Wash the romaine, watercress and radishes. Shake the greens well to remove as much moisture as possible. Roll them up in several thicknesses of paper towels and put in the refrigerator to crisp. Do this several hours ahead of time.Greens must be absolutely dry or dressing will not cling to the leaves. Remove the blossom and stem end of the radishes, and slice them paper thin. Keep them in ice water in the refrigerator until you are ready for them. Remove the coarse stems from the watercress, keeping only the very thin delicate stems and the leaves.Gather watercress together and, using a chopping board and a very large,sharp, heavy knife, chop the watercress as you would parsley, holding the tip of the knife on the board with your other hand.

In a small bowl mix the oil, lemon juice, vinegar, 1/2 tsp. salt, mustard and sugar. Add the chopped watercress and stir well. Chill. Before serving tear or break the romaine leaves into bite-size pieces. Sprinkle the greens with the remaining 1/2 tsp. salt; add the drained, sliced radishes. Pour on dressing and toss.