We develop the notion of "broad-band equilibration" in heavy-ion processesinvolving dense medium. Given density-dependent \Km-masses we show that theequilibration 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 ratioindependent of density. There are experimental indications that this also holdsfor AGS energies. We then proceed to argue that {\it both} $K^+$ and $K^-$ mustget lighter in dense medium at some density $\rho >\rho_0$ due to thedecoupling of the vector mesons. As a consequence, kaon condensation in compactstars could take place {\it before} chiral restoration since the sum of barequark masses in the kaon should lie below $\mu_e$. Another consequence of thedecoupling vector interactions is that the quasi-particle picture involving(quasi)quarks, presumably ineffective at low densities, becomes moreappropriate at higher densities as chiral restoration is approached.
