Unconditional pointer states from conditional master equations

When part of the environment responsible for decoherence is used to extract information about the decohering system, the preferred pointer states rema in unchanged. This conclusion-reached for aspecific class of models-is inve stigated in a general setting of conditional master equations using suitabl e generalizations of predictability sieve. We also find indications that th e einselected states are easiest to infer from the measurements carried out on the environment.