An intersystem or vertical handover is a key enabling mechanism for next generations of mobile communication systems. A vertical handover can cause an abrupt change of up to two orders of magnitude in link bandwidth and latency. It is hard for end-to-end congestion control to adapt promptly to such changes. This is especially a concern for slowly responsive congestion control algorithms, such as TCP-Friendly Rate Control (TFRC). TFRC is designed to provide a smooth transmission rate for real-time applications and, therefore, is less responsive to changes in network conditions than TCP. Using measurements and simulation, we show that TFRC has significant difficulties adapting after a vertical handover. TFRC receives only a fraction of TCP throughput over a fast link, but can be grossly unfair to concurrent TCP flows after handover to a slow link. We show that two proposals based on overbuffering and an explicit handover notification are effective solutions to these problems. Using them, TFRC can quickly adapt to new link characteristics after a handover, while otherwise maintaining a smooth transmission rate.