Under the scenario of an underlay cognitive radio network, we propose in this paper two adaptive schemes using switched transmit diversity and adaptive modulation in order to increase the spectral efficiency of the secondary link and maintain a desired performance for the primary link. The proposed switching efficient scheme (SES) and bandwidth efficient scheme (BES) use the scan and wait combining technique (SWC) where a transmission occurs only when a branch with an acceptable performance is found, otherwise data is buffered. In these schemes, the modulation constellation size and the used transmit branch are determined to minimize the average number of switched branches and to achieve the highest spectral efficiency given the fading channel conditions, the required error rate performance, and a peak interference constraint to the primary receiver (PR). For delay-sensitive applications, we also propose two variations of the SES and BES schemes using power control (SES-PC and BES-PC) where the secondary transmitter (ST) starts sending data using a nominal power level which is selected in order to minimize the average delay introduced by the SWC technique. We demonstrate through numerical examples that the BES scheme increases the capacity of the secondary link when compared to the SES scheme. This spectral efficiency improvement comes at the expense of an increased average number of switched branches and thus an increased average delay. We also show that the SES-PC and the BES-PC schemes minimize the average delay while satisfying the same spectral efficiency as the SES and BES schemes, respectively. © 2012 IEEE.