  Several important processes and analyses at the LHC are sensitive to
higher-order perturbative corrections beyond what can currently be calculated
at fixed order. The formalism of High Energy Jets (HEJ) calculates the
corrections systematically enhanced for a large ratio of the centre-of-mass
energy to the transverse momentum of the observed jets. These effects are
relevant in the analysis of e.g. Higgs-boson production in association with
dijets within the cuts devised to enhance the contribution from Vector Boson
Fusion (VBF).
  HEJ obtains an all-order approximation, based on logarithmic corrections
which are matched to fixed-order results in the cases where these can be
readily evaluated. In this paper we present an improved framework for the
matching utilised in HEJ, which for merging of tree-level results is
mathematically equivalent to the one used so far. However, by starting from
events generated at fixed order and supplementing these with the all-order
summation, it is computationally simpler to obtain matching to calculations of
high multiplicity.
  We demonstrate that the impact of the higher-multiplicity matching on
predictions is small for the gluon-fusion (GF) contribution of Higgs-boson
production in association with dijets in the VBF-region, so perturbative
stability against high-multiplicity matching has been achieved within HEJ. We
match the improved HEJ prediction to the inclusive next-to-leading order (NLO)
cross section and compare to pure NLO in the h->photon photon channel with
standard VBF cuts.
