Fill 2 old-fashioned glasses with ice to chill. Discard ice from 1 glass, and add water, bitters, and sugar; stir to dissolve. Add rye whiskey and a few ice cubes; stir. Discard ice from remaining glass. Fill with a small amount of Pernod, and swirl to coat; discard Pernod. Strain rye mixture into prepared glass. Garnish with a lemon twist.
In keeping with tradition, we prepared this cocktail using two glasses: one for mixing, one for serving. But the drink can also be made in a cocktail shaker and then strained into a Pernod-splashed glass.