  Contributions to the decay rates of P-wave charmonium states that are
proportional to $n_f \alpha_s^3$, where $n_f$ is the number of flavors of light
quarks, are calculated in the framework of nonrelativistic QCD using the
threshold expansion method. Dimensional regularization is used to regularize
the infrared divergences that arise from the emission of a soft gluon. Our
results are consistent with the original calculations of Barbieri et al.
