A test set of 21 radical addition and 28 hydrogen abstraction reactions has been studied at the W1, G4, G3X, G3X(MP2), and G3X(MP2)-RAD levels of theory with a view to establishing whether the recently introduced G4 theory offers improved performance over the G3 methods. All methods tested approximated the benchmark W1 values to within a mean absolute deviation (MAD) of 4 kJ mol(-1) or less, although maximum absolute deviations for problematic reactions (such as radical addition to thiocarbonyl compounds) can be as much as 10 kJ mol(-1) for the G3 methods. The new noncanceling higher-level correction (HLC) term in G4 was found to be capable of mitigating these errors in radical addition, but it introduced a systematic error to the reaction energies of the abstraction reactions, and its format may therefore require re-examination. G3 methods were shown to offer "chemical accuracy" even for these problematic cases, provided they were corrected to the W1 level of theory via an ONIOM-based approach.