The strengths of the CN, NH, and CH bands in the spectra of Population II r
ed giants are discussed based on observations of a sample of both globular
cluster and field giants. We confirm an anticorrelation between the oxygen
abundance and the CN indices and a correlation between the 3883 Angstrom CN
band and the 3360 Angstrom NH band strengths among giants in the globular
clusters M15 and M13. We find one M15 star (IV-38) with a strong 3883 Angst
rom CN band and detectable 4215 Angstrom CN and 3360 Angstrom NH bands. Abu
ndance analysis of M15 IV-38 reveals a comparable carbon abundance to a com
parison star that has much weaker CN bands. One possible reason for this ma
y be that IV-38 is an insipid CH star that has also undergone some deep mix
ing. Alternatively, the atmosphere of IV-38 may have been extensively proce
ssed through the O --> N cycle of hydrogen burning such that carbon has bee
n affected by O --> C conversion. By combining our data set with material f
rom the literature and high-quality B-V photometry, we find that the CN ban
d strength differences among the M5 red giants do not appear to broaden the
giant branch of that cluster within the photometric errors. Using the CN,
CH, and NH bands, we are able to confirm that the metal-poor field giant HD
135148 is a CH-strong star and has not undergone deep mixing.