A cooled component wall (52) with a combustion gas (36) on one side (56) and a coolant gas (48) with higher pressure on the other side (58). The wall includes a cooling chamber (60) with an impingement cooling zone (62), a convective cooling zone (64), and a film cooling zone (66). Impingement holes (70) admit and direct jets (72) of coolant against the wall, thence the coolant passes among heat transfer elements such as channels (76) and fins (78) to the film cooling zone (66) where it passes through holes in the wall that direct a film of the coolant along the combustion side of the wall. The chamber may be oriented with the impingement zone (62) downstream and the film cooling zone (66) upstream, relative to the combustion gas flow (36). This provides two passes of the coolant (84, 79) in opposite directions over the respective opposite sides of the wall (56, 58).