Disclosed are a method and a ball valve structure which provide for an improved seal in a trunnion mounted, double piston ball valve, which is especially useful in applications requiring a seal against high pressures, such as in the oil, gas and chemical process industries. Higher pressures on an inlet side of the valve are used, while the valve moves toward and is maintained in a valve closed position, to create movement of a ball element of the valve so as to bias the ball element against both piston seat elements (or rings) used to create the seals. This movement of the ball element thereby effectively uses such upstream pressure to create and enhance a seal between the ball element and both piston seat elements while in the valve closed position.