In a blender container combine cucumber, water and salt. Cover and puree until smooth. If you want it perfectly smooth, sieve mixture, but this is not essential. Add ice cubes and mint; blend until slushy. Stir in lime juice and sweeten with agave nectar to taste. To serve, add a cucumber spear to each glass. Makes 6 servings.
In a small saucepan combine 1 cup water and 1 cup sugar; heat and stir until sugar dissolves. Cool. Pour into a jar and store in refrigerator for up to 2 weeks.