  We discuss about a recent computation of the mixed QCD--EW corrections to the
hadroproduction of a massive charged lepton plus the corresponding neutrino
through the Drell--Yan mechanism. The calculation, based on an extension of the
$q_T$ subtraction formalism for heavy-quark production in next-to-next-to
leading order QCD, includes for the first time all the real and virtual
contributions due to initial- and final-state radiation, except for the finite
part of the two-loop virtual correction, which is approximated in the pole
approximation. We report results for the fiducial cross section and the
transverse momentum spectrum of the charged lepton.
