Given a system that switches among N linear subsystems, this paper shows an approach that computes N dwell times, one for each of the subsystems, such that the overall system is stable under switching signals that respect the dwell times. The dwell times are obtained progressively starting from the groups of all pairwise switching systems, and increasing the size of the group by one for each step. In each progressive step, a bisection search algorithm is used to obtain the mode-dependent dwell times for that step. When the final step is reached, the N-mode dwell times are obtained. These dwell times are smaller, in terms of their sum, than an existing approach in recent literature for all the examples considered in this paper. (C) 2013 Elsevier Ltd. All rights reserved.