  We present a measurement of $e^+e^-$ pair production in central Pb-Au
collisions at 158$A$ GeV/$c$. As reported earlier, a significant excess of the
$e^+e^-$ pair yield over the expectation from hadron decays is observed. The
improved mass resolution of the present data set, recorded with the upgraded
CERES experiment at the CERN-SPS, allows for a comparison of the data with
different theoretical approaches. The data clearly favor a substantial
in-medium broadening of the $\rho$ spectral function over a density-dependent
shift of the $\rho$ pole mass. The in-medium broadening model implies that
baryon induced interactions are the key mechanism to in-medium modifications of
the $\rho$-meson in the hot fireball at SPS energy.
