In this paper, a cognitive radio (CR) network with multiple spectrum bands available for secondary users (SUs) is considered. For the SU's active spectrum-band selection, two criteria are developed. One is to select the band with the highest secondary channel power gain, and the other is to select the band with the lowest interference channel power gain to primary users (PUs). With the quality-of-service (QoS) requirement concerning delay, the effective capacity (EC) behaviors over secondary links are investigated for both criteria under two spectrum-sharing constraints. To begin by presenting full benefits in these criteria, the constraint imposed on the secondary transmitter (ST) is the average interference limitation to PUs only. Furthermore, taking into account the ST's battery/energy budget, the ST is imposed by joint constraints on its average interference to PUs, as well as on its own average transmit power. For either constraint, we formulate the ST's optimal transmit power allocation to maximize the SU's EC with both band-selection criteria and, correspondingly, obtain the secondary's power allocation and maximum EC in closed forms. Numerical results demonstrated subsequently substantiate the validity of our derivations and provide a powerful tool for the spectrum-band selection in CR networks with multiple bands available. © 1967-2012 IEEE.