  Based on an explicit model, we propose and discuss the generic features of a
possible implementation of the Twin Higgs program in the context of composite
Higgs models. We find that the Twin Higgs quadratic divergence cancellation
argument can be uplifted to a genuine protection of the Higgs potential, based
on symmetries and selection rules, but only under certain conditions which are
not fulfilled in some of the existing models. We also find that a viable
scenario, not plagued by a massless Twin Photon, can be obtained by not gauging
the Twin Hypercharge and taking this as the only source of Twin Symmetry
breaking at a very high scale.
