I suppose that we could have moved the fence a bit closer to the lane, or a bit closer to the house, but we wanted to line it up with the end of the neighbour's garage, since we felt that it would look nicer that way, while providing the right amount of space for parking. So, given that the stump was in the way, we had to figure out what to do about it.
One good solution for stump removal is to rent a stump grinder, and grind the stump down. I talked to the folks at our local hardware store (where they rent stump grinders) about this idea. It would have cost about $70 for the day, which we thought was a bit pricey, and the only grinder that they had would have been overkill for our (relatively) small 6-inch diameter stump.
We decided that for our purposes, it would be fine to leave the underground part of the stump intact, if we could just cut it down so that it was level with the ground, or a little lower. We would have to avoid it when it came time to dig the post holes, but other than that, the fence would go over it just fine, and it seemed like a lot less work than actually trying to dig up the whole stump (especially since we don't know how big the tree was, so it's very hard to know how big the below-ground part of the stump is).
We began this project by using our new shovel to dig down around the stump, so that we would have access to where we needed to cut for it to end up shorter than ground level. Here you can see another much smaller stump that is also in our yard. (This is as far as we've got with it at this point though.)
He was better, but still slow, progress with the saw when our friendly Italian neighbour (whose name I really must ask again) came out to help. He and his elderly wife have surely been living in the neighbourhood for on the order of 40 years, and she has managed to conduct her business entirely in Italian! (You can read more about them, and about our neighbourhood in my first post.) He offered us his axe, which was heavier than ours, his wood saw, which worked much better than a hacksaw for this job. Our neighbour even climbed over the low fence separating our yards to bring the tools, and offer his support. Here is a picture of James in his ferocious battle with the stump.
The best technique for removing the stump was to use the saw to cut a 1 inch groove parallel with the ground along one side of the stump, and then use the axe to chip off that section of the stump. James worked his way around the stump this way in ever-decreasing circles (an age-old technique that can also be used to find your way to a destination when you're lost).
We did eventually emerge victorious from the Battle of the Stump, but it took a lot of patience, and having the right (or at least better) tools certainly helped. We hope that this advice will save you some time the next time you need to level a stump.
If you have any tips or suggestions to add, we'd love to hear them, since we still have one more stump to go! Here is a picture of the ground after the stump was removed, and we had leveled the ground in preparation for putting up the fence.