A relation between the real part of an elastic scattering amplitude at arbitrary energy and its asymptotic parameters in the Regge model is derived. Together with finite-energy sum rules, this relation is applied to forward nucleon-nucleon and antinucleon-nucleon scattering where the unphysical region is approximated by a number of pole terms arising from the exchange of meson states. A fit to high-energy total-cross-section data and to forward-angle real parts at all energies indicates that there is little dependence on isospin exchanges in the $t$ channel at high energies. When allowed to vary below unity, the intercept of the leading trajectory prefers the maximum value, 1. In this case the nucleon-nucleon total cross sections each tend to 33\ifmmode\pm\else\textpm\fi{}1 mb.