Very metal-deficient stars that exhibit enhancements of their carbon abundances are of crucial importance for understanding a number of issues – the nature of stellar evolution among the first generations of stars , the shape of the Initial Mass Function , and the relationship between carbon enhancement and neutron-capture processes , in particular the astrophysical s-process . One recent discovery from objective-prism surveys dedicated to the discovery of metal-deficient stars is that the frequency of Carbon-Enhanced Metal-Poor ( CEMP ) stars increases with declining metallicity , reaching roughly 25 % for [ Fe/H ] < -2.5 . In order to explore this phenomenon in greater detail we have obtained medium-resolution ( 2 Å ) spectroscopy for about 350 of the 413 objects in the Christlieb et al . catalog of carbon-rich stars , selected from the Hamburg/ESO objective prism survey on the basis of their carbon-enhancement , rather than metal deficiency . Based on these spectra , and near-IR JHK photometry from the 2MASS Point Source Catalog , we obtain estimates of [ Fe/H ] and [ C/Fe ] for most of the stars in this sample , along with reasonably accurate determinations of their radial velocities . Of particular importance , we find that the upper envelope of carbon enhancement observed for these stars is nearly constant , at [ C/H ] \sim - 1.0 , over the metallicity range -4.0 < [ Fe/H ] < -2.0 ; this same level of [ C/H ] applies to the most iron-deficent star yet discovered , HE 0107-5240 , at [ Fe/H ] = -5.3 .