A system and method for identifying minor echoes present in an input signal in the situation where a set of major echoes has already been identified from the input signal. The method includes: computing a spectrum F corresponding to a sum of the major echoes; computing a weighted power spectrum SM of the spectrum F; subtracting the weighted power spectrum SM from a weighted power spectrum PIN of the input signal to obtain a difference spectrum; performing a stabilized division of the difference spectrum by a conjugate of the spectrum F to obtain an intermediate spectrum; computing an inverse transform of the intermediate spectrum to obtain a time-domain signal; and estimating parameters one or more of the minor echoes from the time-domain signal. The echo parameters are usable to remove at least a portion of the one or more estimated minor echoes from the input signal.