We present an eikonal model for the small-angle high-energy scattering of nucleons and antinucleons on nucleon targets. The model uses a flat Pomeranchon with a residue function given by a squared dipole. We also use exchange-degenerate trajectories and residue functions for the three pairs of Regge poles (the ω and P', the ρ and A2, and the π and B). Using previous work by Arnold and Blackmon and other work by the present authors to fix trajectories and relative sizes of residue functions, we find that the model satisfactorily describes elastic scattering. We give an interpretation of the secondary maximum in the differential cross section of p̄p scattering which occurs around -t~=0.9 GeV2. We find a crossover in the differential cross sections of pp and p̄p elastic scattering, and we show our results for various polarizations. We also discuss np-->pn and p̄p-->n̄n, which are not described satisfactorily by the model.