  We propose a type of non-anticommutative superspace, with the interesting
property of relating to Lee-Wick type of higher derivatives theories, which are
known for their interesting properties, and have lead to proposals of
phenomenologicaly viable higher derivatives extensions of the Standard Model.
The deformation of superspace we consider does not preserve supersymmetry or
associativity in general; however, we show that a non-anticommutative version
of the Wess-Zumino model can be properly defined. In fact, the definition of
chiral and antichiral superfields turns out to be simpler in our case than in
the well known ${\cal N}=1/2$ supersymmetric case. We show that, when the
theory is truncated at the first nontrivial order in the deformation parameter,
supersymmetry is restored, and we end up with a well known Lee-Wick type of
higher derivative extension of the Wess-Zumino model. Thus we show how
non-anticommutative could provide an alternative mechanism for generation of
these kind of higher derivative theories.
