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This paper demonstrates how techniques applicable for defining and maintaining a special case of binary search trees (BSTs) can be incorporated into "traditional" compression techniques to yield enhanced superior schemes. We, specifically, demonstrate that the newly introduced data structure, the Fano Binary Search Tree (FBST) can be maintained adaptively and in a self-organizing manner. The correctness and properties of the encoding and decoding procedures that update the FBST are included. We also include the theoretical and empirical analysis, which shows that the number of shift operators is large for small files, and it tends to decrease (asymptotically towards zero) for large files.