Self-Organization is based on adaptivity. Adaptivity should start with the very basic fundamental communication tasks such as encoding the information to be transmitted or stored. Obviously, the less signal transmitted the less energy in transmission used. In this paper we present a novel on-line and entropy adaptive compression scheme for streaming unbounded length inputs. The scheme extends the window dictionary Lempel-Ziv compression, is adaptive and is tailored to on-line compress inputs with non stationary entropy. Specifically, the window dictionary size is changed in an adaptive manner to fit the current best compression rate for the input. On-line Entropy Adaptive Compression scheme (EAC), that is introduced and analyzed in this paper, examines all possible sliding window sizes over the next input portion to choose the optimal window size for this portion, a size that implies the best compression ratio. The size found is then used in the actual compression of this portion. We suggest an adaptive encoding scheme, which optimizes the parameters block by block, and base the compression performance on the optimality proof of Lempel Ziv algorithm when applied to blocks. The EAC scheme was tested over files of different types (docx, ppt, jpeg, xls) and over synthesized files that were generated as segments of homogeneous Markov Chains. Our experiments demonstrate that the EAC scheme typically provides a higher compression ratio than LZ77 does, when examined in the scope of on-line per-block compression of transmitted (or compressed) files.