Procedures for accurately predicting the kinetics of hydrogen atom associations with hydrocarbon radicals are described and applied to a series of reactions. The approach is based on CASPT2/cc-pvdz evaluations of the orientation-dependent interaction energies within variable reaction coordinate transition state theory. One-dimensional corrections to the interaction energies are estimated from CAS+1+2/aug-cc-pvtz evaluations for the H + CH3 reaction, and a dynamical correction factor of 0.9 is applied. This corrected CASPT2 approach yields results that are within 10% of those obtained with the full CAS+1+2/aug-cc-pvtz potential for the H + CH3, H + C2H5, H + C2H3, and H + C2H reactions. New predictions are made for the H + iso-C3H7, H + tert-C4H9, H + C6H5, and H + C10H7 reactions. For the H + CH3 and H + C2H3 reactions, where the experimental values appear to be the most well-determined, theory and experiment essentially agree to within their error bars. For the other reactions, the agreement is reasonably satisfactory given the often large dispersion in the experimental results. For the reactions with saturated alkyl radicals, the theory predicts that each additional CH3 group increases the steric factor by approximately a factor of 2. In contrast, for the unsaturated radicals, the H + C6H5 and H + C10H7 high-pressure association rate coefficients are nearly identical to that for H + C2H3.