  The Gap Forcing Theorem, a key contribution of this paper, implies
essentially that after any reverse Easton iteration of closed forcing, such as
the Laver preparation, every supercompactness measure on a supercompact
cardinal extends a measure from the ground model. Thus, such forcing can create
no new supercompact cardinals, and, if the GCH holds, neither can it increase
the degree of supercompactness of any cardinal; in particular, it can create no
new measurable cardinals. In a crescendo of what I call exact preservation
theorems, I use this new technology to perform a kind of partial Laver
preparation, and thereby finely control the class of posets which preserve a
supercompact cardinal. Eventually, I prove the `As You Like It' Theorem, which
asserts that the class of ${<}\kappa$-directed closed posets which preserve a
supercompact cardinal $\kappa$ can be made by forcing to conform with any
pre-selected local definition which respects the equivalence of forcing. Along
the way I separate completely the levels of the superdestructibility hierarchy,
and, in an epilogue, prove that the notions of fragility and
superdestructibility are orthogonal---all four combinations are possible.
