  We develop the notion of "broad-band equilibration" in heavy-ion processes
involving dense medium. Given density-dependent \Km-masses we show that the
equilibration at GSI energies claimed to hold in previous treatments down to
$\sim \rho_0/4$, can be replaced by a broad-band equilibration in which the
\Km-meson and hyperons are produced in an essentially constant ratio
independent of density. There are experimental indications that this also holds
for AGS energies. We then proceed to argue that {\it both} $K^+$ and $K^-$ must
get lighter in dense medium at some density $\rho >\rho_0$ due to the
decoupling of the vector mesons. As a consequence, kaon condensation in compact
stars could take place {\it before} chiral restoration since the sum of bare
quark masses in the kaon should lie below $\mu_e$. Another consequence of the
decoupling vector interactions is that the quasi-particle picture involving
(quasi)quarks, presumably ineffective at low densities, becomes more
appropriate at higher densities as chiral restoration is approached.
