Bring 3 cups water to a boil in a 2-qt. saucepan. Remove from heat, add tea bags, and stir in fresh mint. Cover and steep 10 minutes.
Remove and discard tea bags and mint. Stir in sugar until dissolved.
Pour tea into a 3-qt. container, and stir in 4 cups cold water, rum, and lemonade concentrate. Serve over ice. Garnish, if desired.