  We extend the lowest-order matching of tree-level matrix elements with parton
showers to give a complete description at the next higher perturbative accuracy
in alpha_s at both small and large jet resolutions, which has not been achieved
so far. This requires the combination of the higher-order resummation of large
Sudakov logarithms at small values of the jet resolution variable with the full
next-to-leading order (NLO) matrix-element corrections at large values. As a
by-product this combination naturally leads to a smooth connection of the NLO
calculations for different jet multiplicities. In this paper, we focus on the
general construction of our method and discuss its application to e+e and pp
collisions. We present first results of the implementation in the GENEVA Monte
Carlo framework, where we employ N-jettiness as the jet resolution variable,
combining its next-to-next-to-leading logarithmic resummation with fully
exclusive NLO matrix elements, and PYTHIA8 as the backend for further parton
showering and hadronization. For hadronic collisions, we take Drell-Yan
production as an example to apply our construction. For e+e- -> jets, taking
alpha_s(mZ) = 0.1135 from fits to LEP thrust data, together with the PYTHIA8
hadronization model, we obtain good agreement with LEP data for a variety of
2-jet observables.
