A deployable inflator that includes a quantity of gas generant. The generant is designed to produce a supply of inflation gas during deployment of the inflator. The inflator includes a first burst disk and a second burst disk. The first and second burst disks are separated by a cavity. The inflator also includes an opening (or multiple openings). During deployment, the inflation gas flows into the cavity via the opening(s) and ruptures the first burst disk to allow inflation gas to escape the inflator. The second burst disk ruptures after the pressure in the cavity drops sufficiently below the pressure on the other side of the second burst disk. This inflator reduces the initial onset rate of deployment.