If the tree is slowgrowth, the rings will be thin and the sapwood does not need to be thinned down. In that case, you can strip the bark off and use the branch/log as is, giving you the most wood to work with. I've made two yew bows out of 2½" diameter trees that way. I wouldn't go any smaller than a two inch diameter stick, since that will mean the heart of the wood will be in the finished limbs. That creates some problems with the wood around it lifting when you start tillering.