In a pitcher (at least 2 qt.), combine rum, mint syrup, and lime juice; add about 2 cups ice cubes. Pour into ice-filled glasses and garnish with mint leaves if desired.
Mint Syrup: In a 1- to 2-quart pan, combine 1 1/4 cups lightly packed rinsed fresh mint leaves, 1 cup water, and 1/2 cup sugar. Stir over medium heat until sugar is dissolved and mixture is simmering. Remove pan from heat, cover, and let stand 30 minutes. Pour mixture through a fine strainer into a small pitcher or bowl; discard mint leaves. Use syrup or cover and chill up to 1 week. Makes about 1 cup.