  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. Contributions
from external bottom quarks are neglected, because they are either numerically
suppressed or should be attributed to different processes such as Wt or ttbar
production. A survey of differential NLO QCD cross sections is provided both
for the LHC and the Tevatron. The QCD corrections stabilize the leading-order
prediction for the cross section with respect to scale variations. However, the
scale dependence of the next-to-leading order results for the LHC is only
reduced considerably if a veto against the emission of a second hard jet is
applied. In general, the corrections do not simply rescale the differential
leading-order cross sections. In particular, their shapes are distorted if an
additional energy scale is involved.
