In a small saucepan, heat sugar and water to a boil. Remove from heat and stir in mint leaves. Cover and let steep until mint syrup is cool.
In a bowl combine mint syrup, lime juice and rum. Pour mixture into popsicle molds, adding mint leaves into each one (if desired). Freeze for at least 4 hours.
Notes
* 2 tsp of rum flavored extract can be used in place of the rum (recipe will yield less popsicles)