We discuss how hadronic total cross sections at high energy depend on the details of QCD, namely on the number of colours and the quark masses. We find that while a “Froissart”-type behaviour is rather general, relying only on the presence of higher-spin stable particles in the spectrum, the value of B depends quite strongly on the quark masses. Moreover, we argue that B is of order at large , and we discuss a bound for B which does not become singular in the chiral limit, unlike the Froissart–Łukaszuk–Martin bound.