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Resource management for individual flows can significantly improve quality of service (QoS) in mobile cellular networks. However, its efficiency depends on the availability of information about the movement of mobile terminals. Movement prediction can potentially provide this information, but is costly if performed by the network and usually assumes a certain movement model, which may not adequately reflect each individual user's behavior. Instead, we propose the concept of movement contracts, where a mobile terminal specifies its movement to the network, which in return provides a better QoS as long as the provided specification is sufficiently accurate. We describe approaches to specify the spatial and temporal aspects of movement with a parsimonious parameter set and evaluate these approaches through simulations. We find that movement contracts can significantly reduce both session blocking and handover dropping probability simultaneously, whereas existing approaches have to make a tradeoff between these.