An apparatus for helping to protect an occupant of a vehicle includes a curtain airbag having a packaged condition in which the curtain airbag is rolled and/or folded for installation in the vehicle. The curtain airbag is configured to inflate and deploy between the occupant and a side structure of the vehicle. A deployment wrap includes a sheet of material configured as a loop to extend around the curtain airbag in the packaged condition. The deployment wrap is configured to undergo tension in response to inflation of the curtain airbag. The tension acts on the curtain airbag to help control the initial deployment of the curtain airbag. The deployment wrap is rolled up along its length, forming a roll that takes up the material of the deployment wrap and causes the deployment wrap to constrict around the curtain airbag.

A soft cover for packaging an assemblage of an inflator and a side airbag in a stored condition to form an airbag module for installation in a vehicle, The soft cover is formed as a sheet of material including a central portion configured to form a loop that encircles the inflator and side airbag. A first end portion of the sheet extends from the central portion and is configured to wrap over the inflator and side airbag, closing a first open end of the loop formed by the central portion. The first end portion includes an inflator connector opening configured to be fitted over a connector housing of the inflator, leaving the inflator connector housing exposed outside the airbag module.