  We introduce a general parametrisation for theories where the Higgs is a
Goldstone boson that encompasses all existing models. Our construction deviates
from extra-dimensional or deconstructed theories through the inclusion of
"non-local" interactions in theory space. These terms are necessary to
reproduce the most general 4D effective lagrangian compatible with the
symmetries. After showing the relation of our formalism to the
Callan-Coleman-Wess-Zumino effective lagrangian we apply our framework to
SO(5)/SO(4) composite Higgs models studying the implications for the Higgs
potential, coupling of resonances and S-parameter. We also outline the
relevance of non-minimal terms in effective descriptions of QCD, studying the
electro-magnetic splitting of pions and the correlation between L_9 and L_10 in
the chiral lagrangian.
