Soak the clams in cold water for 5 minutes, then scrub them vigorously. Repeat in fresh changes of water until no sand settles. Discard any that do not clamp shut when handled.

Soak and scrub the mussels the same way. Remove the protruding tuft of fibers from each mussel. Discard any that do not clamp shut.

Put clams and mussels in separate covered pots over high heat. As each shell opens, remove it right away. Discard any shells that never open. Keep the clam juices in the pot.

Remove the meat from the shells, saving half the clam shells and half the mussel shells. Swish each clam gently in its juices to remove any last traces of sand.

Preheat the broiler. In a bowl, mix parsley, garlic, olive oil, and bread crumbs. Add the clam and mussel meat and coat well. Let stand about 20 minutes.

Peel the tomatoes, halve them, and remove the seeds without squeezing. Cut each tomato into 6 thin strips.

Wash the saved shells. Put one clam or mussel back into each shell. Spoon any coating left in the bowl over them, top each clam with a tomato strip, and broil just until a thin crust forms. Serve hot with lemon wedges.