  When part of the environment responsible for decoherence is used to extract
information about the decohering system, the preferred {\it pointer states}
remain unchanged. This conclusion -- reached for a specific class of models --
is investigated in a general setting of conditional master equations using
suitable generalizations of predictability sieve. We also find indications that
the einselected states are easiest to infer from the measurements carried out
on the environment.
