If you still want to use cotton, you will probably want one that is at least needlepunched. Warm and Natural is needlepunched through scrim. If you want a cotton batting that is thinner but won't pull apart, then I would consider Quilter's Dream. QD cotton is needlepunched, but not through scrim, and is a very stable cotton batting. Look at how far apart the batting can be quilted; the further apart the quilting lines can be, the more stable the batting is.