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A model is constructed which can generate a class of scattering amplitudes that have the same analytic properties as conventional perturbation theory, are crossing symmetric, and satisfy the unitarity condition in the elastic region in all three channels. The model consists of a non-linear off-shell integral equation whose solution gives a different amplitude for each different first order term or « generalized potential » that one starts with. The main new condition on these «potentials» is that they cannot have elastic cuts in any channel. The relation of this model to the problem of the uniqueness of the Chew-Mandelstam program is discussed.