When you cut a setup, how do you know you haven’t cut the bit the audience needed?

I’m very good at being told “get to the joke faster” and then deleting so much context that the punchline technically arrives sooner but makes less sense. When you’re tightening a setup, what are you listening for to tell the difference between dead wording and information the audience actually needs? I’ve started trying to cut one sentence at a time rather than doing a heroic rewrite, but I still find it hard to tell whether a shorter setup is actually a better one.