@Ann:
Hi Dan. Thanks for your feedback. Noel will be 5 in November. (I don't know how she spent her first 4 years.) Our fence is 6' so other dogs can't get in…it's her reaction to them that could cause problems. I'm sort of a hyper worrier since Noel has a weak front leg. It was badly broken in December and, when there's squirrel/dog activity around the yard or in the alley behind us, she forgets about her leg and goes into a full run and jump mode. It's great to see her fly over our 2' stone ledge and run the periphery of yard like a guard dog or chase a squirrel back to its tree, but if left outside alone all day there's the potential that she'll overdo it and tire out her leg to the point of pain. I know I'm sounding over-protective...The vet recommends plenty of exercise but in small doses to avoid the fatigue thing. (I'll be posting some queries soon in relation to this!)
OK Ann, now I see your dilemma here. This is a tuff one keeping a Basenji still or low activity especially when you're not there. The only other thing you could do is set up a kennel run or large dog pen to reduce the area. see this picture.
http://www.seefido.com/html/dog_kennel_runs_pen_fence_.htm