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The article examines the algorithms for JPEG and JPEG-2000 compression of various graphic images. The main steps of the operation of both algorithms are given, their advantages and disadvantages are noted. The main differences between JPEG and JPEG-2000 are analyzed. It is noted that the JPEG-2000 algorithm allows re-moving visually unpleasant effects. This makes it possible to highlight important areas of the image and improve the quality of their compression. The features of each step of the algorithms are considered and the difficulties of their implementation are compared. The effectiveness of each algorithm is demonstrated by the example of a full-color image of the BSU emblem. The obtained compression ratios were obtained and shown in the corresponding tables using both algorithms. Compression ratios are obtained for a wide range of quality values from 1 to ten. We studied various types of images: black and white, business graphics, indexed and full color. A modified LZW-Lempel-Ziv-Welch algorithm is presented, which is applicable to compress a variety of information from text to images. The modification is based on limiting the graphic file to 256 colors. This made it possible to index the color with one byte instead of three. The efficiency of this modification grows with increasing image sizes. The modified LZW-algorithm can be adapted to any image from single-color to full-color. The prepared tests were indexed to the required number of colors in the images using the FastStone Image Viewer program. For each image, seven copies were obtained, containing 4, 8, 16, 32, 64, 128 and 256 colors, respectively. Testing results showed that the modified version of the LZW algorithm allows for an average of twice the compression ratio. However, in a class of full-color images, both algorithms showed the same results. The developed modification of the LZW algorithm can be successfully applied in the field of site design, especially in the case of so-called flat design. The comparative characteristics of the basic and modified methods are presented.