In two previous papers, we generated multiple-scattering corrections to a Regge-pole exchange model. In the present paper we show in detail how the multiple-scattering series, which is a sum of Gaussians in momentum transfer, adds up approximately to an exponential in momentum transfer. Special care is required in this evaluation on account of the oscillating nature of the terms in the series. Since the amplitudes at large |t| are dominated by multiple scattering in this model, the large-|t| behaviour of the single-scattering amplitude is obscured. Polarization phenomena in the same model are discussed briefly.