Slice the radishes in quarters. Place radishes in jar. Combine water and ume vinegar. Mix and pour over the radishes.
Place cheesecloth over the mouth of jar and secure with the jar's o-ring or elastic band. Leave on the counter overnight. Remove cheesecloth, place cap on jar, and refrigerate.
Remove one or two pieces of radish as desired and serve with meals. Keeps for 1 month refrigerated.
Per serving - 2 calories, 0 gram fat (20% calories from fat), 0 gram protein, 1 gram carbohydrate, 1 gram fiber, 0 milligram cholesterol, 416 milligram sodium