth correction, corresponding to more extensive correlation recovery via coupled cluster theory with an approximate treatment of quadruple excitations, was examined in a limited number of cases. For the molecules and basis sets considered in this study, failure to consider any of these contributions to the atomization energy can introduce errors on the order of 1-2 kcal/mol. Although some cancellation of error is common, it is by no means universal and cannot be relied upon for high accuracy. With the largest available basis sets (including, in some cases, up through aug-cc-pV6Z), the mean absolute deviation with respect to experiment was found to lie in the 0.7-0.8 kcal/mol range, neglecting the effects of higher order excitations. Worst case errors were 2-3 kcal/mol. Several complete basis set extrapolations were tested with regard to their effectiveness at improving agreement with experiment, but the statistical difference among the various approaches was small.