  An excess of gamma rays at GeV energies has been detected in the Fermi-LAT
data. This signal comes from a narrow region around the Galactic Center and has
been interpreted as possible evidence for light (30 GeV) dark matter particles.
Focussing on the prompt gamma-ray emission, previous works found that the best
fit to the data corresponds to annihilations proceeding into b quarks, with a
dark matter profile going as r^{-1.2}. We show that this is not the only
possible annihilation set-up. More specifically, we show how including the
contributions to the gamma-ray spectrum from inverse Compton scattering and
bremsstrahlung from electrons produced in dark matter annihilations, and
undergoing diffusion through the Galactic magnetic field, significantly affects
the spectrum for leptonic final states. This drastically changes the
interpretation of the excess in terms of dark matter.
