A gas turbine nozzle segment has outer and inner band portions. Each band portion includes a nozzle wall, a cover and an impingement plate between the cover and nozzle wall defining two cavities on opposite sides of the impingement plate. Cooling steam is supplied to one cavity for flow through the apertures of the impingement plate to cool the nozzle wall. Structural pedestals interconnect the cover and nozzle wall and pass through holes in the impingement plate to reduce localized stress otherwise resulting from a difference in pressure within the chamber of the nozzle segment and the hot gas path and the fixed turbine casing surrounding the nozzle stage. The pedestals may be cast or welded to the cover and nozzle wall.