In a hands-free mode of speech communication, a loudspeaker produces acoustic energy of a distant signal from a far-end talker and a microphone produces a near-end signal containing a speech component representing the speech activity of a near-end talker or an acoustic echo component, or both. An echo replica is produced from the distant signal and a residual echo representing the difference between the near-end signal and the echo replica. The residual echo is used as a feedback signal to produce the echo replica. Using one of the near-end signal and the residual echo as a first input signal and the echo replica as a second signal, an estimate of the acoustic echo is produced when the speech activity of the near-end talker is low or zero. Using the acoustic echo estimate, the spectrum of the first input signal is shaped to produce a local signal for transmission to the far-end talker.