Combine sugar and corn starch in top of a double boiler; add milk and eggs, beating well with a wire whisk. Place over boiling water and cook, stirring constantly with a metal spoon, until mixture thickens and heavily coats the spoon. Remove from heat, and let cool to room temperature.
Line bottom of a 2-quart baking dish with one - third of vanilla wafers. Arrange half of sliced bananas over wafers; top with half each of custard and whipped cream. Repeat layers, reserving remaining one-third of vanilla wafers to garnish top of pudding.
Cover and refrigerate at least 5 hours. Spoon into individual serving bowls, and serve chilled.