The problem of expressing the high-energy inelastic amplitudes in terms of the elastic amplitudes that couple through unitarity is discussed. A solution to this problem is given by approximately solving the unitarity equations with assumptions similar to the ones usually made in the absorptive model, together with a high-energy factorization property. The surprising result is obtained that the inelastic amplitudes are completely expressible in terms ofall the elastic ones that have the correct quantum numbers to couple through unitarity. Some general properties of this solution are investigated for π−p and K−p charge exchange by using an exact Fourier-Bessel representation which is derived by means of techniques previously developed. Similarly to what happens in the Byers and Yang droplet model, the high-energy inelastic amplitudes in the forward direction show an exponentially decreasing peak (as function of the momentum transfer), if this is present in at least one of the elastic (initial and final) channels. The question of whether the forward peak of the inelastic amplitude is narrower or wider or comparable to the elastic one is seen to require a very detailed parametrization of the elastic data. In principle, in our model, there are no arbitrary parameters left since the inelastic amplitudes are completely determined from the knowledge ofall the elastic ones. In practice, however, the limitation of experimental information at our disposal forces us to introduce an empirical energy-dependent factor. Within the framework of our model, little can be said about this energy-dependent factor. If, however, one makes the extra assumption that all the elastic channels are comparably equal and that the number of channels open at a given (high) energy have the same energy dependence as the multiplicity, then it can be seen that very good agrement is obtained, in this approximation, for π−→π0n which is the only case for which a sufficiently large statistics exists. No detailed numerical comparison of the theory with experimental data is attempted in this preliminary paper.