Our two Goldens respected an invisible fence, but the Basenji– not so much. Sometimes, they don't even respect the visible ones. We installed a picket fence at our last house, and I decided I wanted those pretty scallops. Our B-girl quickly found she could get a little momentum going and clear the center dip in our 4' fence. Now I have a 6' shadowbox, and that's done the trick.
I wanted to thank everybody for their input. At first, I was extremely disappointed. Part of me was hoping for even one or two positive experiences to make myself feel better about my only option. However, I think the overwhelmingly negative opinions worked in my favor. The boyfriend is coming around… last night we discussed options. He said, "We can have a fence, but you're not going to like what I want." I said "As long as it is a basenji proof physical barrier, I don't care if you put brown and pink lacquered (suggestively shaped boards) all around our yard!"
So it will still be another year before I save up the money, at least, but I wore him down much more quickly than I had hoped!!! Thank you all so much for your help!