Combine all the ingredients in a mixing glass and roll back and forth to mix. Strain into a large goblet or pint glass three quarters filled with ice. Garnish with the lemon and lime wedges on a side plate.
There's something about the Bloody Mary that makes people competitive. Every weekend bartender in America has his own, and of course, his is the best recipe in Western civilization. But this is really the best recipe. A dash celery salt is a nice touch, and New Yorkers traditionally add horseradish. The Bloody Mary oers rich ground for improvisation both in garnish and ingredients. Have fun.