  I consider models in which non-standard supersymmetry breaking terms,
including Dirac gaugino masses, arise from F-term breaking mediated by
operators with a $1/M^3$ suppression. In these models, the supersoft properties
found in the case of D-term breaking are absent in general, but can be obtained
as a special case that is a fixed point of the renormalization group equations.
The $\mu$ term is replaced by three distinct supersymmetry-breaking parameters,
decoupling the Higgs scalar potential from the Higgsino masses. Both
holomorphic and non-holomorphic scalar cubic interactions with minimal flavor
violation are induced in the supersymmetric Standard Model Lagrangian.
