  For the pressure (or free energy) of QCD, four-dimensional (4d) lattice data
is available at zero baryon density up to a few times the critical temperature
$T_c$. Perturbation theory, on the other hand, has serious convergence problems
even at very high temperatures. In a combined analytical and three-dimensional
(3d) lattice method, we show that it is possible to compute the QCD pressure
from about $2 T_c$ to infinity. The numerical accuracy is good enough to
resolve in principle, e.g., logarithmic contributions related to 4-loop
perturbation theory.
