  We present the first calculation of the next-to-leading-order electroweak
corrections to W-boson + jet hadroproduction including leptonic W-boson decays.
The W-boson resonance is treated consistently using the complex-mass scheme,
and all off-shell effects are taken into account. The corresponding
next-to-leading-order QCD corrections have also been recalculated. All the
results are implemented in a flexible Monte Carlo code. Numerical results for
cross sections and distributions of this Standard Model benchmark process are
presented for the Tevatron and the LHC.
