  We study whether, when restricted to using polylogarithmic memory and
polylogarithmic passes, we can achieve qualitatively better data compression
with multiple read/write streams than we can with only one. We first show how
we can achieve universal compression using only one pass over one stream. We
then show that one stream is not sufficient for us to achieve good
grammar-based compression. Finally, we show that two streams are necessary and
sufficient for us to achieve entropy-only bounds.
