This paper presents an adaptive control scheme to improve the data transmission rate of a Laser Communication Terminal by attenuating external vibrations. The main contributors for performance degradation are multiple superimposed vibrations originating from the satellite's reaction wheels, which can excite resonance modes. They are introduced to the terminal through its mounting structure and their influence on the pointing error can be modeled as an output disturbance. The proposed controller estimates this disturbance and then attenuates it based on the principle of destructive interference. For that, a combination of internal model control, spectral analysis and modified pseudo-gradient algorithms is used. The developed controller is compared to a high bandwidth H infinity-baseline controller using a nonlinear simulation framework with varying mounting configurations and model uncertainties. To evaluate the performance and robustness of the proposed scheme, a realistic vibration scenario is investigated with multiple parameter studies. The results show a significant improvement of pointing performance over the entire anticipated uncertainty range.