  We continue our investigations of cavity QED with time dependent parameters.
In this paper we discuss the situation where the state of the atoms leaving the
cavity is reduced but the outcome is not recorded. In this case our knowledge
is limited to an ensemble description of the results only. By applying the
Demkov-Kunike level-crossing model, we show that even in this case, the
filtering action of the interaction allows us to prepare a preassigned Fock
state with good accuracy. The possibilities and limitations of the method are
discussed and some relations to earlier work are presented.
