Disclosed is an improved method and apparatus for estimating and applying a step size value for a least mean squares echo canceller. A power estimate of an excitation signal is compared to a reference power level to determine a shift adjustment. The shift adjustment is added to a reference shift amount to determine a shift amount. The product of an excitation signal and an error signal is then calculated and the product is stored in a memory register comprising a plurality of bits. The bits stored in the memory register are shifted either left or right based upon the shift amount. The shift adjustment may be based in part upon the ratio of the excitation signal power estimate and the reference power level.