In this paper, we optimize the handover procedure in the fast handover for mobile IPv6 (FMIPv6) protocol by using the IEEE 802.21 media independent handover (MIH) services. FMIPv6 is used to enhance the performance of handovers in mobile IPv6 and its basic extension for network mobility (NEMO), i.e., the fundamental mobility management protocols used in vehicular networks. With the aid of the lower three layers' information of the mobile node/router (MN/MR) and the neighboring access networks, we tackle the radio access discovery and candidate access router (AR) discovery issues of FMIPv6. We introduce an "information element container" to store static and dynamic layer 2 (L2) and layer 3 (L3) information of neighboring access networks and propose to use a special cache maintained by the MN/MR to reduce the anticipation time in FMIPv6, thus increasing the probability of the predictive mode of FMIPv6 operation. Furthermore, we propose a cross-layer mechanism for making intelligent handover decisions in FMIPv6. The lower layer information of the available links obtained by MIH services and the higher layer information such as quality-of-service (QoS) parameter requirements of the applications are used by a policy engine to make intelligent handover decision. We will show through analysis and simulations of the signaling procedure that the overall expected handover (both L2 and L3) latency in FMIPv6 can be significantly reduced in the proposed mechanism.