This is the Cook's Illustrated recipe for turning a less expensive, less tender piece of beef like an eye of round into a more tender meal. I am going to try it with venison soon.

"We don't recommend cooking this roast past medium. Open the door as little as possible and remove the roast from the oven while taking its temperature. If the roast has not reached the desired temperature in the time specified in step 4, heat the oven to 225 for 5 minutes, then shut it off again, and continue to cook the roast to the desired temperature. For a smaller (2 1/2 to 3 1/2 pounds) roast, reduce the amount of kosher salt to 3 teaspoonss( 1 1/2 teaspoons table salt) and black pepper to 1 1/2 teaspoons.  Slice as thinly as possible and serve with Horseradish Crean Sauce, if desired. "

PREP TIME AND COOKING TIME ARE INDICATED WITHIN THE RECIPE. The Cook's recipe does give cooking times, but the temperature method is preferred. I have inserted the cooking times as per Cook's recipe.

1. Bone less eye round roast 3 to 4 1/2 pounds
2. 4 Teaspoons kosher salt or 2 table salt
3. 2 teaspoons vegetable oil plus 1 Tablespoon
4. 2 teaspoons black pepper

1. Sprinkle all sides of meat with salt. Wrap with plastic and refrigerate 18 to 24 hours.
2. Pat roast dry, rub with oil and sprinkle all sides with more salt and pepper.
3. Sear all sides of roat in large pan on top of oven.
4. Place roast or rack set on cookie sheet in center of oven pre-heated to 225 degrees. and cook until meat probe inserted into center of roast registers 115 for medium rare or 125 degrees for medium rare.Transfer roast to wire rack set in rimmed baking sheet. Roast until meat-probe thermometer or instant-read thermometer inserted into center of roast registers 115 degrees for medium-rare, 1 1/4 to 1 3/4 hours, or 125 degrees for medium, 1 3/4 to 2 1/4 hours.
5. Turn oven off; leave roast in oven, without opening door until internal yemperature reaches 130 for medium rere or 140 for medium.
6. Transfer roast to carving board, rest 15 minutes and slice thinly as possible and serve.