Step 1Combine water, sugar and lime juice and stir until the sugar is dissolved.
Step 2Pour the lime-sugar mixture into a blender (in batches if necessary). Add the cucumber and blend until smooth. Chill. Serve over ice.
Step 3Cucumber cocktail: Pour 1 ounce of Absolut Currant vodka into an old-fashioned glass filled with ice. Top off with the cucumber cooler. Garnish with a cucumber slice and serve. Serves 1.