A wireless telephone includes an adaptive noise canceling (ANC) circuit that adaptively generates an anti-noise signal from a reference microphone signal and injects the anti-noise signal into the speaker or other transducer output to cause cancellation of ambient audio sounds. An error microphone is also provided proximate the speaker to provide an error signal indicative of the effectiveness of the noise cancellation. A secondary path estimating adaptive filter is used to estimate the electro-acoustical path from the noise canceling circuit through the transducer so that source audio can be removed from the error signal. Sidetone is injected into the transducer output, but is not provided to the coefficient control of the secondary path estimating adaptive filter, so that the ambient noise present in the near-end speech microphone signal, and thus present in the sidetone information, does not destabilize the ANC circuit or otherwise cause improper generation of the anti-noise signal.