In this paper, wavelet packet algorithms based on lowered adaptation rates and backward adaptivity are introduced. The former is proposed for the reduction of side information and computational complexity, and the latter is proposed for the elimination of side information altogether. Experiments were conducted with still images. Additionally, the performances of different cost functions used in the best basis selection part of the proposed algorithms are assessed. The two cost functions investigated are the Shannon entropy and the non-zero count. Results from lowered adaptation rate adaptive wavelet packet experiments were very promising, because a significant reduction in computational complexity was achieved with virtually no loss in rate-distortion performance. The backward adaptive experiments conducted revealed a strong influence of the cost function chosen for the best basis selection component of the algorithm. The Shannon entropy cost proved to be far superior to the non-zero count cost for use in the backward adaptive wavelet packet algorithm.