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This paper introduces a frequency-weighting method for adaptive disturbance rejection. The method constrains the high-frequency gain of the prediction filter in a minimum-variance adaptive controller. In an experimental application, the method is used to control a microelectromechanical system fast steering mirror to suppress laser beam jitter. The paper analyzes the effect of sensor noise on the performance of the adaptive control system and demonstrates that sufficient levels of high-frequency noise and/or disturbance combined with control saturation produce a spiking phenomenon in the output error. The experimental results show that the frequency weighting eliminates the spiking.