I do as Peckish does, but from a different website. A four inch 'D' sleeve about an inch below the top binding.
You could fix yours by hand stitching the top of the sleeve closed all the way across and far enough down so the dowel doesn't show when it's hanging. Stitching it all the way across will keep the tension even and prevent stretching and sagging the same way a full width sleeve does. You don't say how wide your sleeve is, but if it's the standard 4", close the top inch and you'll still be fine for a half inch dowel.