  We investigate the amount of fine tuning of the electroweak scale in the
presence of new physics beyond the MSSM, parametrized by higher dimensional
operators. We show that these significantly reduce the MSSM fine tuning to
Delta<10 for a Higgs mass between the LEPII bound and 130 GeV, and a
corresponding scale M_* of new physics as high as 30 to 65 times the Higgsino
mass. If the fine-tuning criterion is indeed of physical relevance, the
findings indicate the presence of new physics in the form of new states of mass
of O(M_*) that generated the effective operators in the first instance. At
small $\tan\beta$ these states can be a gauge singlet or a SU(2) triplet. We
derive analytical results for the EW scale fine-tuning for the MSSM with higher
dimensional operators, including the quantum corrections which are also
applicable to the pure MSSM case in the limit the coefficients of the higher
dimension operators vanish. A general expression for the fine-tuning is also
obtained for an arbitrary two-Higgs doublet potential.
