We present 9 new tunes of the p?-ordered shower and underlying-event model in PYTHIA 6.4. These ‘‘Perugia’’ tunes update and supersede the older ‘‘S0’’ family. The data sets used to constrain the models include hadronic Z decays at LEP, Tevatron min-bias data at 630, 1800, and 1960 GeV, Tevatron DrellYan data at 1800 and 1960 GeV, and SPS min-bias data at 200, 546, and 900 GeV. In addition to t...