I know something is wrong with me but, after trimming the brisket before smoking as stated by Prisonchef, I like those little bits of fat that tenderizes the brisket. I cut or pull the brisket, fat and all, and if my guest want to trim or remove it in their plate that is fine with me.
I do make sure my wife doesn't see me eating some of that good flavored fat and then I trim some of the fat so she can see it in my plate.

Like, Stevegardner, she can't stand the fat even to look at it.

Smokemullet