Spoon yogurt into strainer lined with cheesecloth. Place over bowl and allow to drain until thick, about 4 hours. Transfer to small bowl and stir in scallions and dill.
If desired, trim crusts from bread. Spread bread with yogurt mixture. Divide cucumbers, watercress and radishes among the slices and arrange them in attractive layers on yogurt mixture.
Cut each slice into four squares or triangles.