I recently purchased a house and over the next 4 years I plan to remodel most of it.  The house has exposed cathedral timber framed ceilings with a large gabled roof in over half of it.  The cedar timbers have pine 1″ x 6″ T&G boards running perpindicular and on top. Above this is rigid Styrofoam insulation.  The walls have R11 batts with 3/4″ Styrofoam sheathing (blue).  If I replace the R11 with R15 in roughly 75% of the exterior walls, will I see any difference in energy savings? I live in Louisiana and it gets hot and humid with short winter.  I’m wondering if I’m fighting a losing battle due to the type of roof construction?