We report the measurement of oxygen and carbon abundances in the halo dwarf HD 103095 from high-resolution, near-infrared spectra of OH and CO lines. We show that spectroscopic analysis based on published Fe I equivalent widths and photometric methods consistently converge at T-eff=5050+/-50 K in conflict with the higher value suggested by King [AJ, 106, 1206 (1993)] as a solution to the halo dwarf oxygen problem. Using a consistent approach which involved deriving solar and stellar abundances from the same grid of model atmospheres, and using the same set of spectral lines to define both the solar and stellar abundance, we obtain [Fe/H]=-1.22+/-0.04, [C/Fe]=-0.32+/-0.05, and [O/Fe]=+0.29+/-0.05, Using the same consistent approach, we rederived oxygen and carbon abundances from published equivalent widths of O I, [O I], and C I. Within the errors, all of the oxygen abundance indicators yield the same oxygen abundance, though there is a suggestion that the high-excitation O I-based abundance is slightly higher. Similarly, the high-excitation C I lines yield a carbon abundance slightly higher than our CO-based value. The [O/C] ratio from molecular indicators is in excellent agreement with that from the high-excitation atomic C I and O I indicators. (C) 1996 American Astronomical Society.