Trim stems and roots from radishes. Slice into thin rounds. Place in non-reactive saucepan along with vinegar and water. Bring mixture to the boil. Reduce heat and simmer over medium heat until radishes are somewhat tender, about 8 to 10 minutes.
Transfer radishes to bowl with a slotted spoon. Reserve cooking liquid. Let cool separately to preserve crispness of radishes. When both have cooled, combine in airtight container and refrigerate overnight. Serve the next day for best results.