Wash mussels under running water; use brush on shells. Boil water, wine, onion, parsley, bay leaf, allspice, and salt and pepper in large kettle. When boiling, add clams, cover tightly and boil 2-4 minutes.
Uncover and as shells open, remove to shallow buttered baking dish. Discard shells, but save broth. Chill in fridge.
Pour marinade over chilled mussels. Let stand 1 hour or longer. Serve iced.