Eye of round steak is extremely lean and very low in fat, which can make for a tougher cut of beef. The best way to break down the tough muscle fibers and create a more tender steak is to mairnade the steaks before cooking. The ideal marinade should contain acidic ingredients like vinegar, citrus juice, wine, yogurt, buttermilk, or soda. While braising is the optimum cooking method to prevent the steaks from drying out, they can also be cooked medium rare by grilling, pan broiling, or skillet frying over low heat.