Among the many examples of Bose condensation considered in physics, electron-hole-pair (exciton) condensation has maintained special interest because of controversy about condensate properties. Although ideal condensates can support an exciton supercurrent, it has not been clear how such a current could be induced or detected. This paper addresses the electrical generation of exciton supercurrents in bilayer condensates (systems in which the electrons and holes are in separate layers) and reaches a surprising conclusion. We find that steady-state dissipationless currents cannot be induced simply by connecting the two layers in series to guarantee opposite currents in electron and hole layers, as has long been supposed. Instead, current should be injected into and removed from the same layer, and a conducting channel supplied to close the counterflow portion of supercurrent in the other layer.