We propose a small set of atomization energies and a small set of barrier heights as benchmarks for comparing and developing theoretical methods. We chose the data sets to be subsets of the Database/3 collection of atomization energies and barrier heights. We show that these data sets, consisting of six barriers and six atomization energies, are very representative of all the atomization energies and barrier heights in Database/3, and we call them the AE6 and BH6 benchmarks, respectively. Benchmark values are tabulated for 80 standard methods, including Hartree-Fock, Moller-Plesset perturbation theory, quadratic configuration interaction, coupled cluster theory, hybrid density functional theory, and multicoefficient correlation methods.