  A central ingredient in establishing the properties of the newly discovered
Higgs-like boson is to isolate its production via vector boson fusion (VBF).
With the typical experimental selection cuts, the VBF sample is contaminated by
a 25% fraction from Higgs + 2 jet production via gluon fusion (ggF) which has
large perturbative uncertainties. We perform a detailed study of the
perturbative uncertainties in the NLO predictions for pp -> H+2 jets via ggF
used by the ATLAS and CMS collaborations, with the VBF selection cuts of their
current H -> gamma gamma analyses. We discuss in detail the application of the
so-called "ST method" for estimating fixed-order perturbative uncertainties in
this case, and also consider generalizations of it. Qualitatively, our results
apply equally to other decay channels with similar VBF selection cuts. Typical
VBF selections include indirect restrictions or explicit vetoes on additional
jet activity, primarily to reduce non-Higgs backgrounds. We find that such
restrictions have to be chosen carefully and are not necessarily beneficial for
the purpose of distinguishing between the VBF and ggF production modes, since a
modest reduction in the relative ggF contamination can be easily overwhelmed by
its quickly increasing perturbative uncertainties.
