An airbag cushion of flexible sheet material has a vent opening with a vent cover of flexible sheet material stitched to an interior surface of the airbag cushion aligned with the vent opening in the airbag cushion to form a pocket. The vent cover has a vent opening therein allowing inflation gas to escape from the cushion via the vent opening. A vent flap of flexible sheet material is disposed at least partially within the pocket and inboard of the vent openings in the airbag cushion and vent cover. A tether extends inboard from vent flap to a tether end that is fixed in a releasable manner to a tether end securing device fixed to a module housing. The tether end is released in response to a sensor signal.