Until recently our cathedral ceiling was open == just decking over 4x8 rafters.
We had it closed in. The contractor installed a ridge vent and soffit and put styrofoam channels from soffit to ridge between the rafters. He then filled the rafters with fiberglass insulation, covered that with one inch of Thermax over the rafters. He then put furring strips along each rafter (over the Thermax) to support the 1x6 t&g pine ceiling.
Looks great and the insulation is excellent. The only problem is that one day last winter we had a very large amount of water dripping down the front inside (north facing) wall of the house.
We hadn't had any precip in at least two weeks and there was no snow on the roof.
Needless to say, this has ruined an otherwise great project for us.....