A ring seal includes a sealing ring including an asymmetric body portion having axially-opposed and radially-offset seal beads. The ring seal may also include a reinforcement ring carried at least partially in the sealing ring to distribute load across the seal beads. The ring seal may further include a skirt depending generally axially from the body portion and defining an inner diameter of the sealing ring and preferably having frusto-conical cross-sectional shape.