QUACQ is a constraint acquisition algorithm that assists a non-expert user to model her problem as a constraint network. QUACQ generates queries as examples to be classified as positive or negative. One of the drawbacks of QUACQ is that generating queries can be time-consuming. In this paper we present TQ-GEN, a time-bounded query generator. TQ-GEN is able to generate a query in a bounded amount of time. We rewrite QUACQ to incorporate the TQ-GEN generator. This leads to a new algorithm called T-QUACQ. We propose several strategies to make T-QUACQ efficient. Our experimental analysis shows that thanks to the use of TQ-GEN, T-QUACQ dramatically improves the basic QUACQ in terms of time consumption, and sometimes also in terms of number of queries.