  We report on the calculation of the next-to-leading order QCD corrections to
the production of W-boson pairs in association with a hard jet at the Tevatron
and the LHC, which is an important source of background for Higgs and
new-physics searches. Leptonic decays of the W bosons are included by applying
an improved version of the narrow-width approximation that treats the W bosons
as on-shell particles, but keeps the information on the W spin. A selection of
differential NLO QCD cross sections is provided both for the LHC and the
Tevatron. The QCD corrections stabilize the LO prediction for the cross section
with respect to scale variations. The differential LO cross sections are
generally not simply rescaled by the corrections. Their shapes are particularly
distorted if an additional energy scale is involved.
