We examine the metallicity distribution function (MDF) and fraction of carbon-enhanced metal-poor (CEMP) stars in a sample that includes 86 stars with [Fe/H]<=-3.0, based on high-resolution, high signal-to-noise spectroscopy, of which some 32 objects lie below [Fe/H]=-3.5. After accounting for the completeness function, the "corrected" MDF does not exhibit the sudden drop at [Fe/H]=-3.6 that was found in recent samples of dwarfs and giants from the Hamburg/ESO survey. Rather, the MDF decreases smoothly down to [Fe/H]=-4.1. Similar results are obtained from the "raw" MDF. We find that the fraction of CEMP objects below [Fe/H]=-3.0 is 23%+/-6% and 32%+/-8% when adopting the Beers & Christlieb (2005ARA&A..43..531B) and Aoki et al. (2007, J/ApJ/655/492) CEMP definitions, respectively. The former value is in fair agreement with some previous measurements, which adopt the Beers & Christlieb criterion.