  Following on our earlier work on leading-logarithmic (LLR) resummations for
the properties of jets with a small radius, R, we here examine the
phenomenological considerations for the inclusive jet spectrum. We discuss how
to match the NLO predictions with small-R resummation. As part of the study we
propose a new, physically-inspired prescription for fixed-order predictions and
their uncertainties. We investigate the R-dependent part of the
next-to-next-to-leading order (NNLO) corrections, which is found to be
substantial, and comment on the implications for scale choices in inclusive jet
calculations. We also examine hadronisation corrections, identifying potential
limitations of earlier analytical work with regards to their $p_t$-dependence.
Finally we assemble these different elements in order to compare matched
(N)NLO+LLR predictions to data from ALICE and ATLAS, finding improved
consistency for the R-dependence of the results relative to NLO predictions.
