Did a quick search and actually found quite a few hits for brining backstrap. Here's one that sounds pretty good...
http://www.liveoutdoors.com/hu...0-venison-back-strap
1 Gallon of Water (could substitute ¼ gal of water for apple juice too!)
¾ Cup of Salt
½ cup of regular (not reduced sodium!) soy sauce
¼ worchestershire sauce
½ cup of brown sugar
½ cup of molasses
1 tbs. rosemary
2 tbs. pepper