This paper describes a compensation system for soft aerial vehicle stabilization. Balancing the arms is one of the main challenges of soft UAVs since the propeller is freely tilting together with the flexible arm. In comparison with previous designs, in which the autopilot was adjusted to deal with these imbalances with no extra actuation, this work introduces a soft tendon-actuated system to achieve in-flight stabilization in an energy-efficient way. The controller is specifically designed for disturbance rejection of aeroelastic perturbations using the Ziegler-Nichols method, depending on the flight mode and material properties. This aerodynamics-aware compensation system allows to further bridge the gap between soft and aerial robotics, leading to an increase in the flexibility of the UAV, and the ability to deal with changes in material properties, increasing the useful life of the drone. In energetic terms, the novel system is 15–30% more efficient, and is the basis for future applications such as object grasping.