  We prove that a large class of presaturated ideals at inaccessible cardinals
can be de-saturated while preserving their presaturation, answering both a
question of Foreman and of Cox and Eskew. We do so by iterating a generalized
version of Baumgartner and Taylor's forcing to add a club with finite
conditions along an inaccessible cardinal, and invoking Foreman's Duality
Theorem.
