  We study a Dirac Dark Matter particle interacting with ordinary matter via
the exchange of a light pseudo-scalar, and analyze its impact on both direct
and indirect detection experiments. We show that this candidate can accommodate
the long-standing DAMA modulated signal and yet be compatible with all
exclusion limits at $99_S$ % CL. This result holds for natural choices of the
pseudo-scalar-quark couplings (e.g.~flavor-universal), which give rise to a
significant enhancement of the Dark Matter-proton coupling with respect to the
coupling to neutrons. We also find that this candidate can accommodate the
observed 1-3 GeV gamma-ray excess at the Galactic Center and at the same time
have the correct relic density today. The model could be tested with
measurements of rare meson decays, flavor changing processes, and searches for
axion-like particles with mass in the MeV range.
