  We present a new approach to the realization of hard fixed-order corrections
in predictions for the processes probed in high energy colliding hadron beam
devices, with some emphasis on the LHC and the future FCC devices. We show that
the usual unphysical divergence of such corrections as one approaches the soft
limit is removed in our approach, so that we would render the standard results
to be closer to the observed exclusive distributions. We use the single
Z/\gamma* production and decay to lepton pairs as our prototypical example, but
we stress that the approach has general applicability. In this way, we open
another part of the way to rigorous baselines for the determination of the
theoretical precision tags for LHC physics, with an obvious generalization to
the future FCC as well.
