  The Regge description of forward hadronic scattering is extended from
$\sim1\gev$ above each threshold up to the multi TeV range. This is achieved
with a simple parametrization, that includes mass effects, a logarithmic growth
based on an improved unitarity bound at intermediate energies and a separate
factorization of singularities. This parametrization can be easily implemented
for phenomenological use, but also sheds light on subdominant trajectories and
the Pomeron logarithmic growth law.
