Conversely, though - if you're completely unwilling to accept a clause that limits your employment after leaving the company, your starting point should be an agreement that doesn't have such a clause in it. Don't give them the impression they can talk you out of it. By giving them a new document to sign, they are the ones who have to confront you if they want to re-add the noncompete.
This is a your-mileage-may-vary thing and there is no easy answer for all cases.
"if you're completely unwilling to accept a clause that limits your employment after leaving the company, your starting point should be an agreement that doesn't have such a clause in it. Don't give them the impression they can talk you out of it."
You don't have to be willing to accept it, just be willing to hear their side of the story.
This is a your-mileage-may-vary thing and there is no easy answer for all cases.