In stage 3 the quantized coefficients are encoded losslessly. We use run length encoding and entropy encoding. The goal of run length encoding is to encode the zeros jointly as they appear in runs. The direction of the scan influences the compression performance. Choices for scan direction include vertical, horizontal and zig-zag scan. Depending on the dominant frequencies corresponding to a particular subband, one scan direction may be better suited for extracting long runs of zeros. After run length encoding, the data is entropy encoded for which we use Huffman coding. We note that it is also possible to search for runs across subbands. This shows potential for improving both the lossy and the lossless compression components. For example, a common device is the EOB codeword which is used to denote that all data remaining in a scan is zero. It is used in both JPEG and the Wavelet Zero-Tree [Sha92] to terminate scans across subbands. The technique is essential for attaining good performance in these image compression systems.