In this paper, optimal resource allocation policies are characterized for wireless cognitive networks under the spectrum leasing model. We propose cooperative schemes in which secondary users share the time-slot with primary users in return for cooperation. Cooperation is feasible only if the primary system's performance is improved over the non-cooperative case. First, we investigate a scheduling problem where secondary users are interested in immediate rewards. Here, we consider both infinite and finite backlog cases. Then, we formulate another problem where the secondary users are guaranteed a portion of the primary utility, on a long-term basis, in return for cooperation. Finally, we present a power allocation problem where the goal is to maximize the expected net benefit defined as utility minus cost of energy. Our proposed scheduling policies are shown to outperform non-cooperative scheduling policies, in terms of expected utility and net benefit, for a given set of feasible constraints. Based on Lyapunov optimization techniques, we show that our schemes are arbitrarily close to the optimal performance at the price of reduced convergence rate. © 2012 IEEE.