When sliced very thin, the pieces of lime in this pop are perfectly edible -- all the way down to the rind.
In a small saucepan, bring sugar and 2 cups water to a boil over high. Reduce heat and simmer, stirring occasionally, until sugar dissolves. Remove from heat, stir in mint, and let syrup cool, 30 minutes.
Pour syrup through a fine-mesh sieve into a medium bowl, pressing on solids (you should have about 3 1/4 cups syrup); discard solids. Stir lime juice into syrup. Fill ten 3-ounce ice-pop molds three-quarters full with syrup. Freeze until slushy, 45 minutes. With an ice-pop stick, submerge 1 lime slice and 1 mint leaf in each pop. Insert ice-pop sticks and freeze until solid, 6 hours (or up to 2 weeks).