Unless I'm missing something, I reckon there's a really obvious improvement on that, but Stack Exchange doesn't let new users leave comments. Think of the old puzzle where you've got 9 bags of gold coins which weight 10 grams each and one bag of shaved coins which weigh only 9 grams each and you need to figure out which bag has the shaved coins in only one weighing. You should be able do the same thing here - add one "Cookie: secret=A", two "Cookie: secret=B" and so on. Because of the limited look-back window in the compressor you'll need to interleave them like ABCD...BCD...CD... but it should give more information.

Edit: Wait, I am. That wouldn't work because it'd compress the repeated subsequences. D'oh.