Medium Rare is the best way to cook all Game meats. It keeps them from getting tough as leather at even " medium", and maximizes their flavor. Because wild meat has so little fat, I like to cook them "wet" by wrapping cuts in aluminum foil, with butter, salt and pepper, onions, peppers, and a sweet, tart apple, all cut up, to roast in the oven or over a fire. The meat should be so tender you can cut it with a fork. That's the best eating! A little wine in the package helps to flavor the meat, too. I don't like grilling anything unless its just to sear the surface to close the meat up and retain the blood in it. That is a 15-30 second " zap" depending on how hot the grill is. Then I bake the meat to complete the cooking to medium rare, for best flavor. Do this with fresh liver, for instance, and bake in a covered roasting pan with water, ( wine added) white onions, and bacon strips on top of the liver steaks, and what you eat you will swear is prime Rib! I developed a cult following of people who liked my liver, and every time I got a deer, a call would go out, and people would gather to help each up all the fresh liver they could stuff down their throats. Someone always brought a new person, just to have them taste " GOOD " liver. That is how the group grew.