MiNNLOPS: optimizing 2→1 hadronic processes

We consider the MiNNLOPS method to consistently combine next-to-next-to-leading order (NNLO) QCD calculations with parton-shower simulations. We identify the main sources of differences between MiNNLOPS and fixed-order NNLO predictions for inclusive observables due to corrections beyond NNLO accuracy and present simple prescriptions to either reduce or remove them. Refined predictions are presented for Higgs, charged- and neutral-current Drell Yan production. The agreement with fixed-order NNLO calculations is considerably improved for inclusive observables and scale uncertainties are reduced. The codes are released within the POWHEG-BOX.