Chill a coupe glass in the freezer for 10 minutes, or fill it with ice water while you build the drink.
Fill a mixing glass three-quarters full with large ice cubes.
Add the gin, Campari, and dry vermouth to the mixing glass.
Stir briskly with a bar spoon for 20 to 30 seconds, until the outside of the mixing glass feels ice-cold and slightly frosted.
Empty the ice water from the coupe glass and strain the cocktail into it. For a drink on the rocks, strain over one large fresh ice cube in a rocks glass instead.
Cut a wide strip of lemon peel and hold it skin-side down over the drink. Twist to express the oils across the surface.
Run the peel around the rim of the glass, then drop it in or perch it on the rim. Serve right away.