It seems reasonable to expect from a good compression method that its output should not be further compressible, because it should behave essentially like random data. We investigate this premise for a variety of known lossless compression techniques, and find that, surprisingly, there is much variability in the randomness, depending on the chosen method. Arithmetic coding seems to produce perfectly random output, whereas that of Huffman or Ziv-Lempel coding still contains many dependencies. In particular, the output of Huffman coding has already been proven to be random under certain conditions, and we present evidence here that arithmetic coding may produce an output that is identical to that of Huffman.