  We compute mixed QCD-electroweak corrections to the neutral-current Drell-Yan
production of a pair of massless leptons in the high invariant mass region. Our
computation is fully differential with respect to the final state particles. At
relatively low values of the dilepton invariant mass, $m_{\ell \ell} \sim 200$
GeV, we find unexpectedly large mixed QCD-electroweak corrections at the level
of -1%. At higher invariant masses, $m_{\ell \ell} \sim 1$ TeV, we observe that
these corrections can be well approximated by the product of QCD and
electroweak corrections. Hence, thanks to the well-known Sudakov enhancement of
the latter, they increase at large invariant mass and reach e.g. -3% at
$m_{\ell \ell} = 3$ TeV. Finally, we note that the inclusion of mixed
corrections reduces the theoretical uncertainty related to the choice of
electroweak input parameters to below the percent level.
