Overboarding versus taking the ceiling down
Overboarding fixes new plasterboard through the existing ceiling into the joists above, then skims the new surface. It is quicker, considerably cleaner and keeps the original ceiling in place — a real advantage in period homes where the old plaster still contributes to the character and integrity of the room.
Where a ceiling is badly sagging, has come away from the laths over large areas, or is soaked through, taking it down is the right call. It is messier and takes longer, but the result is a new ceiling with no legacy problems.

