J/psi and psi ̀produced in high-energy heavy-ion collisions are absorbed by their collisions with nucleons and produced soft particles, leading to two distinct absorption mechanisms. The signature of absorption by produced soft particles, as revealed by psi ̀production data, consists of a gap and a change of the slope in going from the pA line to the nucleus-nucleus line when we make a semi-log plot of the survival probability as a function of the path length. Using this signature, we find from the J/psi production data in pA, O-Cu, O-U, and S-U collisions that the degree of J/psi absorption by produced soft particles is small and cannot account for the J/psi data in Pb-Pb collisions. The anomalous suppression of J/psi production in Pb-Pb collisions can be explained as due to the occurrence of a new phase of strong J/psi absorption, which sets in when the local energy density exceeds about 3.4 GeV/fm3. To probe the chemical content of the new phase, we propose to study the abundance of open-charm mesons and charm hyperons which depends sensitively on the quark chemical potential.