The NASA Geostationary Imaging Fourier Transform Spectrometer (GIFTS) represents a revolutionary step in remote sensing of Earth's atmosphere that will demonstrate the technology and measurement concepts for future NOAA geostationary operational environmental satellites (GOES). GIFTS consists of a 128 x 128 large focal plane array (LFPA) imaging FTS with the spectral coverage from 685 to 1130 cm-1 and 1650 to 2250 cm-1. GIFTS was selected for flight demonstration on NASA's New Millennium Program (NMP) Earth Observing 3 (EO-3) Satellite Mission. GIFTS provides full disk global coverage obtained within an hour at moderate spectral resolutions (e.g. 1.2 cm-1) as well as regional sounding of atmospheric temperature and absorbing gas profiles at high spectral resolution (e.g. 0.6 cm-1). Given the unprecedented data volume produced by GIFTS, lossless data compression is critical for the overall success of the GIFTS experiment where the data is to be disseminated to the user community in real-time and archived for scientific studies and climate assessment. In this paper we will study lossless compression of GIFTS data that has been collected as part of the calibration or Ground Based Tests that were conducted in 2006. Standard compression methods JPEG-2000, JPEG-LS, and CCSDS IDC 9/7M & 5/3 are investigated for compression benchmarks. The bias-adjusted reordering (BAR) preprocessing scheme is also investigated to improve their performance on GIFTS data compression.