  The cosmological relaxation mechanism proposed in [1] allows for a
dynamically generated large separation between the weak scale and a theory
cutoff, using a sharp change of theory behaviour upon crossing the limit
between unbroken and broken symmetry phases. In this note we present a
variation of this scenario, in which stabilization of the electroweak scale in
the right place is ensured by the $Z_2$ symmetry exchanging the Standard Model
(SM) with its mirror copy. We sketch the possible ways to produce viable
thermal evolution of the Universe and discuss experimental accessibility of the
new physics effects. We show that in this scenario the mirror SM can either
have sizeable couplings with the ordinary one, or, conversely, can interact
with it with a negligible strength. The overall cutoff allowed by such a
construction can reach $10^9$ GeV.
