The NA60 experiment has measured low mass muon pair production in In-In collisions at 158A GeV with unprecedented precision. We show that these data are reproduced very well by a dynamical model with parameters scaled from fits to measurements of hadronic transverse mass spectra and Hanbury Brown–Twiss correlations in Pb-Pb and Pb-Au collisions at the same energy. The data are consistent with in-medium properties of rho and omega mesons at finite temperature and density as deduced from empirical forward-scattering amplitudes. Inclusion of the vacuum decay of the rho meson after freeze-out is necessary for an understanding of the mass and transverse momentum spectrum of dimuons with M<~0.9 GeV/c2.