The hydrogen atom yield in pure-H-2 RF and microwave-sustained discharges is investigated both theoretically and experimentally. A particle balance model is developed that provides the concentrations of the H, H-2, H+, H-2+, and H-3+ species. It is also shown that an approximate solution of this model is adequate for calculating the concentration of H atoms (required, for instance, in diamond film deposition) in the 0.1-10 torr range. Next, the validity of the actinometry technique applied to the determination of the H-atom density in pure-H-2 discharges is examined Using this diagnostic, it is observed that the H-atom concentration decreases when the vessel wall temperature increases, owing to the increased efficiency of atomic hydrogen recombination on the wall. To overcome this effect, the discharge tube wall is cooled off with dimethylpolysiloxane, a low-loss dielectric liquid. It improves significantly the H-atom concentration at 2450 MHz provided the pressure is typically below a few torr and the power density is not too high.