1. Prepare yogurt sauce: Combine yogurt, cucumber, onion, mint and salt.
2. Prepare Gyros: Combine garlic, oregano, coriander, salt and allspice in small bowl. Pat minute steak dry on paper toweling. Add to spice mixture.
3. Cook steak in oil in skillet over medium heat until medium-rare, 2 to 3 minutes. Spoon into pita. Garnish with cucumber. Serve with sauce.