Handling mobility at the transport layer is an interesting approach to attain seamless handover in the context of heterogeneous access networks. To support terminal mobility, an extension of SCTP called SCTP-DAR (SCTP Dynamic Address Reconfiguration) (a.k.a. mobile SCTP) has been defined allowing SCTP endpoints to update IP address and inform the remote peer about primary address change. However, mobile SCTP suffers from performance degradation during handover. In this paper, we investigate two handover-related issues: reduction of data rate immediately after handover and packet reordering. The first issue is caused by the congestion control mechanism, which forces the ongoing traffic to enter the slow-start phase when moving into the new path after handover. The second issue is caused by the asymmetric characteristics of access networks such as the different bandwidths and delays in heterogeneous access networks. In order to solve these issues, we propose to use a combination of two mechanisms, congestion control parameter update and buffer retransmission.