Two different approaches have been traditionally considered for dealing with the process of integrity constraints enforcement: integrity checking and integrity maintenance. However, while previous research in the first approach has mainly addressed efficiency issues, research in the second approach has been mainly concentrated in being able to generate all possible repairs that falsify an integrity constraint violation. In this paper we address efficiency issues during the process of integrity maintenance. In this sense, we propose a technique which improves efficiency of existing methods by defining the order in which maintenance of integrity constraints should be performed. Moreover, we use also this technique for being able to handle in an integrated way the integrity constraints