I explore the possibility that the [O(I)] lambda-6300 absorption lines are abnormally weak in the spectra of some bright globular-cluster giants (like M 13 II67) because they are "filled in" by [O(I)] emission from an extensive, cool, slowly expanding outer envelope. The results are promising. A very simple one-zone model shows that an H I region with a radius of about 30 AU can provide the supposed emission. The model leads to a mass-loss rate about five times larger than the Reimers 1975 formula predicts and suggests why the average observed value of [O/Fe] drops near the tip of the giant branch. Absorption in the putative expanding atmosphere qualitatively accounts for the blueshifted Na D line cores that have been observed in the spectra of M 13 II67 and some other bright cluster giants.