This paper proposes a practical approach for damping control of flexible-joint manipulators. High-bandwidth tracking objectives are achieved together with robustness and effective disturbance rejection using motor measurements only. An inner decoupling loop based on the rigid-body approximation is first applied to minimize the effects of robot nonlinearities. The consequences of this approximate linearization are then explicitly taken into account in the control design and analysis, and a simple decentralized linear control strategy is proposed, combining low-authority collocated damping controllers with a high-authority motion loop based on the Generalized Predictive Control. The described approach is experimentally validated on the lightweight and back-drivable CEA ASSIST robot arm.