We present a cautionary study exploring the reliability of the H-delta line in the integrated spectra of galaxies for determining galaxy ages. Our database consists of the observed integrated spectra of ~120 early-type galaxies, of 7 metal-rich globular clusters in M31 and the Galactic globular cluster 47 Tuc, and of the open cluster M67. We have measured H-delta using index definitions designed to assess contamination from the CN molecule in and around H-delta by choosing combinations of bandpasses that both avoid and include a region of CN molecular lines redward of H-delta. We find systematic differences in the ages derived from H-delta measurements among the various definitions when extracting ages from H-delta in old stellar populations with enhanced CN bands due to non-solar abundance ratios. We propose that neighboring CN lines have a strong effect on pseudocontinuum and central bandpass levels. For stellar populations which have non-solar abundance ratios in C and/or N, population synthesis models that do not account for abundance ratio variations cannot reproduce accurately the CN 4216 AA band, which leads to a corresponding inaccuracy in reproducing the various H-delta indices. Hence, caution must be used when extracting galaxy ages from the H-delta line in old stellar populations with significant non-solar abundance ratios.