Improvement of the Froissart bound: cross-sections essentially constant up to ISR energies

By simultaneous use of unitarity in all three channels the author has shown that total pi pi cross-sections are bounded by a constant approximately=130 mb, inelastic ones by 31 mb, up to energies of approximately 300 GeV, and that it is only above that than the logarithmic increase permitted by the Froissart bound could begin to show up. (14 refs).