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This paper describes an algorithm which allows to find out the M-output level quantizer characteristics minimizing the distortion with respect to both the Mean-Squared-Error (MSE) and Mean-Absolute-Error (MAE) criterions. This algorithm can be used with any kind of signal amplitude distributions ranging from analytical probability density functions (pdf) to experimental 'density functions. In the particular case of known pdf like uniform, Gaussian, Laplacian and Gamma densities, it gives results which agree or are better than those previously published /2,4,5,6/. The same type of algorithmic procedure may also be used for block-of-samples quantization; in this case the statistics average must be replaced by the time average. In addition, the simplicity of the proposed algorithm allows to envisage a real-time, microprocessor based, block adaptive quantizer implementation in which the quantizer parameters are periodically updated and transmitted with each data block. This technique can be used, for instance, to optimally quantize the speech coding parameters derived from the low bit rates speech compression algorithm as described in .