In this paper, stability of switched systems is investigated for a class of switching signals which meet some admissibility conditions. Firstly, the admissible edge-dependent divergence time is defined in terms of admissible transition edges and it will vary with the compensation bounds. Then the admissible edge-dependent bounded maximum average dwell time (BMADT) is imposed on switching signals. As a result, a sufficient condition is obtained for globally uniformly exponential stability of switched nonlinear systems with such switching signals. Secondly, by setting the equal compensation bounds for the same reaching subsystems, the mode-dependent divergence time is defined, and then the mode-dependent BMADT is proposed. A stability condition under the mode-dependent BMADT is established. These stability results are then applied to switched linear systems. The numerical example is presented to show that the proposed techniques are less restrictive and more flexible in application, compared with the BMADT.