Spectra for stars located redward of the fiducial red giant branches of the Ursa Minor and Draco dwarf spheroidal galaxies have been obtained with the Hobby-Eberly telescope and the Marcario Low Resolution Spectrometer . From a comparison of our radial velocities with those reported in previous medium-resolution studies , we find an average difference of 10 km s ^ { -1 } with a standard deviation of 11 km s ^ { -1 } . On the basis of these radial velocities , we confirm the membership of five stars in Ursa Minor , and find two others to be nonmembers . One of the confirmed members is a known carbon star which lies redward of RGB ; three others are previously unidentified carbon stars . The fifth star is a red giant which was found previously by Shetrone et al . ( 2001 ) to have [ Fe/H ] = -1.68 \pm 0.11 dex . In Draco , we find eight nonmembers , confirm the membership of one known carbon star , and find two new members . One of these stars is a carbon star , while the other shows no evidence for C _ { 2 } bands or strong atomic bands , although the signal-to-noise ratio of the spectrum is low . Thus , we find no evidence for a population of stars more metal-rich than [ Fe/H ] \simeq - 1.45 dex in either of these galaxies . Indeed , our spectroscopic survey suggests that every candidate suspected of having a metallicity in excess of this value based on its position in the color-magnitude diagram is , in actuality , a carbon star . Based on the census of 13 known carbon stars in these two galaxies , we estimate of the carbon star specific frequency to be \epsilon _ { dSph } \simeq 2.4 \times 10 ^ { -5 } L _ { V, { \odot } } ^ { -1 } , 25-100 times higher than that of Galactic globular clusters .