The high-energy gamma-ray emission discovered using the H.E.S.S. telescopes from the binary system PSR B1259 −63, is modelled using an extension of the approach that successfully predicted it. We find that the simultaneous INTEGRAL and H.E.S.S. data permit both a model with dominant radiative losses, high pulsar wind Lorentz factor and modest efficiency as well as one with dominant adiabatic lo...