There are a few places to start this clean up process. I start by going over the beef brisket to remove any loose pieces of meat or fat. A thin strip of meat hanging off the side is going to dry up and over cook so there is no point in keeping it.
Once you have the loose pieces off I suggest you flip the brisket over to the meat side. Here you will find pieces of membrane similar to that on a rack of BBQ Ribs. While it isn't necessary that you remove all this, I do find that it can block flavor from getting into the meat, so I try to remove at least the larger pieces.
Now, there is the fat. A whole beef brisket has a lot of it, too much in some places. If you know anything about smoking brisket you will know that the fat is what is going to keep the meat moist during cooking and will add flavor to the brisket as it slowly breaks down. Now the most important fat in your brisket is not the big pieces on the fat cap (the fatty side of the brisket), but the fat inside the meat. It is the small ribbons of fat in the meat that is going to do the most good. I am not saying that you need to remove all the fat, but you should cut away some of the large, thick pieces. Don't cut down to the meat, just carve off the excess. By doing this you can reduce the weight of the brisket by a pound or two and thereby reduce the overall cooking time.
It is this final weight that you need to use for your cooking time.
