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To maximize rate distortion performance while remaining faithful to the JPEG syntax, the joint optimization of the Huffman tables, quantization step sizes, and DCT indices of a JPEG encoder is investigated. Given Huffman tables and quantization step sizes, an efficient graph-based algorithm is first proposed to find the optimal DCT indices in the form of run-size pairs. Based on this graph-based algorithm, an iterative algorithm is then presented to jointly optimize run-length coding, Huffman coding, and quantization table selection. The proposed iterative algorithm not only results in a compressed bitstream completely compatible with existing JPEG and MPEG decoders, but is also computationally efficient. Furthermore, when tested over standard test images, it achieves the best JPEG compression results, to the extent that its own JPEG compression performance even exceeds the quoted PSNR results of some state-of-the-art wavelet-based image coders such as Shapiro's embedded zerotree wavelet algorithm at the common bit rates under comparison. Both the graph-based algorithm and the iterative algorithm can be applied to application areas such as web image acceleration, digital camera image compression, MPEG frame optimization, and transcoding, etc.