Combine the rum, lime juice and syrup. Fill a cocktail shaker halfway with ice and fill two-thirds full with the cocktail mixture. Shake for 30 seconds and pour into frosted martini glasses. Serve ice cold.
Note: to make sugar syrup, combine 1 cup sugar and 1 cup water in a sauce pan and bring to a boil. Reduce the heat and simmer until all the sugar is dissolved. Chill.