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The range migration algorithm (RMA) is an accurate algorithm to process spotlight synthetic aperture radar (SAR) data. However, in applying the RMA to process the SAR data, especially for short-dwell data, the data length has to be extended in azimuth by zero-padding it to the length of the azimuth filter. On the other hand, the spectral analysis (SPECAN, which is a deramp followed by a fast Fourier transform) algorithm is efficient, since the data extension is unnecessary, but an assumption is made that all targets have the same FM rate and the same range cell migration. A novel algorithm is introduced here to combine the accuracy of the RMA and the efficiency of SPECAN. It involves bulk azimuth uncompressing the RMA processed data with a single linear FM filter, and then refocusing the data using SPECAN, all done without the azimuth extension in the RMA. Localized artifacts generated can be removed easily. Point target simulations, including one with a high squint angle of 60°, were successfully performed to verify the algorithm.