Thanks to its silicon vertex telescope and 2.5 T dipole field, in the target region, NA60 has a very good dimuon mass resolution (20 MeV at the omega peak) and acceptance down to zero pT for the low mass vector mesons. This allows us to do a high quality measurement of phi yields and pT distributions. This talk presents results obtained in p-Be, p-In and p-Pb collisions at 400 GeV and In-In collisions at 158~GeV per nucleon, as a function of centrality. In particular, we show that the inverse mT slope of the phi measured in In-In collisions, in the dimuon decay channel, increases with Npart, as seen by NA49 with KK decays and contrary to the flat trend observed by NA50 with high pT dimuons. The progress in the analysis of the KK channel from the NA60 data will also be shown. These NA60 results are an important step to solve the so-called phi puzzle.