High-resolution spectra of the 2 μ first-overtone CO bands in the weak G-band giants HR 6766 and 37 Com have been obtained. Synthetic spectra have been computed to obtain carbon abundances and carbon isotope ratios. There is excellent agreement between the carbon abundances derived from these CO data and those determined using features of the CH G-band. Therefore no large enrichment of helium in these stellar envelopes is likely. The 13CO features in 37 Com are strong; a carbon isotope ratio as low as 2 is indicated for this star.