Wash radishes; trim off radish tops and roots. Cut radishes into 1/4-inch slices. In a large nonmetal bowl stir together the 2 1/2 cups water and salt; add radishes. Cover and chill for 1 to 2 hours, stirring occasionally. Pour radish mixture into a colander set in a sink. Rinse with cold water; drain.
In a medium stainless-steel, enamel, or nonstick heavy saucepan combine wine, vinegar, sugar, peppercorns, cloves, and allspice. Bring to boiling, stirring to dissolve sugar; reduce heat. Simmer, covered, for 15 minutes.
Pack radishes into hot sterilized half-pint canning jars, leaving a 1/4-inch headspace. Pour hot vinegar mixture over radishes, distributing the whole spices evenly and maintaining the 1/4-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a boiling-water canner for 10 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks. Makes 5 half-pints.