Several refinements to our reduced dimensionality/adiabatic bend theory of reactive scattering are presented and applied to the H + H-2 and D + H-2 reactions. First, the harmonic treatment of the three-atom bending energy is replaced by an accurate numerical calculation of the adiabatic bending energies. Second, the standard J-shifting approximation for linear transition states is replaced by an adiabatic calculation of the overall rotational energy. In addition, the J-shift approximation is reanalyzed for anharmonic bending motion of the transition state, and an obvious improvement is suggested. Cumulative reaction probabilities and thermal rate constants are calculated for H + H-2 and D + H-2 and compared to accurate quantum ones for selected values of the total angular momentum. Based on these comparisons and previous calculations it is concluded that the new treatment of the adiabatic bending energy is a more significant refinement of the reduced dimensionality theory than is the adiabatic treatment of overall rotation. The thermal rate constant is calculated for D + H-2 using the new theory and compared with other previous calculations, a recent full-dimensional accurate one up to 900 K and with experiment up to 2000 K.