All realistic potential models for the two-nucleon interaction are to some extent based on boson exchange. However, in order to achieve an essentially perfect fit to the scattering data, characterized by a chi2/Ndata ~ 1, previous potentials have abandoned a pure one boson-exchange mechanism (OBE). Using a covariant theory, we have found a OBE potential that fits the 2006 world np data below 350 MeV with a chi2/Ndata = 1.06 for 3788 data. Our potential has fewer adjustable parameters than previous high-precision potentials, and also reproduces the experimental triton binding energy without introducing additional irreducible three-nucleon forces.