If I am clenching/hanging the pipe, I tend to do it on the left. As I take very small, slow, sips/draws I will also allow for a draft of air on the right side of my mouth. This prevents me from pulling too hard on the pipe and getting things all hot and painful. This is also directly connected to my love of VA/VaPer/VaBur/EuroAro blends. Those Va based tobaccos can be very temperature sensitive and jump up to bite if not approached with caution.