Low earth orbit (LEO) satellite constellations could play an important role in future mobile communication networks due to their characteristics, such as global coverage and low propagation delays. However, because of the non-stationarity of the satellites, a call may be subjected to handovers, which can be cell or satellite handovers. Quite many techniques have been proposed in the literature dealing with the cell handover issue. In this paper, a satellite handover procedure is proposed, that investigates and exploits the partial satellite diversity (namely, the existing common coverage area between contiguous satellites) in order to provide an efficient handover strategy, based always on a tradeoff of the blocking and forced termination probabilities for a fair treatment of new and handover calls. Three different criteria were examined for the selection of a satellite. Each one of them could be applied either to new or handover calls, therefore we investigated nine different service schemes. A simulation tool was implemented in order to compare the different service schemes and simulation results are presented at the end of the paper.