The Cross-track Infrared Sounder (CrIS), like most Fourier Transform spectrometers, can be sensitive to mechanical disturbances during the time spectral data is collected. The Michelson interferometer within the spectrometer modulates input radiation at a frequency equal to the product of the wavenumber of the radiation and the constant optical path difference (OPD) velocity associated with the moving mirror. The modulation efficiency depends on the angular alignment of the two wavefronts exiting the spectrometer. Mechanical disturbances can cause errors in the alignment of the wavefronts which manifest as noise in the spectrum. To mitigate these affects CrIS will employ a laser to monitor alignment and dynamically correct the errors. Additionally, a vibration isolation system will damp disturbances imparted to the sensor from the spacecraft. Despite these efforts, residual noise may remain under certain conditions. Through simulation of CrIS data, we demonstrated an algorithmic technique to correct residual dynamic alignment errors. The technique requires only the time-dependent wavefront angle, sampled coincidentally with the interferogram, and the second derivative of the erroneous interferogram as inputs to compute the correction. The technique can function with raw interferograms on board the spacecraft, or with decimated interferograms on the ground. We were able to reduce the dynamic alignment noise by approximately a factor of ten in both cases. Performing the correction on the ground would require an increase in data rate of 1-2% over what is currently planned, in the form of 8-bit digitized angle data.