  We present a method of analyzing invariant-mass spectra of kaon pairs
resulting from decay of $\phi$ mesons produced in high-energy heavy-ion
collisions. It can be used to extract the shifts in the mass and the width
($\Delta M$ and $\Delta \Gamma$) of the $\phi$ mesons when they are inside the
dense matter formed in these collisions. We illustrate our method with the help
of available preliminary data. Extracted values of $\Delta M$ and $\Delta
\Gamma$ are significantly larger than those obtained with an earlier method.
Our results are consistent with the experimentally observed $p_T$ dependence of
the mass shift. Finally, we present a phenomenological relation between $\Delta
M$ and $\Delta \Gamma$. It provides a useful constraint on theories which
predict the values of these two quantities.
