Place 1 teaspoon sugar each into two 12-ounce glasses. Squeeze juice from a lime wedge into each glass and drop in the wedge. Place 2 mint sprigs into each glass. Use a spoon or muddler to mash lime mixture together in the bottom of the glasses.

Fill each glass about half full with crushed ice. Pour 1/4 cup rum into each glass. Fill the glasses with club soda, stir, and garnish with remaining lime wedges.