Fractal image compression is a relatively new and very promising technique for still image compression. However, it is not widely applied due to its very time consuming encoding procedure. In this research, we focus on speeding up 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 175 at the expense of only 0.6 dB degradation in PSNR relative to the unmodified exhaustive search for a typical image encoded with 0.44 bpp.