It's a good way to stay on the offensive even when you're responding to an opponent's brief: write your first draft even before reading your opponent's brief.
Sound nuts? Maybe so, but it will make your written work stronger. It's also Tip #86 in Bryan Garner's The Winning Brief--
This tip will help you develop your case as well as you can. You won't find yourself in the defensive posture of merely responding to what your opponent says. Too many responsive briefs are entirely reactive.
If you prepare a draft explaining why the court's decision was correct, you'll be in an enviable position when your opponent's brief arrives. You'll be able to massage the draft to account for your opponent's points.
Many times, this tip works in the lower courts too. When you respond to discovery or pleadings motions, you often know your best arguments even before your opponent's memorandum arrives. Get started writing now and you'll be sure to write from a position of strength.