Vertical handoff is the switching process between heterogeneous wireless networks. Discovering the reachable wireless networks is the first step for vertical handoff. After discovering the reachable candidate networks, the mobile terminal decides whether to perform handoff or not. We present an adaptive scheme for vertical handoff in wireless overlay networks. Our system discovery method effectively discovers the candidate networks for the mobile terminal. Moreover, we propose two adaptive evaluation methods for the mobile terminal to determine the handoff time that relies on the candidates' resources and the running applications. The simulation results show that the proposed system discovery method can balance the power consumption and the system discovery time. Furthermore, the proposed handoff decision method can decide the appropriate time to perform handoff.