1In each of 2 highball glasses, muddle (crush together) about 1 tablespoon mint leaves with juice squeezed from 2 lime wedges. Add lime wedges to glasses; muddle. Stir 1/4 cup of the rum and 2 tablespoons sugar into each glass. Mix well to dissolve sugar. Add about 3/4 cup ice to each.
2Pour 1/4 cup club soda into each glass; stir well. Garnish with mint.