Can the "standard" unitarized Regge models describe the TOTEM data?

The standard Regge poles are considered as inputs for two unitarization methods: eikonal and U-matrix. It is shown that only models with three input pomerons and two input odderons can describe the high energy data on $pp$ and $\bar pp$ elastic scattering including the new data from Tevatron and LHC. However, it seems that the both considered models (eikonal and U-matrix) require a further modification (e.g., to explore nonlinear reggeon trajectories and/or nonexponential vertex functions) for a more satisfactory description of the data at 19.0 GeV$\leq \sqrt{s}\leq$ 7 TeV and 0.01 $\leq |t|\leq $14.2 GeV$^{2}$.