  Supersymmetric unified models in which the Z' couples to the Higgs doublets,
as in the E6 class of models, have large fine tuning dominated by the
experimental mass limit on the Z'. To illustrate this we investigate the degree
of fine tuning throughout the parameter space of the Constrained Exceptional
Supersymmetric Standard Model (cE6SSM) that is consistent with a Higgs mass m_h
~ 125 GeV. Fixing tan beta = 10, and taking specific values of the mass of the
Z' boson, with M_Z' ~ 2-4 TeV. We find that the minimum fine tuning is set
predominantly from the mass of Z' and varies from ~ 200-400 as we vary M_Z'
from ~ 2-4 TeV. However, this is significantly lower than the fine tuning in
the Constrained Minimal Supersymmetric Standard Model (cMSSM), of O(1000),
arising from the large stop masses required to achieve the Higgs mass.
