Two different approaches have been traditionally considered for dealing with the process of integrity constraints enforcement: integrity constraints checking and integrity constraints 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. Moreover, the methods proposed up to date are only concerned with handling one of the approaches in an isolated manner, without taking into account the strong relationship between the problems to be solved in both cases. In this paper we address efficiency issues during the process of integrity constraints 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 enforcement approaches mentioned above.