  A Weyl invariant extension of Einstein gravity is studied. It simply consists
in the group averaging of Einstein's action under Weyl transformations.
Contradicting cherished beliefs, a conformal anomaly is found in the trace of
the equations of motion if diffeomorphism invariance is to be a symmetry of the
quantum theory. This anomaly however vanishes on shell, which signals the
existence of another gauge in which the anomaly is absent. It can be made also
to vanish off-shell at the price of losing diffeomorphism invariance
