  Composite Higgs models can trivially satisfy precision-electroweak and
flavour constraints by simply having a large spontaneous symmetry breaking
scale, f > 10 TeV. This produces a 'split' spectrum, where the strong sector
resonances have masses greater than 10 TeV and are separated from the pseudo
Nambu-Goldstone bosons, which remain near the electroweak scale. Even though a
tuning of order 10^{-4} is required to obtain the observed Higgs boson mass,
the big hierarchy problem remains mostly solved. Intriguingly, models with a
fully-composite right-handed top quark also exhibit improved gauge coupling
unification. By restricting ourselves to models which preserve these features
we find that the symmetry breaking scale cannot be arbitrarily raised, leading
to an upper bound f < 100-1000 TeV. This implies that the resonances may be
accessible at future colliders, or indirectly via rare-decay experiments. Dark
matter is identified with a pseudo Nambu-Goldstone boson, and we show that the
smallest coset space containing a stable, scalar singlet and an unbroken SU(5)
symmetry is SU(7) / SU(6) x U(1). The colour-triplet pseudo Nambu-Goldstone
boson also contained in this coset space is metastable due to a residual
symmetry. It can decay via a displaced vertex when produced at colliders,
leading to a distinctive signal of unnaturalness.
