We consider a two-stage sensing scheme for cognitive radios where coarse sensing based on energy detection is performed in the first stage and, if required, fine sensing based on cyclostationary detection in the second stage. We design the detection threshold parameters in the two sensing stages so as to maximize the probability of detection, given constraints on the probability of false alarm. We compare this scheme with ones where only energy detection or cyclostationary detection is performed. The performance comparison is made based on the probability of detection, probability of false alarm and mean detection time.