A simple statistical block code in combination with the LZW-based compression utilities gzip and compress has been found to increase by a significant amount the level of compression possible for the proteins encoded in Haemophilus influenzae, the first fully sequenced genome. The method yields an entropy value of 3.665 bits per symbol (bps), which is 0.657 bps below the maximum of 4.322 bps and an improvement of 0.452 bps over the best known to date of 4.118 bps using Matsumoto, Sadakane, and Imai?s lza-CTW algorithm. Calculations based on a compact inverse genetic code show that the genome has a maximum entropy of 1.757 bps for the coding regions, with a possibly lower actual entropy. These results hint at the existence of hitherto unexplored redundancies that do not show up in Markov models and are indicative of more internal structure than suspected in both the protein and the genome.