Sometimes advice comes along and strikes me as so obvious and so unhelpful at the same time. This is like saying "cut out all the boring parts and your story will improve." Didn't Elmore Leonard say something like that? I think so. I get it. Simple, yet difficult to execute and equally unhelpful.
But with respect to dialogue, crisp doesn't always mean short sentences. I've read many great dialogue sequences from authors where characters talk for decently sized paragraphs (looking at you, Bernard Cornwell).
I think the key to making it sound crisp is in the revisions. Write as honestly as you can, getting out what you think needs to be said, and in revisions, trim those lines down to their simplest parts. Let your characters react and interrupt. Let them pause and think and then say only a fraction of the words running through their head.