Preheat the oven's broiler.

Arrange cocktail rye slices on a baking sheet. Top each one with about 2 teaspoons of thousand island salad dressing, then fold about 1/2 slice of corned beef to fit the bread, and lay over the dressing. Place a small amount of sauerkraut over the meat, then top with 1/4 slice of the Swiss cheese, or a slice about as big as the bread.

Broil for 3 to 5 minutes, until cheese is melted. Serve warm.