In current practice, once the initial design of an aircraft is completed, it is often revised based on preliminary control synthesis attempts, creating a back-and-fourth iteration for the refinement of the airframe and the control laws. However, joint optimization of the structure and the controller would be advantageous. In view of this, the present paper proposes a technique for simultaneously tuning the airframe and controller parameters of a flexible aircraft. Specifically, a method is provided for the co-design of the flutter suppression control law and the size of control surfaces of the mini MUTT (Multi Utility Technology Testbed) aircraft. To achieve this, static output feedback is used, and the model of the aircraft is parameterized according to the chord length of the flaps. The flutter suppression problem is articulated as the minimization of a nonlinear cost function that considers the energy in the pitching motion of the aircraft, the control effort, and the weight of the actuators. The assessment of the resulting optimal closed-loop proves that the co-design of structural and control parameters is feasible and converges more efficiently to the global optimum in finite steps than the traditional iterative method.