I use 1/8" hickory, and 3/16" maple as backing woods. You need to clamp (or wrap) your backing to the belly with either another piece of wood, or a form. If you just try and clamp the backing, it will warp. You need to sandwich the thin backing strip between thicker material, so it comes out flat. Check out my Holmegaard Build Along from about a month ago, and you can see how I do it.