An acoustic echo canceller having an adaptive filter, a step size control unit, and (optionally) a stability control unit. The adaptive filter derives an estimate of the echo in a near-end signal using a digital filter (e.g., a FIR filter) and further cancels the echo estimate from the near-end signal to provide an output signal. The step size control unit derives step sizes to be used to adjust the coefficients of the digital filter. The step sizes are determined based on the characteristics of a reference signal and the output signal and (optionally) the characteristics of the coefficients. For example, the step size is set proportional to the reference signal amplitude, inversely proportional to the output signal amplitude, and based on a difference in the coefficient power at two different time instants. The stability control unit constrains the adjustments to the coefficients to prevent instability.