Abstract: A pressure control device can include a housing assembly, a releasable assembly releasably secured relative to the housing assembly, the releasable assembly being configured to seal against a tubular string extending through the pressure control device, and an annular seal assembly that prevents flow through an annular gap formed radially between the housing assembly and the releasable assembly, the annular seal assembly comprising a resilient seal element bonded to a rigid support element. A method of securing a releasable assembly in a housing assembly of a pressure control device can include attaching an annular seal assembly to the releasable assembly, the annular seal assembly comprising a rigid support element bonded to a resilient seal element, and receiving the releasable assembly at least partially in the housing assembly, thereby sealingly engaging the resilient seal element with a seal bore in the housing assembly.