Combined metal-to-metal/compliant material stem sealing means for high pressure, balanced, rising stem gate valve includes at least one seal set at each of the actuator and balance stems. Each seal set comprises a pair of frustoconical metal ring gaskets between which are disposed two make-up rings of compliant, tough material of high lubricity, e.g. tetrafluoroethylene polymer. One make-up ring is adjacent to one gasket, and the other make-up ring is adjacent to the other gasket. A core ring of material that expands substantially less volumetrically upon heating than the make-up rings, e.g. compacted graphite, is disposed between the make-up rings. Around the inner periphery of the core ring adjacent the respective actuator or balance stem is disposed a bearing ring of material like that used for the make-up rings, e.g. tetrafluoroethylene polymer. The seal set is compressed by a packing retainer such that the metal gaskets are coined into metal-to-metal sealing engagement with the stems and adjacent valve body parts. The sandwich stack, consisting of the core ring and bearing ring disposed between the make-up rings, is deformed to conform to the shape of, and fills substantially all of the space between, the compressed metal ring gaskets. The volume of the core ring is approximately one-third of the total volume of the sandwich stack.