The quality of the dimuon measurements made by NA60, in proton-nucleus and heavy-ion collisions, is much better than that reached by previous experiments, such as NA38 and NA50. The most important improvement is due to the use of a radiation-tolerant silicon vertex telescope, placed immediately downstream of the target. This allows NA60 to do a high quality measurement of meson yields and pT distributions. This paper presents results obtained in p-Be, p-In and p-Pb collisions at 400 GeV, from data collected in 2002, and in In-In collisions at 158 AGeV, as a function of centrality, from the 2003 running period. In particular, we show that the inverse mT slope measured in In-In collisions, in the → μμ decay channel, increases with the number of nucleons participating in the collisions, rather than following a flat trend as seen in the NA50 data collected in the same decay channel but restricted to high pT values. We also show that our measurements seem to agree with the values previously measured by NA49, using → KK decays, in Pb-Pb and other collision systems.