In recent years wind turbines have become increasingly large to increase energy yield and cost-effectiveness. This has led to taller turbine towers, subjected to larger loads. As a result, Lagerwey turbines experience lateral tower vibrations at different resonance frequencies. These vibrations result in rotor speed measurement disturbances due to tower top roll motion. Such disturbances affect controller performance and induce undesired generator torque variations. Generator torque excites the tower, thus, a closed-loop interaction between the tower and the torque controller exists. A tower model including two resonance frequencies has been obtained through model identification in a simulation environment, which includes tower top rotational velocity as an output. A Kalman filter based on this model is able to provide an accurate estimate of tower signals using the tower top acceleration measurement and the generator torque set point. The tower top rotational velocity estimate is used to filter the rotor speed measurement. In high-fidelity simulation, it is found that in above-rated conditions (where tower vibrations are most severe) tower loads are reduced by 5.85%. In order to obtain a further load reduction, a state-feedback tower damping controller has been developed. Vibration modes are damped individually with user-defined damping ratios. For the designed controller, an average load reduction of 32.5% is achieved at the cost of a 0.8% increase in standard deviation of electric power.