This paper focuses on spectrum handover in cognitive radio networks where secondary users (SUs) opportunistically use licensed channels as long as the aggregate interference at the primary users (PUs) does not exceed a certain threshold. We incorporate power control into the proposed spectrum handover scheme to reduce the number of spectrum handovers and enhance the spectral efficiency. In our work, when a PU arrives, an SU first calculates the maximum transmission power that the SU does not interfere with the PU. If the SU can still reach its receiver, it lowers its power and continues to transmit; otherwise it switches to an idle band. Analysis results show that our proposed scheme can substantially reduce the spectrum handover ratio and improve the effective data rate by up to 30%.