Data dependencies, or integrity constraints, are used to improve the quality of a database schema, to optimize queries, and to ensure consistency in a database. In the last years conditional dependencies have been introduced to analyze and improve data quality. In short, a conditional dependency is a dependency with a limited scope defined by conditions over one or more attributes. Only the matching part of the instance must adhere to the dependency. In this paper we focus on conditional inclusion dependencies (CINDs). We generalize the definition of CINDs, distinguishing covering and completeness conditions. We present a new use case for such CINDs showing their value for solving complex data quality tasks. Further, we define quality measures for conditions inspired by precision and recall. We propose efficient algorithms that identify covering and completeness conditions conforming to given quality thresholds. Our algorithms choose not only the condition values but also the condition attributes automatically. Finally, we show that our approach efficiently provides meaningful and helpful results for our use case.