Various embodiments of the present invention are directed to methods and systems that reduce acoustic echoes in audio signals in accordance with changing conditions at first and second locations that are linked together in a communication system. In particular, one embodiment of the present invention relates to a method for determining an approximate impulse-response vector for canceling an acoustic echo resulting from an audio signal transmitted from the first location to the second location. This method includes forming a trust region within a search space based on computing a recursive specification vector defining the trust region. The method also includes computing a recursive shadow-impulse-response vector that lies substantially within the trust region, and computing the approximate impulse-response vector based on the recursive shadow-impulse-response vector and the recursive specification vector.