adding (subtracting) the FWHM to (from) the [\[C/Fe\]]{} value found at the minimum of the declining $\chi^{2}$, we conservatively define the value as the upper (lower) limit of the measured [\[C/Fe\]]{}, depending at which edge of the grid the minimum is found. Accordingly, we raise an ‘L’ flag for a lower limit and a ‘U’ flag for an upper limit. In this way, we can ensure to have a clear measurement of the upper or lower limit on \[C/Fe\], rather than a spurious estimate of \[C/Fe\] that can occur in the very low-metallicity (and/or high [$T_{\rm eff}$]{}) regime, due to the weakness of the CH $G$-band.

It is worth mentioning that the [\[C/Fe\]]{} values determined by this approach agree well with the estimates from the $\chi^{2}$ minimization technique. We find in most cases small mean offsets ($< 0.05$ dex) and scatter ($< 0.1$ dex) between the two approaches.

Figure \[fig:example\] provides two examples of clear detections of the CH $G$-band by our spectral fitting method. The left panel is a cool, VMP, moderately carbon-enhanced giant (\[C/Fe\] $= +0.69$), while the right panel shows a warm, VMP, highly carbon-enhanced turnoff star (\[C/Fe\] $= +2.94$). The black line is the observed spectrum; 