As is well known, cooperative sensing can significantly improve the sensing accuracy as compared to local sensing in cognitive radio networks (CRNs). However, a large number of cooperative secondary users (SUs) reporting their local detection results to the fusion center (FC) would cause much overhead, such as sensing delay and energy consumption. In this paper, we propose a fast cooperative sensing scheme, called double threshold fusion (DTF), to reduce the sensing overhead while satisfying a given sensing accuracy requirement. In DTF, FC respectively compares the number of successfully received local decisions and that of failed receptions with two different thresholds to make a final decision in each reporting sub-slot during a sensing process, where cooperative SUs sequentially report their local decisions in a selective fashion to reduce the reporting overhead. By jointly considering sequential detection and selective reporting techniques in DTF, the overhead of cooperative sensing can be significantly reduced. Besides, we study the performance optimization problems with different objectives for DTF and develop three optimum fusion rules accordingly. Simulation results reveal that DTF shows evident performance gains over an existing scheme.