Peel and slice cucumbers very finely. Sprinkle with salt and place under a weight in a glass bowl for at least 1 hour. Wash well; drain and dry thoroughly with a clean tea towel.
Combine water and wine vinegar, to taste; add sugar and white pepper and pour over cucumber slices. Leave salad in the refrigerator for 1 hour.
Just before serving, sprinkle with finely chopped parsley.