  We report on a recent next-to-leading order perturbative determination of the
dilepton rate from a hot QCD plasma for frequency and momentum of the order of
the temperature and for much smaller invariant mass $M\sim gT$. We briefly
review the calculation, which generalizes the previous one for the photon case
($M=0$). We then analyze the consequences of the new calculation for the
extraction of the photon rate from the small mass dilepton measurements. We
then review a recent NLO determination at large $M$ and we show how to match
and merge its results with the low-mass ones, resulting in a single rate which
is NLO-accurate over the phenomenologically relevant region.
