This paper presents performance analysis and design of ducted propellers for lighter-than-air vehicles. High-fidelity computational fluid dynamics simulations were first performed on a detailed model of the propulsor, and the results were in very good agreement with available experimental data. Additional simulations were performed using a simplified geometry, to quantify the effect of the duct and of the blade twist on the propeller performance. It was shown that the duct is particularly effective at low flight speed and that the blades with relatively high twist have better performance over the flight envelope. Design of the optimal twist distribution and of the duct shape was also attempted by coupling the flow solver with a quasi-Newton optimisation method. Flow gradients were computed by solving the discrete adjoint of the Reynolds-averaged Navier-Stokes equations using a fixed-point iteration scheme or a nested Krylov method with deflated restarting. The results show that the ducted propeller propulsive efficiency can be increased by 2%.