  Infinite games with imperfect information are known to be undecidable unless
the information flow is severely restricted. One fundamental decidable case
occurs when there is a total ordering among players, such that each player has
access to all the information that the following ones receive.
  In this paper we consider variations of this hierarchy principle for
synchronous games with perfect recall, and identify new decidable classes for
which the distributed synthesis problem is solvable with finite-state
strategies. In particular, we show that decidability is maintained when the
information hierarchy may change along the play, or when transient phases
without hierarchical information are allowed. Finally, we interpret our result
in terms of distributed system architectures.
