  We determine the degree of fine-tuning needed in a generalised version of the
NMSSM that follows from an underlying Z4 or Z8 R-symmetry. We find that it is
significantly less than is found in the MSSM or NMSSM and extends the range of
Higgs mass that have acceptable fine-tuning. Remarkably the minimal fine-tuning
is achieved for Higgs masses of around 130 GeV.
