Many display devices nowadays still allow a limited number of colors, called color palette, to be displayed simultaneously. Besides, images and videos in most World Wide Web databases are in compressed formats. Therefore, it becomes an important issue to retrieve a suitable color palette from compressed domain in order to have fast and faithful color reproduction for these devices. In this paper, the color palette design methods for compressed images and videos are presented. The proposed approaches use the reduced, rather than the whole, image for the color palette design to avoid the heavy computation in image or video decompression. Also, for compressed videos, a shifting-window scheme is proposed to smooth out color variations in the change of color palette. In these methods, we extend the dependent scalar quantization algorithm of a single image to accomplish the color palette design. Experimental results show that the output image quality of the proposed methods is acceptable to human eyes. In addition, empirical results show that the proposed shifting-window scheme can reduce the main problem of displaying quantized image sequences, screen flicker.