Wash the English cucumber thoroughly under cold water and slice it into manageable chunks, about two inches long.

Using a citrus juicer, extract the juice from fresh limes until yielding at least 1/3 cup of lime juice.

In a high-speed blender, combine cucumber chunks, lime juice, splash of agave nectar, pinch of salt, and coconut water. Blend on high for about 30 seconds.

For a pulp-free drink, strain the mixture using a fine mesh strainer over a pitcher.

Fill glasses with ice and pour the strained mixture over the ice. Garnish with cucumber slices or lime wedges before serving.