Methods based on Haar wavelets and coincidence characteristics are proposed to compress multi-streams. The main contributions include: (1) Energy conservation law of Haar wavelets transform is proved to compress data streams. (2) The relation between the coincidence measure and trend of streams is revealed as along with the invariability under parallel shift and the equivalence law over coincidence measure to approximately express data-streams by the wavelet coefficient of the characteristic stream and its energy. (3) Multi-Scales energy decomposition model is proposed to improve the compression precision. (4) The multi-scales compression algorithm and the energy conservation reconstruction algorithm are designed. (5) Extended experiments show that the compression ratio of the new methods is 2~4 times as the traditional method.