This work describes a fluid–structure interaction (FSI) design optimization framework and applies it to improving the structural performance of a water brake used to stop aircraft landing on short runways. Inside the water brake, a dissipative torque is exerted on a rotor through interactions between rotor blades and a surrounding fluid. We seek to optimize blade shape over a parameterized design space, to prevent potentially-damaging stress concentrations without compromising performance. To avoid excessive numbers of costly simulations while exploring the design space, we use a surrogate management framework that combines derivative-free pattern search optimization with automated construction of a low-fidelity surrogate model, requiring only a handful of high-fidelity FSI simulations. We avoid the difficult problem of generating fluid and structure meshes at new points in the design space by using immersogeometric FSI analysis. The structure is analyzed isogeometrically: its design geometry also serves as a computational mesh. This geometry is then immersed in an unfitted fluid mesh that does not depend on the structure’s design parameters. We use this framework to make significant improvements to a baseline design found in the literature. Specifically, there is a 35% reduction of von Mises stress variance and a 25% reduction of maximum of stress, while the resisting torque and mass of the optimized blades remain uncompromised.