We examine properties of small-radius jets, focusing on phenomenological applications to the inclusive jet spectrum. We match fixed-order calculations with the leading-logarithmic resummation of the jet radius (LLR), and propose a new prescription to evaluate theoretical uncertainties for next-to-leading order (NLO) predictions. We also examine the R-dependent next-to-next-to-leading order (NNLO) corrections, and include them in our calculation. We discuss hadronisation corrections, which are derived from Monte Carlo generators. Finally, we assemble these elements and compare the ratio of the inclusive jet spectra at two R values obtained from our matched (N)NLO+LLR predictions to data from ALICE and ATLAS, finding improved agreement.