While the wing kinematics of many flapping insects have been well characterized, understanding the underlying sensory, neural, and physiological mechanisms that determine these kinematics is still a challenge. Two main difficulties in understanding the physiological mechanisms arise from the complexity of the interaction between a flapping wing and its own unsteady flow, as well as the intricate mechanics of the insect wing hinge, which is among the most complicated joints in the animal kingdom. These difficulties call for the application of reduced-order approaches. Here this strategy is used to model the torques exerted by the wing hinge along the wing-pitch axis of maneuvering fruit flies as a damped torsional spring with elastic and damping coefficients as well as a rest angle. Furthermore, we model the air flows using simplified quasistatic aerodynamics. Our findings suggest that flies take advantage of the passive coupling between aerodynamics and the damped torsional spring to indirectly control their wing-pitch kinematics by modulating the spring parameters. The damped torsional-spring model explains the changes measured in wing-pitch kinematics during roll correction maneuvers through modulation of the spring damping and elastic coefficients. These results, in conjunction with the previous literature, indicate that flies can accurately control their wing-pitch kinematics on a sub-wing-beat time scale by modulating all three effective spring parameters on longer time scales. © 2015 American Physical Society.