  We show how to obtain the leading energy dependence of hadronic total cross
sections, in the framework of the nonperturbative approach to soft high-energy
scattering based on Wilson-loop correlation functions, if certain nontrivial
analyticity assumptions are satisfied. The total cross sections turn out to be
of "Froissart" type, $\sigma_{\rm tot}^{(hh)}(s) \mathop\sim B\log^2 s$ for ${s
\to
  \infty}$. We also discuss under which conditions the coefficient $B$ is
universal, i.e., independent of the hadrons involved in the scattering process.
In the most natural scenarios for universality, $B$ can be related to the
stable spectrum of QCD, and is predicted to be $B_{\rm th}\simeq 0.22~{\rm
mb}$, in fair agreement with experimental results. If we consider, instead, the
stable spectrum of the quenched (i.e., pure-gauge) theory, we obtain a quite
larger value $B^{(Q)}_{\rm th} \ge 0.42~{\rm mb}$, suggesting (quite
surprisingly) large unquenching effects due to the sea quarks.
