Abstract: One of the numerical criteria for color image quantization is to minimize the maximum discrepancy between original pixel colors and the corresponding quantized colors. This is typically carried out by first grouping color points into tight clusters and then finding a representative for each cluster. In this article we show that getting the smallest clusters under a formal notion of minimizing the maximum intercluster distance does not guarantee an optimal solution for the quantization criterion. Nevertheless, our use of an efficient clustering algorithm by Teofilo F. Gonzalez, which is optimal with respect to the approximation bound of the clustering problem, has resulted in a fast and effective quantizer. This new quantizer is highly competitive and excels when quantization errors need to be well capped and when the performance of other quantizers may be hindered by such factors as low number of quantized colors or unfavorable pixel population distribution. Both computer-synthesized and photographic images are used in experimental comparison with several existing quantization methods.