  A general analysis is performed on the dimension-six operators mixing an
almost hidden Z' to the Standard Model (SM), when the Z' communicates with the
SM via heavy mediators. These are fermions charged under both Z' and the SM,
while all SM fermions are neutral under Z'. We classify the operators as a
function of the gauge anomalies behaviour of mediators and explicitly compute
the dimension-six operators coupling Z' to gluons, generated at one-loop by
chiral but anomaly-free, sets of fermion mediators. We prove that only one
operator contribute to the couplings between Z' charged matter and on-shell
gluons. We then make a complete phenomenological analysis of the scenario where
the lightest fermion charged under Z' is the dark matter candidate. Combining
results from WMAP/PLANCK data, mono-jet searches at LHC, and direct/indirect
dark matter detections restrict considerably the allowed parameter space.
