An important problem that arises when updating a deductive database is that of integrity maintenance. That is, given a consistent database and an update request, to obtain all possible updates of base facts such that the request is satisfied and no integrity constraint is violated. This problem becomes more complex when views may be present in the integrity constraints definition since a repair of a constraint could be a view update, which requires a translation into base fact updates. 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 integrate view updating into integrity maintenance and we propose a technique for translating view updates efficiently, aimed at reducing the number of alternatives considered during the process of view updating and the EDB accesses required to perform this translation.