-- Last Updated: Nov-03-11 2:53 PM EST --
Might have better chances of avoiding people during the off-season. At least then you won't have the big outfitter groups that book the best sites way ahead of time.
The catch is that backcountry camping permits may not be issued at certain times due to bear encounter potential. For instance, NPS won't allow camping at Yellowstone Lake before mid- to late-July many years. Maybe you could go while the bears are still denning. Just plan on being very, very cold. Water might not be open yet.