We show that the high precision dN/dt UA4/2 data at = 541 GeV are compatible with the presence of Auberson-Kinoshita-Martin (AKM) type of oscillations at very small momentum transfers. These oscillations seem to be periodic in , the corresponding period being 2·10-2 GeV. The existence of such visible oscillations suggests a general mechanism of saturation of axiomatic bounds. As an illustration the consequences for extracting the parameter = Re

The odderon intercept is calculated directly, from its expression via an average energy of the odderon Hamiltonian, using both trial wave functions in the variational approach and the wave function recently constructed by Janik and Wosiek. The results confirm their reported value for the energy. Variational calculations give energies some 30% higher. However, they also predict the odderon intercept to be quite close to unity. In fact, for realistic

We propose a QCD-inspired two-component Pomeron form which gives an excellent description of the pp, p, Kp, p and total cross-sections. Our fit has a better 2/dof for a smaller number of parameters as compared with the PDG fit. Our 2-Pomeron form is fully compatible with weak Regge exchange-degeneracy, universality, Regge factorization and the generalized vector dominance model.