Geometries, barriers, and enthalpies have been calculated at a variety of levels of theory for a test set of seven H-atom abstraction reactions: CH2X. + CH3Y --> CH3X + CH2Y. for (X,Y) = (H,H), (F,H), (Li,H), (Li,F), (CN,H), (OH,H), and (OH,CN). The objective was to select reliable yet cost-effective theoretical procedures for studying H-atom abstraction reactions that involve carbon-centered radicals, to facilitate the study of these reactions in biological and polymerization applications. To this end, geometry optimizations have been observed to be relatively insensitive to the level of theory, although the Hartree-Fock (HF) and Moller-Plesset second-order perturbation (MP2) methods should be avoided for spin-contaminated systems. The QCISD/6-31G(d) method provided excellent agreement with CCSD(T)/6-311G(d,p) and would provide a suitable benchmark level of theory when the latter could not be afforded, whereas MPW1K/6-31+G(d,p) provided excellent low-cost performance and would thus be suitable for larger systems. Barriers and enthalpies were more sensitive to the level of theory; nonetheless, the various high-level composite procedures (including the G3, G3-RAD, CBS, and W1 families of methods) were generally in excellent agreement with each other. However, in the spin-contaminated reactions, the spin-correction term in the CBS-QB3 procedure seems to be introducing a systematic error and may require some adjustment. The MPW1K/6-311+G(3df,2p) method provided excellent low-cost performance, and would be suitable for larger systems, whereas the RMP2/6-311+G(3df,2p) method also performed well, especially for predicting the reaction enthalpies and other thermochemical properties.