Jim - What is your test for doneness? A rib should not be anywhere near rare.
Some judge by how far the meat draws up on the bone (about 1/2") while some use the bend test ( hold a full slab with a pair of tongs. If the slab bends i the middle and met begins to break apart - they're done). Also, the "toothpick" test. If you can push a toothpick between the bones with the thickest meat with little resistance, the ribs are done.
Hope this makes sense and helps a little.