There are such Rescues where dogs are placed in foster homes, rather than in a shelter environment, where they can be assessed and trained appropriately. A dog coming from this sort of environment may be better suited to your needs. I have to add, many are pure breed puppies. I've had two in just the past several months.
You might want to call several Rescues in your area to familiarize yourself with the work they do. You may be awfully surprised with what you find. If you're in Quebec, many of us here can recommend some awesome Rescues.
"Education is a progressive discovery of our own ignorance." -Will Durant