Put the fish fillets in the bottom of a large frying pan, and add enough water to cover by at least 1/2 inch and the salt. Bring to a boil, reduce the heat, and cook gently until the fish flakes. Lift the fish out with slotted spoons and put it on a platter. Allow it to drain well and then pour off any water remaining on the platter.

While the fish is still warm, sprinkle it with the parsely and capers and dress it with olive oil and the juice of 1 of the lemons. Cover with black olives (preferably Greek of Sicilian olives packed in brine). Slice the last lemon into rounds and arrange them around the edge of the platter. Let the fish stand for at least half an hour in the refrigerator, marinating in the oil and lemon. Serve cold.