If you do medallion your backstraps, try wrapping them in bacon to help retain moisture. We do this on our moose hunt and cook on a flame, not BBQ and it is simply delish!!!!! Season as you wish, last year we let it sit in a garlic/beer bath for 10 hours, rapped the bacon and right to the grill...was melt in your mouth. On a gas bbq no more than 10 minutes a side and if you slow roast or low open flame double it...it will be rare but full of juice and flavour...just the way game is suppose to be cooked

Hint use skewers, soak in water if wooden for 15 minutes and place 2 medallions per skewer, this will hold the bacon in place. We also cut our medallions an 1" thick, so if you do less than drop your cook time accordingly. If you like it more cooked bacon on the top while you grill the under side and then rotate it as you flip, will also keep it moist. I prefer it rare, but have done this for those who don' t like it rare and they loved it.