1. A method for efficient one-pass cache-aware compression by a processor device in a computing storage environment, the method comprising: linking an output of a fast compressor to Huffman encoding for achieving the one-pass cache-aware compression by using a predetermined Huffman-tree upon determining by the fast compressor a final representation of each data byte; and retaining relevant data in an L1 cache during the Huffman encoding process without extracting data from an L2 cache during the Huffman encoding.