Textured images are generally difficult to compress because they contain a large number of high frequency components which are difficult to capture with traditional compression schemes such as transform coding, especially at high compression ratios. Since many textures possess a high degree of self-similarity at different scales, the fractal compression technique can be applied to effectively encode such textured images by exploiting this self-similar property. The main drawback of fractal compression is that the fractal encoding procedure is very time consuming. In this research, we focus on the speed up of this procedure by introducing three schemes: dimensionality reduction, energy-based classification, and tree search. We have developed an algorithm that combines these three schemes together and achieves a speed-up factor of 177 at the expense of only 0.4 dB degradation in PSNR relative to the unmodified exhaustive search for a typical textured image encoded with 0.44 bpp.