Dynamic history multistream long range compression (DHC) techniques are described for efficiently compressing multiple, prioritized data streams received over a channel. A history buffer is associated with each received stream and a DHC compressor dynamically allocates fixed sized history sections to and from each history buffer. In implementations, the DHC compressor makes stream history size adjustments prior to compressing a block of data and sends information identifying the change in history size to a DHC decompressor. The DHC decompressor sends signaling information to the DHC compressor that is used to ensure that the DHC decompressor can operate with a fixed amount of total history memory.