You might also want to try puppy litter. It is compressed pellets and you work with the puppies to use it like kitty litter. If you were to blockade your kitchen off and have the litter box - that might make your clean up easier. I am set to take private messages (I think) so if you want to email me any litter information I might be able to shed some light on things to look for and any history I might be aware of.
Welcome to the Forum, Beth, Missi & Cooper.
I've read this whole thread - you've gotten some great advice! I have one more extremely helpful tidbit.
You might invest in the Basenji Owner's Manual from the Evergreen Basenji Club. Here is the link: http://www.evergreenbasenjiclub.org/
I bought this last year when after I got Duke, who's a Basenji-terrier mix. I only wish I had it when he was a young puppy. The advice and training tips given in the manual for this cute little stubborn breed is invaluable. We have just adopted another Basenji-mix who is now 12 weeks old. I got the manual out last week. I am following the age-based training guide with pleasure this time around with my young puppy. It only costs, I think $9 or $10. I highly suggest you check it out on the website.
Much luck to you and your roomy with Missi & Cooper. I'm so glad that they have such wonderful caring Basenji slaves. 
Hey thanks! A Basenji owner's manual is exactly what I've been looking for. The more I learn about these amazing creatures, the more I realize that everything I've ever known about dogs and puppy training is pretty much useless! These guys have rules of their own! I will send for my copy right away.
I really appreciate all of the help I've received from everyone here so far. It's already proven extremely helpful. No help like that from those with "on the job" experience!
I look forward to sharing my experiences with Missi and Cooper as well. Thanks again!
~Beth
