This may seem like a very exact method, but ritual is very much part of mixing a Southern drink.
Fill Sazerac glasses with ice cubes to chill.
Remove ice from one chilled glass. Place lump of sugar, dash of Angostura bitters, dash of Peychaud's bitters, and a dash of water in glass. Mash together with muddler or back of a spoon. Add rye and crushed ice.
Remove ice cubes from remaining glass. Give glass 2 or 3 dashes Herbsaint, roll in hands, and empty over sink, letting Herbsaint drip out of glass.
Strain mixture into the glass coated with Herbsaint. Squeeze a small piece of lemon peel into drink. Rub rim of glass with peel and place in glass as a garnish. Serve immediately.