  Hydrostatic models of Wolf-Rayet stars typically contain low-density outer
envelopes that inflate the stellar radii by a factor of several and are capped
by a denser shell of gas. Inflated envelopes and density inversions are
hallmarks of envelopes that become super-Eddington as they cross the iron-group
opacity peak, but these features disappear when mass loss is sufficiently
rapid. We re-examine the structures of steady, spherically symmetric wind
solutions that cross a sonic point at high optical depth, identifying the
physical mechanism by which outflow affects the stellar structure, and provide
an improved analytical estimate for the critical mass loss rate above which
extended structures are erased. Weak-flow solutions below this limit resemble
hydrostatic stars even in supersonic zones; however, we infer that these fail
to successfully launch optically thick winds. Wolf-Rayet envelopes will
therefore likely correspond to the strong, compact solutions. We also find that
wind solutions with negligible gas pressure are stably stratified at and below
the sonic point. This implies that convection is not the source of variability
in Wolf-Rayet stars, as has been suggested; but, acoustic instabilities provide
an alternative explanation. Our solutions are limited to high optical depths by
our neglect of Doppler enhancements to the opacity, and do not account for
acoustic instabilities at high Eddington factors; yet they provide useful
insights into Wolf-Rayet stellar structures.
