A method and apparatus for damping stick-slip oscillations in a drill string. In one embodiment a method includes damping the stick-slip oscillations using a drilling mechanism at the top of said drill string. The speed of rotation of the drilling mechanism is controlled using a PI controller. The control is characterized by tuning the PI controller so that the drilling mechanism absorbs most torsional energy from the drill string at a frequency that is at or near a frequency of the stick-slip oscillations.