  We re-examine the effects of Compton scattering on the emergent spectra of
hot DA white dwarfs in the soft X-ray range. Earlier studies have implied that
sensitive X-ray observations at wavelengths $\lambda < 50$ \AA might be capable
of probing the flux deficits predicted by the redistribution of
electron-scattered X-ray photons toward longer wavelengths. We adopt two
independent numerical approaches to the inclusion of Compton scattering in the
computation of pure hydrogen atmospheres in hydrostatic equilibrium. One
employs the Kompaneets diffusion approximation formalism, while the other uses
the cross-sections and redistribution functions of Guilbert. Models and
emergent spectra are computed for stellar parameters representative of HZ 43
and Sirius B, and for models with an effective temperature $T_{\rm eff} = 100
000$ K. The differences between emergent spectra computed for Compton and
Thomson scattering cases are completely negligible in the case of both HZ 43
and Sirius B models, and are also negligible for all practical purposes for
models with temperatures as high as $T_{\rm eff} = 100 000$ K. Models of the
soft X-ray flux from these stars are instead dominated by uncertainties in
their fundamental parameters.
