The impact of higher-order correlation effects on dissociation energies was measured for three diatomic molecules (HF, N-2, and CO) using standard coupled cluster theory, including a perturbative treatment of triple excitations, as the baseline for comparison. Among the higher-order methods examined were two variations of coupled cluster theory [CCSDT and CCSD(TQ)] and two approximations to full configuration interaction. Basis sets were chosen from the correlation-consistent family of basis sets, with the largest being the aug-cc-pVQZ set. Polarized valence double zeta quality basis sets were found to yield corrections that differed substantially from larger basis set results. At the double zeta level, higher order corrections increased the binding energies, whereas calculations with triple and quadruple zeta basis sets gave the opposite effect. Although the absolute magnitude of the higher-order corrections was small for these diatomics, they were nonetheless significant in light of a target accuracy of +/- 1 kcal/mol. Among molecules composed of first-through-third period elements, such as those in the G2 and G2/97 collections, the contribution to D-0 from higher order correlation effects could easily exceed 1 kcal/mol. If further studies corroborate the present findings, CCSDT should provide an effective method of determining the magnitude of the higher-order correction, at least when basis sets of triple zeta or better quality can be used. CCSD(TQ) often overestimated the higher order correction, sometimes exceeding the estimated full configuration interaction result by a factor of three.