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Cognitive radio networks require fast and reliable spectrum sensing to achieve high network utilization by secondary users. Optimization approaches to spectrum sensing to-date have largely focused on maximizing throughput for secondary users while considering only a single parameter variable pertinent to sensing - notably the threshold or duration, but not both. In this work, we investigate the impact of true joint minimization under two performance criteria: a) minimization of the average time to detection of a spectrum hole and b) joint maximization of the aggregate opportunistic throughput. We show that the resulting non-convex problem is actually biconvex under practical conditions for which effective algorithms can be developed that yields reliable numerical procedures to solve the resulting optimization problem. The results show that the proposed approach can considerably improve system performance (in terms of the mean time to detect a spectrum hole and also the aggregate opportunistic throughput of both primary and secondary users), relative to the scenarios with only a single sensing variable or a sub-optimal ad-hoc optimization approach used for two variable case.