Abstract. Control co-design is a promising approach for wind turbine design due to the importance of the controller in power production, stability, load alleviation, and the resulting coupled effects on the sizing of the turbine components. However, the high computational effort required to solve optimization problems with added control design variables is a major obstacle to quantifying the benefit of this approach. In this work, we propose a methodology to identify if a design problem can benefit from control co-design. The estimation method, based on post-optimum sensitivity analysis, quantifies how the optimal objective value varies with a change in control tuning. The performance of the method is evaluated on a tower design optimization problem, where fatigue load constraints are a major driver, and using a linear quadratic regulator targeting fatigue load alleviation. We use the gradient-based multi-disciplinary optimization framework Cp-max. Fatigue damage is evaluated with time-domain simulations corresponding to the certification standards. The estimation method applied to the optimal tower mass and optimal cost of energy show good agreement with the results of the control co-design optimization while using only a fraction of the computational effort. Our results additionally show that there may be little benefit to using control co-design in the presence of an active frequency constraint. However, for a soft–soft tower configuration where the resonance can be avoided with active control, using control co-design results in a taller tower with reduced mass.