Cognitive radio networks have emerged in the last decade as a solution for two problems: spectrum underutilization and spectrum scarcity. The main idea is to manage the radio spectrum more efficiently, where secondary users (SUs) are allowed to exploit the spectrum holes in primary user's (PUs) frequency bands. We consider a paid-sharing approach where SUs pay for spectrum utilization. A challenging aspect in these mechanisms is how to proceed when a PU needs certain amount of bandwidth and the free capacity is insufficient. We assume a preemptive system where PUs have strict priority over SUs, when a PU arrives to the system and there are not enough free channels to accommodate the new user, one or more SUs will be deallocated. The affected SUs will then be reimbursed, implying some cost for the PUs service provider (SP). This paper bears on the design and analysis of an optimal SU admission control policy, i.e. that maximizes the long-run profit of the SP. We model the optimal revenue problem as a Markov Decision Process and we use dynamic programming and further techniques such as sample-path analysis to characterize properties of the optimal admission control policy. We introduce different changes to one of the best known dynamic programming algorithms incorporating the knowledge of the characterization. In particular, those proposals accelerate the rate of convergence of the algorithm when is applied in the considered context. Our results are validated through numerical examples