In this paper, an area and power efficient two-stage spectrum sensing scheme for cognitive radios (CRs) is proposed. A typical parallel spectrum sensing using filter bank has advantages of lowest mean detection time, less interference to primary users and better throughput over serial spectrum sensing. However, these advantages come at the huge cost of increased area complexity and power consumption. The two-stage spectrum sensing consists of basic sensing stage using energy detection (ED) followed by advanced sensing stage using cyclostationary feature detection (CFD). The computation complexity and power consumption of CFD are very high compared to ED. Based on several spectrum occupancy measurement surveys conducted worldwide, we conclude that not all the CFD blocks in a typical parallel sensing scheme are fully utilized due to relatively sparse spectrum. Motivated by this observation, we propose a spectrum sensing scheme with reduced number of CFD blocks optimized based on spectrum occupancy information. The proposed scheme offers substantial reductions in area and power consumption while achieving same performance in terms of mean detection time compared with other existing spectrum sensing schemes.