Untreated cedar?
You're a better man than I,
@Sam Harris. I've learned to move about a foot or two over from the existing posts and dig there. I pulled one concrete chunk out a few years ago and promised myself to never do that again. I dug three this spring and they're all offset the same. When the time comes to replace the fence, they're all in place and it's all above-ground work. With the wind we had a few weeks back I'm sure glad I did them earlier.
Now I'm about to embark on a deck replacement that requires min. 8"x36" concrete caissons to support it. Oh, boy. Auger rental time....