The cat perch I'm building has an 1" thick base and 3  1/4" thick shelves. I drilled  1" holes, but discovered the 36" long dowel's diameter is oversized by 1/16". 
Rather than sand the entire length of the dowel, I came up with a way to ream out the holes.
Take an undersized dowel piece (3/4" x  2" long) and in the center drill out a hole for a 4" long wood screw. The extra 2" length of the screw is the drill bit. Keep the dowel pressed tight against the drill.
Next, tightly wrap the "reamer" in cardboard taped to the dowel. Now use glue to attach the medium coarse sandpaper on to the cardboard making sure the wrap of the sandpaper is in the opposite direction as the drill turn. This will give an even removel of the wood for the too tight holes.