Three-terminal laser-transistors with a quantum well active region and a resonant-tunnelling collector are proposed and considered. It is shown that the laser-transistor is controlled by the collector voltage due to electron extraction via the resonant-tunnelling structure. The current-voltage and light-voltage characteristics are calculated. Both of them reflect effective voltage control and possible bistable behaviour of the laser-transistor in a certain range of the collector voltage. The electron heating due to electron injection and extraction can significantly affect the controllability and bistability of the laser-transistor.