  A simple multipole Pomeron and Odderon model for elastic hadron scattering,
reproducing the structure of the first and second diffraction cones is used to
analyze $pp$ and $\bar{p}p$ scattering. The main emphasis is on the delicate
and non-trivial dynamics in the dip-bump region, at $|t| \approx 1$ GeV$^2$ and
at the second cone. The simplicity of the model and the expected smallness of
the absorption corrections enables one the control of various contributions to
the scattering amplitude, in particular the interplay between the C-even and
C-odd components of the amplitude, as well as their relative contribution,
changing with $s$ and $t$. The role of the non-linearity of the Regge
trajectories is verified. A detailed analysis of the LHC energy region, where
most of the exiting models may be either confirmed or ruled out, is presented.
