I think of myself as a problem solver rather than a disciplinarian.
Exactly. I always try to approach as a discussion rather than an attack or accusation. This helps you understand the background and all sides of the situation before handling it. This helps to avoid things getting heated which you definitely don't want, especially if it's a group of people.
I had a fairly large problem at the theater at which I worked this past summer. There was a lot of conflict among the female members of the company and they weren't getting along at all, scapegoating one actress in particular. Although the situation involved all of them, I spoke with each girl individually (there were about 7 of them) so that they could let the emotions flow on me before they confronted each other. In the end I ended up sitting with them in the dressing room for an hour after the show one night. Each girl was allowed to speak on each "sub-problem" that made up the situation, while I served as moderator.
This worked to great success, and I believe they went home and baked cookies together afterward. I never had another problem for the rest of the season.
You just have to get a feel for your company.