  Models that seek to produce a line at ~130 GeV as possibly present in the
Fermi data face a number of phenomenological hurdles, not the least of which is
achieving the high cross section into gamma gamma required. A simple
explanation is a fermionic dark matter particle that couples to photons through
loops of charged messengers. We study the size of the dimension 5 dipole (for a
pseudo-Dirac state) and dimension 7 Rayleigh operators in such a model,
including all higher order corrections in 1/M_{mess}. Such corrections tend to
enhance the annihilation rates beyond the naive effective operators. We find
that while freezeout is generally dominated by the dipole, the present day
gamma-ray signatures are dominated by the Rayleigh operator, except at the most
strongly coupled points, motivating a hybrid approach. With this, the Magnetic
inelastic Dark Matter scenario provides a successful explanation of the lines
at only moderately strong coupling. We also consider the pure Majorana WIMP,
where both freezeout and the Fermi lines can be explained, but only at very
strong coupling with light (~200 - 300 GeV) messengers. In both cases there is
no conflict with non-observation of continuum photons.
