  We study the nonstationary-support iteration of Prikry forcings below a
measurable cardinal \kappa, characterizing all the normal measures it carries
in the generic extension. We then analyze the restriction of ultrapower
embeddings, taken with such a normal measure in the generic extension, to the
ground model. We prove that every such restriction is an iterated ultrapwer of
the ground model, and provide a sufficient condition for its definability
there. This is done without core-model theoretic arguments: the assumption that
GCH holds in the ground model up to \kappa suffices.
