By solving the Bogoliubov–de Gennes equation self-consistently in the presence of a nonequilibrium quasiparticle distribution, we compute the current-voltage characteristic of a phase-coherent superconducting island with a tunnel barrier at one end. The results show significant structure, arising from the competition between scattering processes at the boundaries of the island and modification of the order parameter by quasiparticles and superflow. This structure is not present in non-self-consistent descriptions of normal-superconducting nanostructures.