It is shown that, in contrast to recent claims, oxygen (and helium) may not be extraordinarily underabundant in the new galactic halo planetary nebula (GHPN) PN G135.9+55.9 (hereafter PN G135). Determining elemental abundances in hot, highly ionized objects such as PN G135 depends critically on a proper description of the collisional excitation of the hydrogen Balmer lines, the departure from Case B recombination of hydrogen, the underlying stellar absorption lines, the shape of the primary continuum and the ionization equilibrium of highly ionized species of both oxygen and neon. Conversely, PN G135 provides unique checks of atomic data in unusual conditions: the H I collision strengths obtained by Aggarwal et al. (\cite{agg91}) for 1s-n transitions (3 7.2 (>1/30 solar) and values 0.6 dex larger are possible, depending on the assumed C/O abundance ratio. Plausible variations in the geometry of the nebula, the primary stellar continuum and the atomic data do not alter this conclusion. The C/O ratio is less than 10 by number and Ne/O is at most solar. A satisfactory model for PN G135 can be obtained in which elemental abundances are nearly the same as those of a new detailed model for K 648, the prototypical GHPN in the old globular cluster M 15 (with 12 + log(O/H) = 7.58 ˜ 1/13 solar), although C/O may be smaller. Nonetheless, given the paucity of argon and iron in the nebula, PN G135 is likely to be a more extreme Population II object than K 648, reinforcing the idea of an endogenous origin for part of the oxygen in very metal-poor PNe. Assuming a standard H-burning post-Asymptotic Giant Branch evolution, timescale and spectroscopic considerations lead to an optimal solution, in which the distance to PN G135 is 8 kpc, the effective temperature of the nucleus slightly less than 1.3×10⁵ K, its luminosity 1.4×10³⁷ erg s^-1, its mass 0.59 M_&sun; , the age of the ionized shell 10⁴ yrs, the ionized mass 0.05 M_&sun; and the abundances by number (H:He:C:O:Ne) = (10⁶:81 500:90:30:4.5), with C/H being rather an upper limit and O/H and Ne/H uncertain by ±0.3 and ±0.1 dex respectively. Line intensities that could be used as diagnostics of the nebular elemental abundances are provided. Detailed imaging together with ultraviolet and very deep far-red spectra of PN G135 will be essential to definitely narrow the range of acceptable parameters and help us decide whether this exceptional PN is so oxygen-poor as to possibly influence current views on stellar evolution.