To achieve a kilojoules-per-mole level of accuracy consistently in Computational thermochemistry, the inclusion of post-CCSD(T) correlation effects cannot be avoided. Such effects are included in the W4 and HEAT computational thermochemistry protocols. The principal bottleneck in carrying out such calculations for larger systems is the evaluation of the (T) over cap (3)-(T) term. We propose a cost-effective empirical approximation for this term that does not entail any reliance on experimental data. For first-row molecules, our W3.21ite protocol yields atomization energies with a 95% confidence interval of similar to 0.4 kcal/mol at the expense of introducing two such parameters. W3.21ite has been successfully applied to aromatic and aliphatic hydrocarbons such as benzene, fulvene, phenyl radical, pyridine, furan, benzyne isomers, trans-butadiene, cyclobutene, [1.1.1]propellane, and bicyclo[1.1.1]pentane. The W3.21ite predictions for fulvene, phenyl radical, cyclobutene, and [1.1.1]propellane are impossible to reconcile with experiment and suggest that remeasurement may be in order.