  There exist full leading-order-in-alpha_s numerical calculations of the rates
for massless quarks and gluons to split and join in the background of a
quark-gluon plasma through hard, nearly collinear bremsstrahlung and inverse
bremsstrahlung. In the limit of partons with very high energy E, where the
physics is dominated by the Landau-Pomeranchuk-Migdal (LPM) effect, there are
also analytic leading-log calculations of these rates, where the logarithm is
ln(E/T). We extend those analytic calculations to next-to-leading-log order. We
find agreement with the full result to within roughly 20% for E(less) >~ 10 T,
where E(less) is the energy of the least energetic parton in the
splitting/joining process. We also discuss how to account for the running of
the coupling constant in the case that E/T is very large. Our results are also
applicable to isotropic non-equilibrium plasmas if the plasma does not change
significantly over the formation time associated with particle splitting.
