If you remember that everyone is worried that their most important constraints are the ones that are going to be forgotten or overruled, then one of the best ways to maintain collective trust—which is basically the whole ballgame—is to visibly record their constraints. Effectively it's an intermediate record of consensus about the shape of a solution, even before you reach a conclusion.
What's really nice is that you can pretty much always deploy this technique, even if it's not part of any formal process. Even in an ad hoc group making a one-off decision, I like to try to take stock and list the constraints I think I've heard identified so far. (In fact it's especially useful in these situations, because an ad hoc team will often not have a strong basis of trust to start from.) Capturing the constraints reassures people that they can work to meet other people's constraints without fear of sacrificing their own.