We investigate the problem of refining SQL queries to satisfy cardinality constraints on the query result. This has applications to the many/few answers problems often faced by database users. We formalize the problem of query refinement and propose a framework to support it in a database system. We introduce an interactive model of refinement that incorporates user feedback to best capture user preferences. Our techniques are designed to handle queries having range and equality predicates on numerical and categorical attributes. We present an experimental evaluation of our framework implemented in an open source data manager and demonstrate the feasibility and practical utility of our approach.