High-resolution high signal-to-noise spectra of the Li I 6707 angstrom line in the subdwarfs HD 19445 and HD 84937 have been analyzed for the presence of Li-6. By measurement of the Li I lines's wavelength and analysis of its profile, the atmosphere of HD 84937 is shown to have a small amount of Li-6: R = Li-6/Li = 0.05 +/- 0.02. For HD 19445, an upper limit is set of R < 0.02. The presence of Li-6 in HD 84937 is consistent with the mild depletion of Li-6 predicted by standard (nonrotating) models and the initial presence of Li-6 in the halo produced by (principally) alpha-on-alpha fusion reactions involving the cosmic rays that are required to account for the Be and B observed in subdwarfs. Depletion of Li-6 in the lower mass star HD 19445 is expected to remove the initial Li-6 content and, hence. the absence of Li-6 is expected. If Yale models of rotating subdwarfs are adopted, the predicted severe depletion of Li-6 and the observed survival of Li-6 in HD 84937 have to be reconciled. Four suggestions are made: the rotating models are inapplicable to halo dwarfs, production of Li-6 by cosmic rays has been underestimated, the required high initial Li-6 abundance of the halo was produced prior to the formation of the Galaxy, or the Li-6 was produced in stellar flares.