1. Set a large fine-mesh sieve over a large bowl or pitcher. In a food processor or blender, puree watermelon. Pour watermelon puree through sieve, pressing on solids with a rubber spatula (you should have about 2 cups juice). Puree English cucumber and pour through sieve into watermelon juice.

2. In a small bowl or measuring cup, stir together lime juice and honey. Add to watermelon and cucumber juices, along with vodka. Adjust sweetness with more honey if desired. To serve, fill four glasses with ice and top each with cocktail. Garnish with cucumber slices.