A model for S-wave scattering is proposed which could be realistic in an energy range from threshold up to above 1 GeV, where inelasticity is dominated by the channel. The T-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order exactly for the , amplitudes and approximately for . It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili–Omnès problem, thus allowing one to compute the and form factor matrix elements of the scalar current from the T-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the , resonances, as well as the chiral results of the and scalar radii, which are predicted to be remarkably small at . This T-matrix model could be used for a unified treatment of the final-state interaction problem in processes such as , , or the initial-state interaction in .