You will usually find brisket in two different main cuts in the store. There is: Flat cut:  This is the most common cut you will find in the grocery store and the one I usually use. The fat or deckle has been removed from this piece. Point cut: This is the fatty part of the brisket, which is called the deckle. This cut is marbled throughout with fat or "deckle." This brisket cut is less common in grocery stores and it is a softer and more flavorful brisket cut. Ask your butcher for this cut.