- Preference elicitation is a serious bottleneck in many decision support applications and agent specification tasks. CP-nets were designed to make the preference elicitation process simpler and more intuitive for lay users by graphically structuring a set of Ceteris Paribus (CP) preference statements preference statements most people find natural and intuitive. In various contexts, CP-nets with an underlying cyclic structure emerge naturally. Often, they are inconsistent according to the current semantics, and the user is required to revise them. In this paper we show how optimization queries can be meaningfully answered in many "inconsistent" networks without troubling the user with requests for revisions. We also describe a method for focusing users' revision process when revisions are truly needed. In the process, we provide a formal semantics that justifies our approach and we introduce new techniques for computing optimal outcomes.