  Evolution of purity in case of factorizable interaction between an open
system and an environment is investigated. We derive a simple expression for
purity decrease at the first instants of evolution (when purity is close to
unity). We find that purity at very small times is maximal when an initial
state of an open system coincides with one of the eigenstates of the
interaction operator, no matter how weak the interaction is. On the other hand
it is widely known that in general eigenstates of the interaction are not
pointer states. Therefore the procedure of selecting pointer states by purity
maximization (known as "purity sieve") should not rely on short-time purity
behavior. We propose a modification of the purity sieve criterion which
approximately takes into account purity evolution at longer times. As an
example of its applicability we recover known results for pointer states of a
particle undergoing quantum Brownian motion; we point out that the criterion is
not applicable for some other models, however. It is argued that the proposed
modified purity sieve may be used for selecting pointer states of a particle
undergoing decoherence through collisions.
