Optical depolarizers for monochromatic waves which work independent of input polarization can be built from cascaded electrooptic rotating waveplates. If the waveplate retardations deviate from their desired values then the worst-case residual degree-of-polarization DOPmax is larger than its desired value 0. In a depolarizer consisting of one rotating halfwave and one rotating quarterwave plate, DOPmax roughly equals the retardation error, which is <<1. However, with just one rotating quarterwave plate more, DOPmax roughly equals the square of the retardation error which is a much smaller value. Thereby depolarizer accuracy is substantially improved. Waveplate sequence and rotation frequency combinations suitable for fast depolarization are discussed.