Summary form only given. We present comparative results obtained in the context of 24-bit true color image encoding by using searchless vs. search-based fractal compression techniques in a perceptually uniform color space. A pixel in the color space is represented as a vector with each component corresponding to a color channel. The least squares approximation of an image block by an iterated function system (IFS) is adapted to reflect the added color dimensions. To account for the nonlinearity of the human visual perception, compression in the L*a*b* uniform color space is proposed. In this color space, two pairs of colors with the same Euclidean distance metric are perceptually almost equally similar or different. Comparisons are presented both with regard to compression in the RGB and YIQ color spaces vs. the perceptually uniform L*a*b* color space, as well as with regard to fractal color image compression in the L*a*b* color space obtained by means of an extension of Monro and Dudbridge's bath fractal transform (BFT) vs. an adaptation of Jacquin's iterated transform technique (ITT) for 3-dimensional color. The use of a uniform color space produced rate-distortion results comparable with recently reported fractal compression results, but yielded compressed images with visibly less noticable color distortion than other methods.