TeV Scale Cross-Sections and the Pomeranchuck Singularity

We have investigated the detailed structure of $l$-plane singularities of scattering amplitude saturating the Froissart bound. A self-consistent analysis of these singularities provides us secondary terms in the Froissart bound. These secondary terms lead to ghosts in the $l$-plane, which can only be removed by introducing an odderon singularity. Phenomenological implications of this analysis are also discussed.