Hi, I am going to be installing a travertine floor in my bathroom. Here is a diagram of my current setup. On top of the joists (16" OC) sits 3/4" plywood sub-floor. On top of that are 3/4" thick furring strips (builder loved this technique for some reason). On top of the furring strips is another layer of 3/4" plywood. This is what the current tile is installed on and they are popping right off, making demolition pretty easy.
My question is can I install my travertine tiles (12x12) right onto the plywood or do I need yet another layer for an underlayment. I will be installing radiant heat as well. I'd rather not have to put down another 3/4" thick board to get to the 1-1/8" thick recommended underlayment thickness for travertine if I can avoid it. Is this setup strong/flexible enough?