  We consider a generic composite Higgs model based on the coset SO(5)/SO(4)
and study its phenomenology beyond the leading low-energy effective lagrangian
approximation. Our basic goal is to introduce in a controllable and simple way
the lowest-lying, possibly narrow, resonances that may exist is such models. We
do so by proposing a criterion that we call partial UV completion. We
characterize the simplest cases, corresponding respectively to a scalar in
either singlet or tensor representation of SO(4) and to vectors in the adjoint
of SO(4). We study the impact of these resonances on the signals associated to
high-energy vector boson scattering, pointing out for each resonance the
characteristic patterns of depletion and enhancement with respect to the
leading-order chiral lagrangian. En route we derive the O(p^4) general chiral
lagrangian and discuss its peculiar accidental and approximate symmetries.
