Operational SAR satellite missions impose new requirements to on-board data compression such as a higher data reduction ratio, more flexibility, and faster data throughput. A recent approach is Entropy-Constrained Block Adaptive Quantization (ECBAQ). This method outperforms currently-used Block Adaptive Quantization with respect to Signal-to-Quantization-Noise-Ratio. The ECBAQ algorithm can be implemented using an architecture that is essentially not more complicated than that of a BAQ encoder and suitable for high-speed implementations. Moreover, the method features bit rate programmability with non-integer rates. This allows the SAR information throughput to be optimized for different types of applications. This paper presents a new ECBAQ version including a rate control loop, avoiding the need for the multiplexing of block variance levels into the compressed data stream and further reducing the complexity of the implementation. The presented method is very well suited for application with frequency domain data due to its high instantaneous dynamic range and non-integer rate capabilities. Preceded by an FFT device which transforms the data in both range and azimuth direction, more data reduction can be achieved by frequency filtering and decimation. In addition, using variable bit allocation matched to the SAR processor's weighting functions, even higher compression ratios can be achieved. Overall, the compression improvement may range over 100% as compared to the conventional BAQ method while maintaining the same image quality. In conclusion, FFT-ECBAQ is a strong candidate for application in future SAR missions.