Disagree about it always making a bigger mess. If you're careful and go slow, you can definitely clean up most of the soot as it falls. It just takes a bit more prep work with drop cloths.
Honestly I was on the "just do it slow" side for years. Then one windy day sent a pile of old soot and a dead bird right into my living room. Now I'm a total believer in checking the draft first, no exceptions.