Compression only works on files that have lots of redundancy. For example, source code files (C, Python, etc) have lots of redundancy because some symbols are more common than others. Executable files have less redundancy and cannot be compressed as well. To be effective, bitcoin dat files should have low redundancy. Encryption techniques also reduce redundancy in files because redundancy provides clues to an attacker.
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On the other hand, you could use Electrum or Multibit, as suggested above. They are thin clients and don't need to download the entire blockchain data.