In this paper, it has been performed an optimization of compression factor of quasi-logarithmic quantizer for the case when a signal with Laplacian probability density function is brought on the input of quantizer. There has been proposed a new two-step method for determination of optimal compression factor in terms of the mean-square error (MSE) distortion. Two different manners for compression factor optimization have also been considered, by using the Muller’s iterative method and the new two-step method. Emphasis is placed on locating slightly less accurate but much simpler solution, by comparing the Muller’s iterative method and the new two-step method. Analysis of procedures is described in detail.