Measurements of [ C/Fe ] , [ Ca/H ] , and [ Fe/H ] have been derived from Keck I LRISb spectra of 35 giants in the Draco dwarf spheroidal galaxy . The iron abundances are derived by a spectrum synthesis modeling of the wavelength region from 4850 to 5375 Å , while calcium and carbon abundances are obtained by fitting the Ca ii H and K lines and the CH G band respectively . A range in metallicity of -2.9 \leq { [ Fe / H ] } \leq - 1.6 is found within the giants sampled , with a good correlation between [ Fe/H ] and [ Ca/H ] . The great majority of stars in the sample would be classified as having weak absorption in the \lambda 3883 CN band , with only a small scatter in band strengths at a given luminosity on the red giant branch . In this sense the behavior of CN among the Draco giants is consistent with the predominantly weak CN bands found among red giants in globular clusters of metallicity { [ Fe / H ] } < -1.8 . Over half of the giants in the Draco sample have { [ Fe / H ] } > -2.25 , and among these there is a trend for the [ C/Fe ] abundance to decrease with increasing luminosity on the red giant branch . This is a phenomenon that is also seen among both field and globular cluster giants of the Galactic halo , where it has been interpreted as a consequence of deep mixing of material between the base of the convective envelope and the outer limits of the hydrogen-burning shell . However , among the six Draco giants observed that turn out to have metallicities -2.65 < { [ Fe / H ] } < -2.25 there is no such trend seen in the carbon abundance . This may be due to small sample statistics or primordial inhomogeneities in carbon abundance among the most metal-poor Draco stars . We identify a potential carbon-rich extremely metal-poor star in our sample . This candidate will require follow up observations for confirmation .