A computer compressed memory system for storing and retrieving data in a processing system, includes a memory including at least one memory device for storing at least one of uncompressed data and compressed data, a compressor for encoding data blocks into smaller compressed data blocks for storage in the memory, a decompressor for reconstituting encoded data into original uncompressed data blocks, a memory controller for generating, receiving and responding to memory access requests from processing and input/output units and responsively controlling access to the memory from the compressor and the decompressor for storing and retrieving data, and a hardware priority filter associated with the memory controller for selecting specific memory access requests according to attributes and access type within prescribed rates and under specific conditions.