Making use of the extrema bounds for the soft pomeron intercept, recently determined by fits to pp and <img id="_x0000_i1026" src="../../img/revistas/bjp/v34n1a/a25img08.gif" align=absbottom>data (from both accelerator and cosmic-ray experiments), we investigate the total cross sections for pion-proton, kaon-proton, gamma-proton and gamma-gamma scattering. We show that by means of global fits, the extrema bounds are in agreement with the bulk of experimental data presently available, and that extrapolations to higher energies indicate different behaviors for the rise of the total cross sections. We also discuss factorization and quark counting, showing that both bounds are in agreement with these properties.