Chill a lowball or rocks glass. Once chilled, add the anise liqueur and swirl around the glass to rinse.
Add the sugar, water, and bitters to the glass. Muddle the sugar to dissolve.
Pour in the Sazerac rye. Swirl the glass to mix and garnish with a lemon peel. Serve immediately, while the glass is still cold.
Too strong? Serve this Sazerac cocktail over a large ice cube to dilute. Lemon peel garnish tip: Use a veggie peeler to cut a section of lemon peel 1 ½ to 2 inches long. You can trim the edges or use as-is. Twist the peel before adding to the glass.