  In the minimal composite Higgs model (MCHM), the size of the Higgs mass and
vacuum expectation value is determined, via the Higgs potential, by the size of
operators that violate the global SO(5) symmetry. In 5D holographic
realisations of this model, this translates into the inclusion of brane
localised operators. However, the inclusion of all such operators results in a
large and under-constrained parameter space. In this paper we study the level
of fine-tuning involved in such a parameter space, focusing on the MCHM${}_5$.
It is demonstrated that the gauge contribution to the Higgs potential can be
suppressed by brane localised kinetic terms, but this is correlated with an
enhancement to the S parameter. The fermion contribution, on the other hand,
can be enhanced or suppressed. However this does not significantly improve the
level of fine tunings, since the Higgs squared term, in the potential, requires
a cancellation between the fermion and gauge contributions. Although we focus
on the MCHM${}_5$, the fermion holographic Lagrangian - including all possible
brane localised mass and kinetic terms - is derived in the appendix and will
have applications to a wider range of composite Higgs models.
