This paper describes an algorithm for grayscale image compression based on non-uniform quantizers designed for discrete input samples. Non-uniform quantization is performed in two steps for unit variance, whereas design is done by introducing a discrete variance. The best theoretical and experimental results are obtained for those discrete values of variance which provide the operating range of quantizer located in the vicinity of maximal signal value that can appear on the entrance. The experiment is performed by applying proposed quantizers for compression of standard test grayscale images as a classic example of discrete input source. The proposed fixed non-uniform quantizers, designed for discrete input samples, provide up to 4.93 [dB] higher PSQNR compared to the fixed piecewise uniform quantizers designed for discrete input samples. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. III44006 and Grant no. TR32035]