The distinctive quasiparticle distribution existing under nonequilibrium in a superconductor-insulator-normal metal-insulator-superconductor mesoscopic line is proposed as a novel tool to control the supercurrent intensity in a long Josephson weak link. We present a description of this system in the framework of the diffusive-limit quasiclassical Green-function theory and take into account the effects of inelastic scattering with arbitrary strength. Supercurrent enhancement and suppression, including a marked transition to a pi junction, are striking features leading to a fully tunable structure.