The ATOMIC protocol is a quantum-chemical thermochemistry protocol designed to obtain accurate atomization energies and derived heats of formation. It reduces errors of computationally tractable composite schemes through the use of bond separation reactions, which are implemented in a consistent ab initio framework. The present work explores possible simplification of previously introduced ATOMIC models. While coupled cluster calculations with singles and doubles excitations and perturbational treatments of connected triples excitations [CCSD(T)] are still required for high accuracy, basis-set truncations are possible in the CCSD-MP2 and CCSD(T)-CCSD components. The resulting models B-4, B-5, and B-6 show root-mean-square (RMS) errors of only 0.21 to 0.46 kcal/mol for the AE set, which is a benchmark comprising complete-basis-set CCSD(T)(full) atomization energies of 73 neutral, closed-shell molecules composed of H, C, N, O, and F atoms. The evaluation of connected triples excitations can be avoided at medium levels of accuracy if the complete-basis-set MP2 energy is augmented with an empirically calibrated fraction of the difference between MP3 (or CCSD) and MP2 energies, calculated with small basis sets. The corresponding E-MP3 and E-CCSD models show RMS errors of 1.01 and 0.70 kcal/mol, respectively. Spin-component scaling is an option to rely entirely on the MP2 level of theory and still cut the RMS error of 4.38 kcal/mol by roughly a factor of 2 and achieve an accuracy comparable to accurate density functionals, such as M05-2X. The proposed new models are additionally tested with the HOF benchmark, a subset of G3/99 heats of formation that includes only neutral closed-shell molecules composed of H, C, N, O, and F atoms. The assessment shows that a number of experimental reference values are in error and should be replaced with more recent data. Results obtained with the new models are compared to original HOF (G3/99) reference data, to updated reference data, and to accurate ATOMIC/A theoretical data.