I got a tip from an "old gardener" which has proved very effective, which is to put lots of copper nails into the old stump..it has worked for me in 3 cases so far (one of which was an old maple stump that was quite persistent in putting out lots of shoots). Once it is really dead it should be easier to get out. I've also hacked a couple of stumps to death with a splitting maul (works better than an axe), but it's pretty vigorous work!
