We have analyzed the latest NA50 data on J/psi suppression in Pb + Pb collisions. J/psi production is assumed to be a two-step process: (i) formation of a cc- pair, which is accurately calculable in QCD, and (ii) formation of a J/psi meson from the cc- pair, which can be conveniently parametrized. The parameters of the model were fixed from experimental data on the total J/psi cross section as a function of effective nuclear length. The model gives an excellent description of NA50 data on the ET dependence of the J/psi-to-Drell-Yan ratio. It was applied to the ET dependence of J/psi at RHIC energies, and predicts a much larger suppression of J/psi, in agreement with other model calculations.