Vertical handoffs between different wireless technologies usually lead to dramatic changes in the link capacity. A successful QoS solution for vertical handoffs must be able to fast track the capacity changes and agilely adapt the delivery rates and qualities of the ongoing applications. Though traditional AIMD-based source adaptation schemes (as found in TCP, TFRC, etc.) have been well designed for mild, gradual rate adjustments required by load fluctuations and network congestion, their response time is inadequate when the rate must be adjusted to the drastic network capacity changes that are typical in vertical handoff scenarios. To expedite the response to such changes, we propose in this paper two adaptive algorithms, named the Fast Rate Adaptation (FRA) and Early Rate Reduction (ERR), that are launched when the handoff is from low to high capacity (LOW-to-HIGH) or from high to low capacity (HIGH-to-LOW), respectively. We also propose two vertical handoff notification mechanisms to work with FRA and/or ERR, i.e. the Implicit Handoff Notification (IHN) and Explicit Handoff Notification (EHN). We show by simulation that our proposed schemes are able to provide better QoS support than the traditional AIMD based schemes during vertical handoffs.