Set a large fine-mesh sieve over a large bowl or pitcher.

In a food processor or blender, puree the cubed watermelon.

Pour watermelon puree through sieve, pressing on solids with a rubber spatula to extract the juice. You should get about 2 cups of juice.

Puree the peeled and chunked English cucumber in the food processor or blender.

Pour cucumber puree through the sieve into the watermelon juice.

In a small bowl or measuring cup, stir together fresh lime juice and honey until well combined.

Add the lime juice and honey mixture to the watermelon and cucumber juices.

Add vodka to the mixture and stir gently.

Adjust sweetness with more honey if desired, tasting as you go.

To serve, fill four glasses with ice.

Top each glass with the watermelon-cucumber cocktail.

Garnish with cucumber slices.