A bumper for use at a loading dock has two ranges of front-to-back movement: one range for sealing the gap that might otherwise exist between the rear edge of a truck and the front face of the bumper and a second range for absorbing the impact of the truck backing into the dock. In some cases, a spring provides a relatively light sealing force between the bumper and the truck, and a compressible core provides a much greater impact-absorbing force that helps stop the rearward movement of the truck. In some embodiments, the bumper pivots by gravity when operating in the sealing range.