In this paper an algorithm for grayscale image compression based on usage of three fixed uniform quantizers designed for discrete input samples is presented. The algorithm is based on the alternating use of these three quantizers. Number of quantization levels and quantizer range size increases from the first to the third quantizer. Experimental results show that choice of the quantizer range has an impact on system performance. While selecting a range of the first two quantizers (with a lower number of quantization levels) it is necessary to make a compromise between quality and bit rate (larger quantizer range leads to lower average bit rate but the quality of reconstructed image is also lower). It is shown that the range of the third quantizer should be set up to cover as many as possible high number of input samples making sure that the overload distortion does not become dominant. [Projekat Ministarstva nauke Republike Srbije, br. III 044006]