Optical high-resolution spectra of V652 Her and HD 144941, the two extreme helium stars with exceptionally low C/He ratios, have been subjected to a non-LTE abundance analysis using the tools TLUSTY and SYNSPEC. Defining atmospheric parameters were obtained from a grid of non-LTE atmospheres and a variety of spectroscopic indicators including HeI and HeII line profiles, and the ionization equilibrium of ion pairs such as CII/CIII and NII/NIII. The various indicators provide a consistent set of atmospheric parameters: Teff=25000+/-300K, logg=3.10+/-0.12(cgs), and {xi}=13+/-2km/s are provided for V652 Her, and Teff=22000+/-600K, logg=3.45+/-0.15(cgs), and {xi}=10km/s are provided for HD 144941. In contrast to the non-LTE analyses, the LTE analyses-LTE atmospheres and an LTE line analysis-with the available indicators do not provide a consistent set of atmospheric parameters. The principal non-LTE effect on the elemental abundances is on the neon abundance. It is generally considered that these extreme helium stars with their very low C/He ratio result from the merger of two helium white dwarfs. Indeed, the derived composition of V652 Her is in excellent agreement with predictions by Zhang & Jeffery (2012MNRAS.419..452Z), who model the slow merger of helium white dwarfs; a slow merger results in the merged star having the composition of the accreted white dwarf. In the case of HD 144941, which appears to have evolved from metal-poor stars, a slow merger is incompatible with the observed composition but variations of the merger rate may account for the observed composition. More detailed theoretical studies of the merger of a pair of helium white dwarfs are to be encouraged.