I've been taught that "just" is placed before the element it modifies. As in:
Can I use your computer just for a few minutes?
In this case the emphasis is that it will take no longer than a few minutes.
So far, so good.
But then I've come across this sentence:
Can I just use your computer for a few minutes?
I can't make sense of "just" before "use", because nobody would think that you might want to sell, steal or smash my computer, and that you are pointing out that you just want to use it.
Is it the case that "just" still modifies "for a few minutes" though it is "displaced"? Is there any other explanation for the position of "just" in the sentence?