  The NA60 experiment has studied low mass muon pair production in In-In
collisions at 158 AGeV with unprecedented precision. With these measurements
one can constrain the in-medium modifications of hadrons embedded in nuclear
matter more thoroughly than from previous experiments. In the present paper we
argue that these constraints could be significantly further tightened and
theoretical uncertainties in modeling of the medium evolution reduced by an
additional experiment measuring low mass di-muon production in Pb-Pb collisions
at 158 AGeV with the same resolution as provided by NA60 for the In-In system.
