  We study a new confining gauge theory with fermions in a vectorial
representation under the SM gauge group that allows for Yukawa interactions
with the Higgs. If the fermion masses are smaller than the confinement scale
this realizes a type I two Higgs doublet model where a composite Higgs mixes
with the elementary Higgs. This class of models interpolates between an
elementary and a composite Higgs and has interesting phenomenology with
potentially observables effects in collider physics, EDMs and SM couplings but
very weak bounds from indirect searches. The very same framework can be used to
realize the cosmological relaxation of the electro-weak scale recently
discussed in the literature.
