A unitarization method is investigated which is based on dispersion relations for the inverse amplitude; the zeros of the partial-wave amplitudes are taken from the Veneziano model and the discontinuity across the right-hand cut is given by elastic unitarity, whereas crossing symmetry yields the left-hand cut discontinuity (for large negatives-values the latter is assumed to be constant). Two free subtraction constants are fixed by minimizing the violation of crossing symmetry-expressed in terms of a number of exact conditions on the partial-wave amplitudes. It was not possible to satisfy all of the crossing constraints simultaneously, but we arrived at a unique solution of the dispersion relations (with a very broadI = 0S-wave resonance) which is unitary and approximately crossing symmetric.