Barb, I'm glad you posted this. I have recently done two similar repairs & didn't think until after that I should have taken before & after pics. Anyway, I was thinking that the ways people have handled repairs would make a really interesting thread. With that small of a core,I would probably not even attempt to pull it from the end, my thought would be to slide the braid back both ways, cut & knot the core, splice the ends together over the knot & put a button over the splice. Just a thought, be interesting to see what other ideas turn up& keep us posted on what you do. Buck