Place cucumber slices between layers of paper towels to remove excess moisture.
In a small bowl, combine butter and watercress; spread on one side of each slice of bread. Lay cucumber slices onto the buttered side of 8 slices of bread. Sprinkle with salt. Cover each with 1 tablespoon alfalfa sprouts and top with the remaining slices of bread, buttered side down.
Carefully cut the crusts from each sandwich with a sharp knife. Cut the sandwiches in half diagonally and then cut in half again. Yields 8 whole sandwiches, 16 halves or 32 fourths.