Back when I was a kid, my Dad decided to repaint the outside of our garage. The garage was at the end of a driveway that bordered the property line with our neighbor, so one of the side walls was visible from the neighbor's house (and not really from anywhere else). Dad approached the neighbors and asked what color they would like the wall painted.
It was an unusual request, and if I recall the story correctly they thought at first that Dad was asking them to help pay for the project. No. He just recognized that since the wall was only visible from their property they were the ones with an interest in its color and it didn't hurt us to have the color be different from the rest of the garage. They chose something that suited them and Dad bought the paint.
I don't think we ever had any serious negotiations with our neighbors, but suppose we had. Dad's simple act of generosity would likely have earned him their trust and goodwill, greatly improving the chances that any difficult discussion went well.
One of the most important lessons of negotiation success is that your most profitable work is done away from the table -- sometimes when there isn't anything to negotiate! We don't always know where we'll find ourselves needing to negotiate, so even cynics should look for ways to strengthen their relationships and in particular their reputation for taking the other party's interests seriously.
Opportunities to generate goodwill, at low or no cost, are all around us. The challenge is to be mindful of the opportunities so that the next time we're painting a garage or have some other chance to help someone out, we take it.