We explore the nature of carbon-rich ([C/Fe]_{1D,LTE} > +0.7), metal-poor ([Fe/H_{1D,LTE}] < -2.0) stars in the light of post 1D,LTE literature analyses, which provide 3D-1D and NLTE-LTE corrections for iron, and 3D-1D corrections for carbon (from the CH G-band, the only indicator at lowest [Fe/H]). High-excitation C~I lines are used to constrain 3D,NLTE corrections of G-band analyses. Corrections to the 1D,LTE compilations of Yoon et al. and Yong et al. yield 3D,LTE and 3D,NLTE Fe and C abundances. The number of CEMP-no stars in the Yoon et al. compilation (plus eight others) decreases from 130 (1D,LTE) to 68 (3D,LTE) and 35 (3D,NLTE). For stars with -4.5 < [Fe/H] < -3.0 in the compilation of Yong et al., the corresponding CEMP-no fractions change from 0.30 to 0.15 and 0.12, respectively. We present a toy model of the coalescence of pre-stellar clouds of the two populations that followed chemical enrichment by the first zero-heavy-element stars: the C-rich, hyper-metal-poor and the C-normal, very-metal-poor populations. The model provides a reasonable first-order explanation of the distribution of the 1D,LTE abundances of CEMP-no stars in the A(C) and [C/Fe] vs. [Fe/H] planes, in the range -4.0 < [Fe/H] < -2.0. The Yoon et al. CEMP Group I contains a subset of 19 CEMP-no stars (14% of the group), 4/9 of which are binary, and which have large [Sr/Ba]_{1D,LTE} values. The data support the conjectures of Hansen et al. (2016b, 2019) and Arentsen et al. (2018) that these stars may have experienced enrichment from AGB stars and/or spinstars.
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