Methods and apparatus compensating for background noise associated with a transmitted signal. In a first embodiment, an adder combines an echo estimate with the the transmitted signal to form a processed signal, a noise reduction circuit uses a background noise estimate to subtract the background noise from the processed signal, and a non-linear processor uses the background noise estimate to combine a compensating background noise signal with the proccssed signal. In another embodiment, the noise reduction circuit divides the processed signal into sub-bands. With variations of an embodiment, the nonlinear processor is a sub-band non-linear processor, the processed signal is divided into sub-bands, and the background estimate includes sub-band noise estimates.