A nonstatistical phase space theory is presented which is equivalent to the statistical phase space theory of Light, Pechukas, and Nikitin in one limit. The theory treats channels with low relative orbital angular momentum and low translational energy statistically but uses a partial statistical approximation for large relative orbital angular momenta and high translational energies. It corrects for the properties that the statistical theory generally predicts too large a cross section, never predicts vibrational population inversion, and has the wrong behavior at high energy. The theory may be used in an ab initio way but in the present article it is applied semiempirically to the reaction K + HCl → KCl + H. The calculated reaction cross sections account within experimental error for the behavior of the cross section at high initial translational energy and for the effect of initial vibrational excitation on the cross section. The theory predicts the reaction cross section will decrease if the initial relative translational energy is raised above 12 kcal/mol.