For thermochemistry, our results demonstrate that the BH&H-LYP+D3 functional with 50% HF exchange often exhibits satisfactory accuracy as compared to B3LYP+D3. Errors for the former are < 1 kcal/mol for many thermochemical data sets. Furthermore, for problems that are dominated by SIE, the half-and-half functional may even outperform the best contemporary density-functional approximations, exemplified here by ωB97M-V. A notable exception is that atomization energies are significantly less accurate, even as compared to B3LYP+D3, for the entire one-parameter B(α)LYP+D3 family of functionals.