1. A method of audio signal processing, said method comprising performing each of the following acts using a device configured to process audio signals: based on information from a first audio signal, producing an anti-noise signal; separating a target component of a second audio signal from a noise component of the second audio signal to produce a separated target component; and based on a result of mixing the anti-noise signal and the separated target component, producing an audio output signal, wherein the second audio signal includes (A) a first channel that is based on a signal produced by a first microphone and (B) a second channel that is based on a signal produced by a second microphone that is arranged to receive a user's voice more directly than the first microphone, wherein said separating includes performing a spatially selective processing operation on the second audio signal to produce the separated target component.