Is there any scenario whereby randomly shufflying a sequence improves it's compressibility?
I now think that it's because of this:-


  ZPAQ has 5 compression levels from fast to best. At all but the best level, it uses the statistics of the order-1 prediction table used for deduplication to test whether the input appears random. If so, it is stored without compression as a speed optimization. 


... from https://en.wikipedia.org/wiki/ZPAQ#Compression

I'm referring to LZMA in my question, but I'm not familiar with how it's implemented in code. If it followed the same speed optimisation strategy as ZPAQ, the hypothesis would be consistent with my observations. You can imagine in edge cases where $ \frac{\text{size compressed shuffled}} {\text{size compressed original}} = 1 - \epsilon $, that an $n$ order predictor decides that there is insufficient advantage to be had due to the necessary compression encoding overhead. My $\alpha \approx 0.01$, but recently I've seen it as high as 0.04.