3/8", 1/2", 5/8", or 3/4" board, glued to the ceiling. I'd recommend a heavy dose of Liquid Nails builder's adhesive. Some people recommend placing a few layers of deadener before gluing a board on, but I do not.
The reason for different thicknesses of wood being a possibility is because your headliner may make it so you wouldn't be able to properly install her back on after.
It also depends how much flex you are obtaining with your roof too. If it isn't much, or you have a smaller system, just throw a few CLD Tiles all over the place.