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A novel algorithm is introduced for estimating the echo path responses for stereophonic acoustic echo cancellation. When the Wiener solution for the echo path responses is non-unique, the echo paths are estimated in two stages. In a first stage, one of the non-unique Wiener solutions is estimated. Then in a second stage, a disturbance is introduced and the left and right misalignment vectors can be formulated as the Wiener solution with respect to the residual signals appearing after adding the disturbance. The aim is to take advantage of the knowledge about the specific disturbance which is introduced. Adaptive algorithms based on this two stage idea are used. It is shown with a series of numerical simulations that the proposed algorithm converges much faster than a corresponding conventional one stage adaptive algorithm.