Coarsely chop the tomatoes, cucumber, jalapeño (with seeds), and watermelon. Purée in a food processor, in batches if necessary, until smooth. Transfer to a bowl and stir in the salt and pepper. Set aside for about thirty minutes to allow the ﬂavors to develop.
Pour purée into a large bowl lined with two layers of cheesecloth. Gather the edges of the cheesecloth and secure with a piece of kitchen twine or an elastic band. Tie the bundle to a wooden spoon and suspend across a deep bowl so that the bundle hovers above, and the water gathers below. Place in the fridge or a cool corner and drain for about 4 hours.
Once the liquid has drained, discard the bundle and give the water a stir. Taste and add a little salt if necessary.
Serve very cold with a good squeeze of fresh lime juice and small drizzle of olive oil.