I recommend the Easy Walk Harness if the main goal is to reduce pulling during daily walks. The nice thing about the Easy Walk Harness is that you can order them in 'tweener sizes. Most basenjis are a S/M 'tweener.
http://www.premier.com/View.aspx?page=dogs/products/behavior/easywalk/productdescription
For a collar that is difficult to slip out of I would recommend a correctly adjusted martingale collar. If they are ajusted properly they are difficult to slip, http://allhoundsapparel.com/custom/list.asp?c=20620
For loose leash walking, I really recommend working on eye contact/attention, then loose leash, then add the walking. For eye contact/attention, I start with name response. Say her name when she begins to turn to look click and treat. At first you may have to click for even the smallest motion towards you but usually they start turning pretty quickly for that treat. After a while of working name response, often they will start to stare at you anticipating the click for turning toward you when that starts to happen start clicking and treating for eye contact. My favorite obedience instructor always said this was the most important thing we should work on for class because you can't train butts you can only train heads so we need them to focus their head on us. Once you have built attention, you can start working loose leash, at first just stand in place and click for the clip of the leash hanging down loosely. This should be about 10 click/treats (break the treats up small) then try taking one step and click for loose leash. It is really slow going but it does work. There are several other methods for teaching loose leash. Here is another method, http://www.shirleychong.com/keepers/LLW/index.html
I've used White Pine Outfitters for years and love their product. I use the limited slip collar (it's a martingale) and have one for each of my basenjis.
http://www.whitepineoutfitters.com/
This is the nicest feeling new product I've ever put my hands on. (Well worn leather is hard to beat, but takes a while to get there.) The collars won't break hair or discolor the fur when it gets wet. And last forever if nobody uses them as a chew toy. I used another brand for years, but when I got one of these, I never looked back. I don't know of anyone who has been disappointed in this product.
They also have harnesses, but I haven't used used harnesses on my dogs.
As far as your training goes, is she getting her exercise before your walk or are you expecting the walk to be her exercise?
Hey Lisa, can you get the Easy Walk at like a Pet Smart in the States? or do they need to be ordered from the site?? Living in Europe makes these shipping things such a pain 
You can get it from PetSmart and Petco but not in the 'tweener sizes.
Thanks a bunch
Schouiffy, I have 4 Easy Walk Harness (size M, S) I only use them when I walk a dog at a time so have 3 available. If you want one just tell me and I will send it to you for shipping price!
One of mine tries to slip his collar, I use a gentle leader on him but have a link to a normal collar as well.
For helping with the pulling, I second the Easy Walk Harness. I got some a while back and they are very helpful. Most of the time I still prefer regular collars though. A good martingale or limited slip should be better at keeping in your dog than a harness. Just make sure the collar is adjusted well. The Premier collar is a martigale:
http://www.premier.com/View.aspx?page=dogs/products/collars/other#premiercollars
Thanks for the tip Lisa, I didn't know they made "tweener" sizes now! I have mediums, and it's doable, but a close call for little girls. I don't like how narrow the webbing is on the smalls, so nice to see they have something in between with a bigger web.
If you're worried about chafing, I recommend walking harnesses that are made by weight pull harness makers. Not sure how good these are for escape artists though?
Thank you for the link to the web master harness. Does it do anything to prevent pulling? Also, are we wasting our time trying loose leash training on our Basenji? Do they just pull all the time and that is that?
For pulling I don't think the web master really does much for correcting the pull, but it does provide more comfort to you and the dog; one wonderful benefit of it is a handle that you can quickly grab your dog out of any sticky situation it can get in (I've had to do this a few times). Also having dealt with much stronger dogs than basenjis (I do know how strong a basenji is though, they are quite strong little buggers) in the pulling angle I would go with the web master harness hands down over any other harness. The Easy Walk harness is a good tool also to help with teaching to walking, but if your girl is hardheaded about slipping a collar she could slip an Easy Walk or any other standard harness.
If you are looking to go for loose leash walking you can look into the Gentle Leader and start from there. It is a head collar and has the same concept as horse halter - where the head goes the body will follow. This is a training tool and make sure you read the book and watch the dvd also, but dogs can do wonderful on the gentle leader when used correctly.
The first step though is always remember PATIENTS and TIME is key especially with hard headed stubborn breeds. Basenjis aren't dumb, they just want to do things their way and you have to find they way to work around their thinking.
Have you maybe considered a obedience class for you and her? Don't think that she's untrainable, they just take more patients and a little more finesse LOL
If you are looking to go for loose leash walking you can look into the Gentle Leader and start from there. It is a head collar and has the same concept as horse halter - where the head goes the body will follow. This is a training tool and make sure you read the book and watch the dvd also, but dogs can do wonderful on the gentle leader when used correctly.
The first step though is always remember PATIENTS and TIME is key especially with hard headed stubborn breeds. Basenjis aren't dumb, they just want to do things their way and you have to find they way to work around their thinking.
I would highly recommend the Gentle Leader (speaking as a prior B owner and a current horse owner/trainer). It is a no-combative and gentle way to help teach your B to walk with you… not 20 leagues ahead of you sprinting left and right every-which-way. HOWEVER, timing is everything. Watch the video (comes with the head collar) and read the information. Just like clicker training, your timing has to be spot-on or they learn to pull against it also.
Keep up the patient work and remember, you can convince a B to work with you and not against you. Although in their mind, the "against you" is much more entertaining for them. grin
http://www.woofandwag.com/servlet/the-1/Puppia-Dog-harness,/Detail
I use a Puppia harness for Shelby. It's been a life saver since she does like to pull a bit. I can guide her much much easier. We don't leave home without it.
