The use of user preferences for database retrieval promises a high degree of personalization by cooperatively combating the information flood. But most of the time preferences are only given for a subset of the available domain values and thus can still lead to unmanageable result sets especially in the presence of many attributes in a query. To limit such result sets preferences need to be completed interactively in tight cooperation with the user. In our framework the user is therefore enabled to specify additional preference information and also explicit equivalences between certain domain value combinations. However, whenever new information has to be integrated into the retrieval process the system has to make sure that the newly specified information is also consistent with what has been specified before. In this paper we study sufficient conditions for testing the consistency of new preference and equivalence information into a preference-based retrieval process. The benefits are that if the preference information fulfills a quite intuitive condition (which we call Cartesian) all new information can simple be added to the existing information without need for further consistency checks.