Magnetic torques generated through spin-orbit coupling(1-8) promise energy-efficient spintronic devices. For applications, it is important that these torques switch films with perpendicular magnetizations without an external magnetic field(9-14). One suggested approach(15) to enable such switching uses magnetic trilayers in which the torque on the top magnetic layer can be manipulated by changing the magnetization of the bottom layer. Spin currents generated in the bottom magnetic layer or its interfaces transit the spacer layer and exert a torque on the top magnetization. Here we demonstrate field-free switching in such structures and show that its dependence on the bottom-layer magnetization is not consistent with the anticipated bulk effects(15). We describe a mechanism for spin-current generation(16,17) at the interface between the bottom layer and the spacer layer, which gives torques that are consistent with the measured magnetization dependence. This other-layer-generated spin-orbit torque is relevant to energy-efficient control of spintronic devices.