Step 1 Combine the soda, lime juice and sugar in a non-reactive saucepan over low heat, stirring just until the sugar is dissolved. Remove from heat. Stir in the rum and lime zest. Place a few mint leaves in each popsicle mold, then pour over some of the mixture, leaving about a half-inch of space at the top of each mold. Place the lid on the molds and fit each with a wooden stick. Freeze until solid, 3 to 4 hours. Remove the popsicles, run the molds briefly under warm water to loosen, then pull the popsicles from the molds. Wrap the popsicles in plastic wrap and freeze if not serving immediately. The frozen popsicles will keep 1 to 2 weeks.