The supercurrent in a Josephson SF1S1F2sIS spin valve (“S” is for superconductor, “F” is for ferromagnet, and “I” is for insulator) is studied theoretically. It is found that by rotating the magnetization of one of the ferromagnetic layers, a smooth switching of the system between two states with different critical currents is possible. The operating range of the device can be adjusted by varying the thickness of the intermediate s-layer. The proposed structure is a promising scalable control element for the use in superconducting electronics.