  In this article, we consider iteration principles for contraction, with the
goal of identifying properties for contractions that respect conditional
beliefs. Therefore, we investigate and evaluate four groups of iteration
principles for contraction which consider the dynamics of conditional beliefs.
For all these principles, we provide semantic characterization theorems and
provide formulations by postulates which highlight how the change of beliefs
and of conditional beliefs is constrained, whenever that is possible. The first
group is similar to the syntactic Darwiche-Pearl postulates. As a second group,
we consider semantic postulates for iteration of contraction by Chopra, Ghose,
Meyer and Wong, and by Konieczny and Pino P\'erez, respectively, and we provide
novel syntactic counterparts. Third, we propose a contraction analogue of the
independence condition by Jin and Thielscher. For the fourth group, we consider
natural and moderate contraction by Nayak. Methodically, we make use of
conditionals for contractions, so-called contractionals and furthermore, we
propose and employ the novel notion of $ \alpha $-equivalence for formulating
some of the new postulates.
