Are you a conflict avoider? That could really work against you in a team leader role. And it's unhealthy for your team not to deal with conflict situations -- which are inevitable when you have more than one person involved in a situation. Conflict is not a bad thing. Unresolved conflict is a bad thing. It can undermine all the good work you and your team try to do.
I believe that conflict is created from miscommunication and assumptions. If we teach people how to really listen instead of just "waiting out their turn to talk," conflict could be dramatically reduced. The power of communication is in listening, not talking. Make sure that your team gets some good quality listening training and on the job practice to minimize the opportunity for conflict.
Here's a great process you can use for a conflict discussion. Make sure you identify ground rules for the discussion right at the beginning. You can have the participants come up with a few and add some yourself where you think there might be problems. A key ground rule should be to attack the problem, not the person. Post the ground rules in clear view and then enforce them throughout the session.
Do not allow participants to cop out during this discussion. If they say something won't work, they should be held accountable for offering an alternative solution.
How about you? Do you have a process you use to resolve conflict situations?