  We study dynamic screening problems where elements are subjected to noisy
evaluations and, in every stage, some of the elements are rejected while the
remaining ones are independently re-evaluated in subsequent stages. We prove
that, ceteris paribus, the quality of a dynamic screening process is not
monotonic in the number of stages. Specifically, we examine the accepted
elements' values and show that adding a single stage to a screening process may
produce inferior results, in terms of stochastic dominance, whereas increasing
the number of stages substantially leads to a first-best outcome.
