  The problem of restoring Froissart bound to the BFKL-Pomeron is studied in an
extended leading-log approximation of QCD. We consider parton-parton scattering
amplitude and show that the sum of all Feynman-diagram contributions can be
written in an eikonal form. In this form dynamics is determined by the phase
shift, and subleading-logs of all orders needed to restore the Froissart bound
are automatically provided. The main technical difficulty is to find a way to
extract these subleading contributions without having to compute each Feynman
diagram beyond the leading order. We solve that problem by using nonabelian cut
diagrams introduced elsewhere. They can be considered as colour filters used to
isolate the multi-Reggeon contributions that supply these subleading-log terms.
Illustration of the formalism is given for amplitudes and phase shifts up to
three loops. For diffractive scattering, only phase shifts governed by one and
two Reggeon exchanges are needed. They can be computed from the
leading-log-Reggeon and the BFKL-Pomeron amplitudes. In applications, we argue
that the dependence of the energy-growth exponent on virtuality $Q^2$ for
$\gamma^*P$ total cross section observed at HERA can be interpreted as the
first sign of a slowdown of energy growth towards satisfying the Froissart
bound. An attempt to understand these exponents with the present formalism is
discussed.
