  We calculate the pressure for pure-glue QCD at high temperature to two-loop
order using hard-thermal-loop (HTL) perturbation theory. At this order, all the
ultraviolet divergences can be absorbed into renormalizations of the vacuum
energy density and the HTL mass parameter. We determine the HTL mass parameter
by a variational prescription. The resulting predictions for the pressure fail
to agree with results from lattice gauge theory at temperatures for which they
are available.
