  In the theory of General Relativity, gravity is described by a metric which
couples minimally to the fields representing matter. We consider here its
"veiled" versions where the metric is conformally related to the original one
and hence is no longer minimally coupled to the matter variables. We show on
simple examples that observational predictions are nonetheless exactly the same
as in General Relativity, with the interpretation of this "Weyl" rescaling "\`a
la Dicke", that is, as a spacetime dependence of the inertial mass of the
matter constituents.
