Method and arrangement in a mobile terminal in a wireless communication system, for supporting a handover from a serving cell to a target cell. The method comprises determining 104a if the mobile terminal has moved in a predefined way in relation to at least one potential target cell. The determining is based on Doppler shift measurements 102a. The method further comprise adjusting 106a at least one handover related parameter, in order to enable a fast handover, when it is determined that the mobile terminal has moved in the predefined way in relation to the at least one potential target cell.