word order - Differences between "just might" and "might just?"

Can someone help me understand more precisely the connotative differences between "just might" and "might just

I came upon this dilemma while working on a short comic strip. In the first panel, a person is attempting an unorthodox approach to a problem, saying:

It might just work.

The second panel, moments later:

It didn't work.

I'm unsure if the effect would be significantly altered if the words were swapped.

Answer

"might just work" sounds like "it might simply work--that is, without the complications one might predict."

"just might work" has a blossoming optimism. It suggests that something that you'd think wouldn't work actually has a decent shot at working.