Methods of operating a variable speed wind turbine as a function of a wind speed, the wind turbine having a rotor with a plurality of blades, and one or more pitch mechanisms for rotating the blades. The method comprising a sub-nominal zone of operation for wind speeds below the nominal wind speed and a supra-nominal zone of operation for wind speeds above the nominal wind speed. In the supra-nominal zone, the blades are pitched so as to maintain the rotor speed substantially constant, and a tip speed ratio of the wind turbine is substantially continuously being determined and wherein an instantaneous minimum pitch angle is substantially continuously being determined based on the instantaneous tip speed ratio, and the blades are never pitched below the instantaneous minimum pitch angle. The disclosure further relates to a wind turbine suitable for carrying out such methods.