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Complex phase history data in synthetic aperture radar (SAR) systems require extensive processing before useful images can be obtained. Spotlight mode SAR systems are able to obtain useful images very efficiently by weighting and transforming the 2-D phase history data using a series of 1-D operations. Aperture weighting and inverse Fourier transforms are applied to the 2-D phase history data on a row by row basis followed by the same processing on a column by column basis. In this paper we are concerned with the compression of the complex phase history data obtained by a spotlight SAR system. We exploit knowledge of the aperture weighting direction along with Fourier transform processing to attach a "gain" factor to each complex phase history data sample. This gain factor is then used to efficiently allocate bits to the phase history data during quantization. Performance evaluations are presented for this compression system relative to other existing SAR phase history data compression systems.