Monte Carlo tuning in the presence of Matching

We consider the impact of varying alpha_s choices (and scales) on each side of the so-called "matching scale" in MLM-matched matrix-element + parton-shower predictions of collider observables. We explain how inconsistent prescriptions can lead to counter-intuitive results and present a few explicit examples, focusing mostly on W/Z + jets processes. We give a specific prescription for how to improve the consistency of the matching and also address how to perform consistent tune variations (e.g., of the renormalization scale) around a central choice. Comparisons to several collider processes are included to illustrate the properties of the resulting improved matching, relying on Alpgen+Pythia6, with the latter using the so-called Perugia 2011 tunes, developed as part of this effort.