Echelle spectroscopy reported in the literature has provided evidence that the element oxygen is heterogeneously distributed within globular clusters. Star-to-star differences in the oxygen abundance have been identified in the clusters M92, M3, and M13 by Pilachowski, Brown et al., Sneden et al., and Kraft et al., and found to be accompanied by an O-N abundance anticorrelation. Such observations indicate that the material within the atmospheres and envelopes of the N-rich or CN-strong giants in these clusters has been processed through the CNO bicycle of hydrogen burning. In this paper it is shown that the occurrence of variable amounts of interior O --> N processing within metal-poor globular-cluster red giants, such as those in M3 and M13, can also reconcile two other of the observed properties of these stars, namely the existence of a CN-C abundance anticorrelation yet substantial [C/Fe] depletions.