  We consider the class of inclusive hadron collider processes in which one or
more energetic jets are produced, possibly accompanied by colourless particles.
We provide a general formulation of a slicing scheme for this class of
processes, by identifying the various contributions that need to be computed up
to next-to-leading order (NLO) in QCD perturbation theory. We focus on two
novel observables, the one-jet resolution variable $\Delta E_t$ and the $n$-jet
resolution variable $k_{T}^{\mathrm{ness}}$, and explicitly compute all the
ingredients needed to carry out NLO computations using these variables. We
contrast the behaviour of these variables when the slicing parameter becomes
small. In the case of $k_{T}^{\mathrm{ness}}$ we also present results for the
hadroproduction of multiple jets.
