In an embodiment, a processor comprises a plurality of processing cores and a compression accelerator to compress an input stream comprising a first data block and a second data block. The compression accelerator comprises a first compression engine to compress the first data block; and a second compression engine to update state data for the second compression engine using a sub-portion of the first data block; and after an update of the state data for the second compression engine using the sub-portion of the first data block, compress a second data block using the updated state data for the second compression engine. Other embodiments are described and claimed.