Prepare the marinade. In a small bowl, whisk together the olive oil, lemon juice, minced garlic, fresh rosemary, smoked paprika, salt, and pepper.

Marinate the venison. Place the venison backstrap in a resealable bag or a shallow dish and pour the marinade over it. Massage the marinade into the meat to ensure it's evenly coated. Marinate in the refrigerator for 4 hrs or overnight.

Smoke or sear in skillet and then bake at 350 until 135 internal, check after 5-7 minutes. Medium rare.