What's the difference between "Natural" and "Brut" Champagne?

Hello there! I'm Dr. Vinifera, but you can call me Vinny. Ask me your toughest wine questions, from the fine points of etiquette to the science of winemaking. And don't worry, I'm no wine snob—you can also ask me those "dumb questions" you're too embarrased to ask your wine geek friends! I hope you find my answers educational, empowering and even amusing. And don't forget to check out my most asked questions and my full archives for all my Q&A classics.
Dear Dr. Vinny,
It may be a simple question, but what is the difference between Natural and Brut Champagne?
—Harold S., Enterprise, Ala.
Dear Harold,
It's not as simple you might think. Champagnes and other sparkling wines often have terms on the bottle to let you know how sweet or dry they are. The order from dry to sweet is typically Brut, Extra Dry or Extra Sec, Sec, Demi-Sec and Doux. It's confusing enough that "Brut" is actually drier than "Extra Dry," but to further boggle the mind, some producers break down Brut—the driest of categories—even further, into "Extra Brut" and "Brut Natural." In these cases, Natural will be the driest of the dry, indicating that no sugar at all has been added (referring to the dosage—that addition of sweetened wine or spirit after the sediment is disgorged from the bottle).
—Dr. Vinny