Constraint acquisition assists a non-expert user in modeling her problem as a constraint network. In existing constraint acquisition systems the user is only asked to answer very basic questions. The drawback is that when no background knowledge is provided, the user may need to answer a great number of such questions to learn all the constraints. In this paper, we introduce the concept of generalization query based on an aggregation of variables into types. We present a constraint generalization algorithm that can be plugged into any constraint acquisition system. We propose several strategies to make our approach more efficient in terms of number of queries. Finally we experimentally compare the recent QUACQ system to an extended version boosted by the use of our generalization functionality. The results show that the extended version dramatically improves the basic QUACQ.