  We investigate some aspects and consequences of the extrema bounds for the
soft Pomeron intercept, recently determined by means of global fits to $pp$ and
$\bar{p}p$ total cross section data at both accelerator and cosmic-ray energy
regions (scattering data). We also examine the effects of the secondary
Reggeons by introducing fitted trajectories from Chew-Frautschi plots
(spectroscopy data) and determining new constrained bounds for the Pomeron
intercept. In both cases we extend the analysis to $baryon-p$, $meson-p$,
$baryon-n$, $meson-n$, $gamma-p$ and $gamma-gamma$ scattering, presenting tests
on factorization and quark counting rules. We show that in all the cases
investigated, the bounds lead to good descriptions of the bulk of experimental
data on the total cross sections, but with different extrapolations to higher
energies. Our main conclusion is that the experimental information presently
available on the above quantities is not sensitive to an uncertainty of 2% in
the value of the soft Pomeron intercept. At 14 TeV (CERN LHC) the extrema and
constrained bounds allow to infer $\sigma_{tot}$ = 114 $\pm$ 25 mb and 105
$\pm$ 10 mb, respectively.
