  We reanalyse $\bar p p$ and $pp$ high energy data of the elastic scattering
above $\sqrt{s}=5$ GeV on the total cross-section $\sigma_{tot}$ and on the
forward $\rho$-ratio for various models of Pomeron, utilizing two methods. The
first one is based on analytic amplitudes, the other one relies on assumptions
for $\sigma_{tot}$ and on dispersion relation for $\rho$. We argue that it is
not possible, from fitting only existing data for forward scattering, to select
a definite asymptotic growth with the energy of $\sigma_{tot}$. We find
equivalent fits to the data together with a logarithmic Pomeron giving a
behavior $\sigma_{tot} \propto \ln ^\gamma s$, $\gamma\in [0.5,2.20]$ and with
a supercritical Pomeron giving a behavior $\sigma_{tot} \propto s^\epsilon $,
$\epsilon\in [0.01,0.10]$.
