  We introduce the notion of effective Axiom A and use it to show that some
popular tree forcings are Suslin+. We introduce transitive nep and present a
simplified version of Shelah's "preserving a little implies preserving much":
If I is a Suslin ccc ideal (e.g. Lebesgue-null or meager) and P is a transitive
nep forcing (e.g. P is Suslin+) and P doesn't make any I-positive Borel set
small, then P doesn't make any I-positive set small.
