Two quantization rules, optimum (minimum mean-square error) and logarithmic companding, are compared for application to digital speech transmission. Comparison is made on the basis of signal-to-quantizing noise ratio (S/N), subjective quality judgments, idle channel noise, and dynamic range. These quantizers are considered in both PCM and differential PCM configurations. A computer algorithm is described that yields the optimum quantizer levels for a given speech record. It has been found that the improvement in S/N which optimum quantization affords over conventional logarithmic quantization is offset by the greater idle channel noise and smaller dynamic range (range of talker volumes handled with a lower limit on S/N) of the optimum law.