@Patty:
I consider I'm lucky to have a large play area around the house where my dogs are obviously off leads but I always take them for their walks on lead where they might chase and kill running animals. Obviously you feel confident in letting Maya run free but please as I said before don't be too complacent.
I know of one Basenji who always ran free in his own country park, nowhere near a public road and obediently came back when called. One day he was startled by a bicycle that appeared apparently from nowhere and he panicked running across a very large field onto a busy road and was hit by a car. He did survive despite horrible injuries but had many major ops to rebuild his face.
Obviously you are lucky that Maya hasn't got a strong hunting instinct but others aren't so lucky.
It's your choice to let her off lead but free running is not the bea all and end all and many don't have the facilities or the opportunity.
When I review my post it does seem a bit stern - I'm not in any way intending to be so. Please don't take it amiss, Jess.
I understand that a lot of basenji owners feel the same as you which is why I would never tell people that the way I exercise Maya is the way people should exercise their own basenji's, that is down to each individual to decide and no one can tell anyone else how to do something like that, we can only give our opinions from oour own experiences. But as for the story of the basenji getting hit by the car, I could tell you countless almost identical stories of dogs getting scared or chasing things and getting hit by cars. Gundogs, working dogs, toy dogs - it is not something that is unique to basenjis, i think that is what a lot of basenji owners forget. Yes there is always a risk, but theres a risk when walking them on the lead, they might pull it out of your hands when they chase after something and get hit by a car! At least by walking my dog off lead well away from any roads I am dramatically reducing the risk of any such accident.
I have no intention of swaying anyone to my way of thinking about exercising, I was merely giving an opposing opinion to some others based on my own experience with my own dog. I have only had the experience of one basenji, but I have had a lot of different breeds in for training over the years and have not found her to be much different to any other dog in terms of the pack mentality they have and their trainability. I cant help to think the basenjis used for hunting in africa wouldnt be much good at all if they were all so disobedient as everyone thinks basenji's are… :rolleyes: And I do stand by what I said, I believe giving my dog a good run every day is very important to her health, both physically and mentally. They are a hunting dog with very high activity level and I personally believe that it is an important part of Maya's general care that I provide her with what I believe to be the correct exercise. All of my dogs have the same exercise as to me free running a dog is the best form of exercise so I believe, it is the "be all and end all" 
I dont mind if other people dont agree that it is the correct exercise, no one else knows my dog like me. But please accept that it is my choice and I do it for the welfare of my dog as I see it, she is a part of a pack as the breed are designed to be, and as such she doesnt stray far from them at all. I waited many years until I was in a position to cater to the needs of a basenji and i am very happy I did as she is a lovely, well balanced dog to live with and I put a lot of that down to her exercise regime! If she doesnt have her daily runs she is quite literally bouncing off the walls and a nightmare in the house 
