In scale-invariant theories of gravity the Planck mass M-p, which appears due to spontaneous symmetry breaking, can be the only scale at the classical level. It was argued that the second scale can be generated by a quantum nonperturbative gravitational effect. The new scale, associated with the Higgs vacuum expectation value, can be orders of magnitude below M-P, leading to the hierarchy between the Fermi and the Planck scales. We study a theory in which the nonperturbative effect is sensitive both to the physics at energy scales as high as M-p and to the low-energy, Standard Model physics. This makes it possible to constrain the mechanism from experiment. We find that the crucial ingredients of the mechanism are non minimal coupling of the scalar fields to gravity, the approximate Weyl invariance at high energies, and the metastability of the low-energy vacuum.