The invention relates to a method for operating a wind energy installation (10), in which the wind energy installation (10) has a rotor (12, 13, 22), at least one rotor blade (14) with an adjustable angle, a mechanical brake device (19) for braking the rotor (14), an operational control device (15, 15′) and a safety system (16, 20). The invention also relates to a corresponding wind energy installation (10). The method according to the invention is defined by the following method steps: braking of the rotor (12, 13, 22) by means of an angular adjustment (28) with an average angular adjustment rate of less than 8.5°/s of the at least one rotor blade (14) after a fault signal (30) occurs, braking of the rotor (12, 13, 22) by means of the mechanical brake device (19) as soon as the rotational speed of the rotor (12, 13, 22) exceeds a predefinable first rotational speed limit, and triggering of the safety system (16, 20) as soon as the rotational speed of the rotor (12, 13, 22) exceeds a predefinable second rotational speed limit.