Under the scenario of an underlay cognitive radio network, we propose in this paper an adaptive scheme using switched transmit diversity and adaptive modulation in order to minimize the average number of switched branches at the secondary transmitter while increasing the capacity of the secondary link. The proposed switching efficient scheme (SES) uses the scan and wait (SWC) combining technique where a transmission occurs only when a branch with an acceptable performance is found, otherwise data is buffered. In our scheme, the modulation constellation size and the used transmit branch are determined to achieve the highest spectral efficiency with a minimum processing power, given the fading channel conditions, the required error rate performance, and a peak interference constraint to the primary receiver. Selected numerical examples show that the SES scheme minimizes the average number of switched branches for the average and the high secondary signal-to-noise ratio range. This improvement comes at the expense of a small delay introduced by the SWC technique. For reference, we also compare the performance of the SES scheme to the selection diversity scheme (SDS) where the best branch verifying the modulation mode and the interference constraint is always selected.