We present a method for performing acoustic echo cancellation in a channel with rapidly varying gain and thus a rapidly varying channel characteristic. This is a situation in which standard AEC approaches perform poorly. Our method involves learning a scale-free channel characteristic (H-). We then apply this to a windowed version of the signal and remove the projection of the transformed signal from the output signal. We also develop a "ramp projection" method that allows for a linear variation in gain within the window. We show results in a telephony application with 3 dB to more than 8 dB of improvement over conventional AEC using the simple projection and an additional 1 dB using the ramp projection.