  We show how the necessary constraints to project out all the components of a
chiral superfield except for some scalar degrees of freedom originate from
simple operators in the microscopic theory. This is in particular useful in
constructing the simplest models of a goldstone boson/inflaton; or extracting
the Standard Model Higgs doublet from a supersymmetric electroweak sector. We
use the Fayet-Iliopoulos model as an example of the origin for the
supersymmetry breaking. We consider the regime where both gauge symmetry and
supersymmetry are spontaneously broken, leaving (in the decoupling limit) the
goldstino as the only light mode in this sector. We show in three different
ways, both in components and in superspace language, how the nilpotent
goldstino superfield emerges. We then use it to write different effective
operators and extract some of the consequences for the low energy spectrum.
