The $q_T$ subtraction formalism has proven to be a very effective method to carry out NNLO QCD computations for a wide class of processes where colour singlets and/or heavy quarks are produced in hadron collisions. In the case in which hard jets are produced at Born level $q_T$ cannot be directly applied, and jettiness subtraction is considered as a natural extension of $q_T$. We consider the production of an arbitrary number of jets in hadron collisions and we discuss a new variable that smoothly captures the N+1 to N-jet transition. This variable, that we dub $k_T^{ness}$, represents an effective transverse momentum controlling the singularities of the N+1-jet cross section when the additional jet is unresolved. The $k_T^{ness}$ variable offers novel opportunities to perform higher-order calculations. We study the singular behavior of the N+1-jet cross section as $k_T^{\ness}\to 0$ and, as a phenomenological application, we use the ensuing results to evaluate NLO corrections to some sample jet processes at the LHC. We show that our variable performs extremely well as a resolution variable and appears to be very stable with respect to hadronization and multiple-parton interactions.