A number of economical modifications to the high-accuracy extrapolated ab initio thermochemistry (HEAT) model chemistry are evaluated. The two resulting schemes, designated as mHEAT and mHEAT+, are designed for efficient and pragmatic evaluation of molecular energies in systems somewhat larger than can be practically studied by the unapproximated HEAT scheme. It is found that mHEAT+ produces heats of formation with nearly subchemical (±1 kJ/mol) accuracy at a substantially reduced cost relative to the full scheme. Total atomization energies calculated using the new thermochemical recipes are compared to the results of the HEAT-345(Q) model chemistry, and enthalpies of formation for the three protocols are also compared to Active Thermochemical Tables. Finally, a small selection of transition states is studied using mHEAT and mHEAT+, which illuminates some interesting features of reaction barriers and serves as an initial benchmark of the performance of these model chemistries for chemical kinetics applications.