  We present new high-resolution chemical-abundance analyses for the well-known
high proper-motion subdwarfs G64-12 and G64-37, based on very high
signal-to-noise spectra (S/N ~ 700/1) with resolving power R ~ 95,000. These
high-quality data enable the first reliable determination of the carbon
abundances for these two stars; we classify them as carbon-enhanced metal-poor
(CEMP) stars based on their carbonicities, which both exceed [C/Fe] = +1.0.
They are sub-classified as CEMP- no Group-II stars, based on their location in
the Yoon-Beers diagram of absolute carbon abundance, A(C) vs. [Fe/H], as well
as on the conventional diagnostic [Ba/Fe]. The relatively low absolute carbon
abundances of CEMP-no stars, in combination with the high effective
temperatures of these two stars (Teff ~ 6500 K) weakens their CH molecular
features to the point that accurate carbon abundances can only be estimated
from spectra with very high S/N. A comparison of the observed abundance
patterns with the predicted yields from massive, metal-free supernova models
reduces the inferred progenitor masses by factors of ~ 2-3, and explosion
energies by factors of ~ 10-15, compared to those derived using previously
claimed carbon abundance estimates. There are certainly many more warm CEMP-no
stars near the halo main-sequence turnoff that have been overlooked in past
studies, directly impacting the derived frequencies of CEMP-no stars as a
function of metallicity, a probe that provides important constraints on
Galactic chemical evolution models, the initial mass function in the early
Universe, and first-star nucleosynthesis.
