  We propose a new class of models called Little Z' models in order to reduce
the fine-tuning due to the current experimental limits on the Z' mass in E_6
inspired supersymmetric models, where the Higgs doublets are charged under the
extra U(1)' gauge group. The proposed Little Z' models allow a lower mass Z'
due to the spontaneously broken extra U(1)' gauge group having a reduced gauge
coupling. We show that reducing the value of the extra gauge coupling relaxes
the experimental limits, leading to the possibility of low mass Z' resonances,
for example down to 200 GeV, which may yet appear in LHC searches. Although the
source of tree level fine-tuning due to the Z' mass is reduced in Little Z'
models, it typically does so at the expense of increasing the vacuum
expectation value of the U(1)'-breaking standard model singlet field, reducing
the fine-tuning to similar levels to that in the Minimal Supersymmetric
Standard Model.
