  The Higgs spectrum of the minimal composite Higgs model, based on the
SO(5)/SO(4) coset, consists of a unique Higgs doublet whose phenomenology does
not differ greatly from the Standard Model (SM). Nevertheless, extensions
beyond this minimal coset structure exhibit a richer Higgs spectrum and
therefore very different Higgs physics. We explore one of these extensions, the
SO(6)/SO(5) model, whose Higgs spectrum contains a CP-odd singlet scalar, eta,
in addition to the Higgs doublet. Due to the pseudo-Nambu-Goldstone nature of
these Higgs bosons, their physical properties can be derived from symmetry
considerations alone. We find that the mass of eta can be naturally light,
opening up the possibility that the SM Higgs decays predominantly to the
singlet, and therefore lowering the LEP bound on its mass to 86 GeV. We also
show that eta can have interesting consequences in flavour-violating processes,
as well as induce spontaneous CP-violation in the Higgs sector. The model can
also have anomalies, giving rise to interactions between the SM gauge bosons
and eta which, if measured at the LHC, would give quantitative information
about the structure of the high energy theory.
