  We analyze the recent NA48 data for the reaction K_L -> pi0 gamma gamma with
and without the assumption of vector meson dominance (VMD). We find that the
data is well described by a three-parameter expression inspired by O(p^6)
chiral perturbation theory. We also find that it is impossible to fit the shape
of the decay distribution and the overall rate simultaneously if one imposes
the VMD constraints on the three parameters. We comment on the different fits
and their implications for the CP-conserving component of the decay K_L -> pi0
e+ e-.
