Shoshone National Forest campgrounds

I am planning to visit Yellowstone next summer and have been trying to research the campgrounds between Cody Wyoming and the east entrance to Yellowstone. Wapiti, Rex Hale, Three Mile, etc. About the only information I can find is what is on the NFS website. What I am wanting to know is how full are these campgrounds during the summer months? A couple of them do take reservations, but I would like to avoid doing that if I can. The NFS website decribes the usage of the campgrounds as "heavy", but I don't know if that means usually full. I plan to be there the end of July and the first week of August. I could call the ranger station, but thought maybe someone on this board has first hand experience with these campgrounds and could share their experiences and what to expect. Last summer when I visited Glacier National Park I stayed at the Devil Creek Campground on hwy 2 in the Flathead National Forest, midway between the east and west entrances to the park and it was a great experience. The campground was lightly used and well maintained. Because of this good experience, I would like to stay at NFS campgrounds again. 
