A consistent query answer in an inconsistent database is an answer obtained in every (minimal) repair. The repairs are obtained by resolving all conflicts in all possible ways. Often, however, the user is able to provide a preference on how conflicts should be resolved. We investigate here the framework of preferred consistent query answers, in which user preferences are used to narrow down the set of repairs to a set of preferred repairs. We axiomatize desirable properties of preferred repairs. We present three different families of preferred repairs and study their mutual relationships. Finally, we investigate the complexity of preferred repairing and computing preferred consistent query answers.