Recent LTE analyses (Israelian et al. 1998 and Bosegaard et al. 1999) of the OH bands in the optical-ultraviolet spectra of nearby metal-poor subdwarfs indicate that oxygen abundances are generally higher than those previously determined. The difference increases with decreasing metallicity and reaches delta([O/Fe]) ~ +0.6 dex as [Fe/H] approaches -3.0. Employing high resolution (R = 50000), high S/N (~ 250) echelle spectra of the two stars found by Israelian et al. (1998) to have the highest [O/Fe]-ratios, viz, BD +23 3130 and BD +37 1458, we conducted abundance analyses based on about 60 Fe I and 7-9 Fe II lines. We determined from Kurucz LTE models the values of the stellar parameters, as well as abundances of Na, Ni, and the traditional alpha-elements, independent of the calibration of color vs $T_{eff}$ scales. We determined oxygen abundances from spectral synthesis of the stronger line (6300 A) of the [O I] doublet. The syntheses of the [O I] line lead to smaller values of [O/Fe], consistent with those found earlier among halo field and globular cluster giants. We obtain [O/Fe] = +0.35 +/- 0.2 for BD +23 3130 and +0.50 +/- 0.2 for BD +37 1458. In the former, the [O I] line is very weak (~ 1 mA), so that the quoted [O/Fe] value may in reality be an upper limit. Therefore in these two stars a discrepancy exists between the [O/Fe]- ratios derived from [O I] and the OH feature, and the origin of this difference remains unclear. Until the matter is clarified, we suggest it is premature to conclude that the ab initio oxygen abundances of old, metal-poor stars need to be revised drastically upward.