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In this study, the authors present an efficient technique for compression and coding of memoryless Laplacian sources, which uses variable-length code (VLC). That technique is based on the combination of two companding quantisers in the first case and three companding quantisers in the second case. These quantisers have disjoint support regions, different number of representation levels and different compressor functions. The closed-form expressions are obtained for the distortion, average bit rate and signal to quantisation noise ratio (SQNR). The presented numerical results point out the effects of rate-distortion (R-D) optimisation on the system performances. Since our model assumes the general case of Laplacian distribution, it has wide applications like the coding of speech and images. It is shown that the difference of SQNR of our model and classical companding quantiser based model is 2.8 dB for two quantisers and 4.2 dB in three quantisers model. The authors have also made a comparison between our model, combination of the optimal uniform quantiser and Huffmann lossless coder and combination of optimal companding quantiser and simple lossless coder.