A model for both proton and photon total cross-sections is presented and
compared with data. The model is based on the eikonal representation, with QCD
mini-jets to drive the rise and soft gluon kt-resummation into the Infrared
region to tame the excessive rise due to low-x perturbative gluons. We discuss
the effects of a singular but integrable expression for the Infrared gluon
spectrum on the high energy behaviour of the total cross-section expected in
this model.Comment: 13 pages, 4 figures, Tenth Workshop on Non-Perturbative Quantum
Chromodynamics at l'Institut Astrophysique de Paris, June 8-12, 200
