  We present calculations of Higgs boson production via gluon-gluon fusion in
association with one or two additional jets at next-to-leading order in QCD.
The calculation of H+jet is exact in the treatment of the top-quark mass,
whereas for the H+2 jets calculation the two-loop virtual amplitudes are
approximated via a reweighting with leading-order mass effects, while keeping
all top-quark mass effects in the real radiation contributions. For H+jet
production, this study extends a previous calculation, revealing an error in
the previous results. For total and differential cross sections, we present new
results and compare the QCD corrections with the infinite top-mass limit, for
which we find a strikingly good agreement if all amplitudes are rescaled by the
leading-order mass dependence.
