Trial by Declaration. Submit your side of the story, and 80% of the time the officer doesn't want to do the paper work. They get overtime for showing up to court, they do not get overtime for paperwork. I've won all but one ticket by Trial by Declaration. If you do not win the TbD you still have a chance to go to court to plead your case with a judge, or choose traffic school. This is a no harm way to attempt to get out of it, regardless of guilt.
It's not about how much power you have, it's about how well you use it.