The technology described this document can be embodied in a method that includes receiving an error signal captured using a microphone, the error signal representing a difference between the sinusoidal component of a noise signal and an output of an acoustic transducer. The output of the acoustic transducer is configured to reduce the effects of the sinusoidal component of the noise signal. The method includes processing the error signal to compensate for effects due to a signal path between the acoustic transducer and the microphone, and determining a current estimate of one or more first parameters of the error signal. Based on such parameters, a current estimate of a time-varying step size associated with an adaptive process is determined, and based on the current estimate of the time-varying step size, a driver signal configured to change the output of the acoustic transducer is generated.