Adaptive filtering algorithm training signals incorporate adaptation-enhancing signals having properties, such as spectral whiteness and rapidly decaying auto-correlation between samples, which allow the adaptive filtering algorithms to converge more quickly as compared to conventional algorithms. Exemplary adaptation-enhancing signals are incorporated such that the training signals are not perceptibly altered as compared to conventional training signals. For example, in a hands-free telephony application, an adaptation-enhancing signal according to the invention is dynamically tailored so that it is masked by a loudspeaker signal (the conventional training signal) and is thus inaudible to hands-free telephone users.