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Detailed study of high resolution, high signal-to-noise chromospheric Fe II emission line profiles, obtained with the Goddard High Resolution Spectrograph on the Hubble Space Telescope, provides an opportunity to probe the flow velocities in the outer atmospheres/winds of cool, low-gravity stars. We have previously reported seeing the acceleration of the outflowing wind in such data from several M-giant stars, including $\gamma$~Cru (M3.4~III), $\mu$~Gem (M3~IIIab), and $\alpha$~Tau (K5~III). Early attempts to do the same with the M-supergiant $\alpha$~Ori (M2~Iab) met with limited success, due to the high-opacity of its outer atmosphere and the significant differences in the character and behavior of the observed line profiles in the supergiant spectrum. Further analysis of the GHRS observations of Fe~II lines in $\alpha$~Ori has now enabled us to detect the accelerating outflow in it's wind as well. A detailed comparison of the observed Fe~II profiles and the flows inferred from those profiles, with those for the less-luminous, but similar T$_{eff}$ M-giant $\gamma$~Cru are presented.
