  In a self-contained way, we deal with revised countable support iterated
forcing for the reals. We improve theorems on preservation of the property UP,
weaker than semi proper, and we hopefully improve the presentation. We continue
[Sh:b, Ch.X,XI] (or see [Sh:f, Ch.X,XI]), and Gitik and Shelah [GiSh:191] and
[Sh:f, Ch.XIII,XIV] and particularly Ch.XV. Concerning ``no new reals'' see
lately Larson and Shelah [LrSh:746] math.LO/0011187. In particular, we fulfill
some promises from [Sh:f] and give a more streamlined version.
