Remember that your credibility is on the line to keep your end of the bargain, especially in a sensitive situation like a conflict negotiation. Many other cultures recognize the often subconscious effect that the physical arrangements have on the outcome of a conflict resolution. Don't sit or stand in front of the door, psychologically barring exit. Don't wear wild or loud colors, especially in the red or orange family. Use a low, moderate tone of voice.
Few people know what they really sound like.
You may want to use a tape recorder or have a coach help you with modulating your voice to an unabrasive tone. Make sure the room is comfortable- not too warm, cold, noisy, or drafty. Such irritants can add to the sensitivity of the participants or cause them to cut the session shorter than it needs to be. Avoiding conflict is not possible, or even desirable. The diversity of opinions and experiences you bring to the table have their place, as do everyone else's.