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This paper has two achievements. The first aim of this paper is optimization of the lossy compression coder realized as companding quantizer with optimal compression law. This optimization is achieved by optimizing maximal amplitude for that optimal companding quantizer for Laplacian source. Approximate expression in closed form for optimal maximal amplitude is found. Although this expression is very simple and suitable for practical implementation, it satisfy optimality criterion for Lloyd–Max quantizer (for R >= 6 bits/sample). In the second part of this paper novel simple lossless compression method is presented. This method is much simpler than Huffman method, but it gives better results. Finally, at the end of the paper, we join optimal companding quantizer and lossless coding method together in one generalized compression method. This method is applied on the concrete still image and good results are obtained. Besides still images, this method also could be used for compression speech and bio-medical signals.