With the discovery of a 125 GeV Standard Model (SM) like Higgs boson and rising lower bounds on the masses of superpartners, minimal models of low energy supersymmetry (SUSY) appear to be increasingly fine tuned. In the Minimal Supersymmetric Standard Model (MSSM) large stop masses, needed to obtain the observed Higgs mass, give a significant contribution to fine tuning. U(1) extensions of the MSSM that solve the mu-problem have new F- and D-term contributions to the Higgs mass, allowing a 125 GeV Higgs with lighter stops and so alleviating the associated fine tuning. However, it was recently demonstrated, within a constrained version of the Exceptional Supersymmetric Standard Model (E(6)SSM) defined at the Grand Unification (GUT) scale, that the presence of a massive Z' boson introduces a substantial new source of tuning in these theories at tree level. Here we consider the impact of this tuning when we remove the fine tuning that depends on assumptions about the SUSY breaking scale, by setting the SUSY breaking parameters at low energies. We find that the existing experimental bounds on the Z' mass impose an effective lower bound on the fine tuning, which does not depend on assumptions about SUSY breaking. We compare our results against the tuning in the phenomenological MSSM (pMSSM), where the SUSY breaking terms are also defined at low energies.