I've gone through much of the detail on how to properly grill a backstrap of venison (or elk, antelope, bison, moose etc.) above, but remember that this is done over high heat with the grill top open, and that it takes a good 15 to 20 minutes. Be patient and you will be rewarded.
Coat the venison backstrap in oil and salt well. Set aside for 20 minutes at room temperature.
Get your grill hot, clean the grates and lay the venison on the grill. Paint with the BBQ sauce. Keep the grill cover open. Let this cook 5 to 8 minutes without moving, depending on how hot your grill is and how thick your venison loin is. You want a good sear, with good grill marks, on that side of the meat. Flip and repeat on the other side, painting that side with more BBQ sauce.
Do the finger test to check for doneness. If the venison needs some more time, turn it to sides that have not had direct exposure to the grill and cook for 2 to 3 more minutes, checking all the way. Paint those sides with BBQ sauce, too.
When the meat has been cooked to your liking, take it off the fire and let it rest, tented with foil, for 10 minutes. Serve with BBQ sauce on the side.
If you use a barbecue sauce with this recipe, serve the venison with a side salad like potato, macaroni or bean salad, plus maybe some tomatoes and basil, corn on the cob, dinner rolls --- you get the idea. Nothing overly fancy.