The present invention, in particular embodiments, is directed to methods, apparatuses and systems that provide an efficient compression technique for data streams transmitted to storage devices or over networks to remote hosts. Local storage as well as network transmission of streams is made more efficient by awareness and utilization of repeated sequences of data blocks. Such data blocks can be placed in a dictionary on persistent storage and shared across all streams. The dictionary is hierarchically indexed (two or more levels of indexing) to combine high efficiency search with efficient access to the stored data blocks. Additionally, data blocks, in particular implementations, are stored sequentially in order to improve overall performance.