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An inflatable vehicle occupant protection device (14), such as an air bag, includes first and second inflatable structures (72,74). The first inflatable structure (72) has an inflated location between the occupant's thorax and a side portion (20) of the vehicle. A second inflatable structure (74) has an inflated location between the occupant's head and the side portion (20) of the vehicle. A valve (80) increases the pressure of inflation fluid in the second inflatable structure (74) in response to engagement of the occupant's thorax with the first inflatable structure (72) prior to subsequent engagement of the occupant's head with the second inflatable structure (74). The valve (80) has an open condition permitting inflation fluid to flow from the first inflatable structure (72) to the second inflatable structure (74) under the influence of pressure in the first inflatable structure (72), and has a closed condition blocking the inflation fluid from flowing back from the second inflatable structure (74) to the first inflatable structure (72) under the influence of the pressure in the second inflatable structure (74).