Last Encounter Routing (LER) algorithms for mobile ad hoc networks rely only on encounter histories at every node to route packets, and therefore do not need control traffic to track topology changes due to node mobility. LER exploits the fact that past information about a node`s mobility helps to locate that node in the future. As we have pointed out in earlier work \cite{mg}, the performance of LER algorithms depends on the mobility processes of nodes. In this paper, we ask whether LER can work under the random waypoint (RWP) mobility model. This question is important for several reasons. First, as shown in \cite{mg}, a good performance for the RWP model is harder to achieve than for another prominent mobility model, the random walk. This is because the RWP model has a much shorter relaxation time, i.e., a time-horizon over which past information is still useful. Also, the RWP model has a much less favorable ratio of number of encounters between nodes and the traveled distance. Second, in contrast to the random walk, the RWP model is predictable. This provides us with an opportunity to exploit additional information collected in an encounter (such as speed, direction, etc.) to improve routing. We formally define the RWP model, and compute the optimal predictors for several observation sets, i.e., observed parameters of node mobility. We develop a new LER algorithm tuned to the RWP model called GREASE-RWP, and present simulation results that demonstrate that an efficient and scalable LER for the RWP model is possible.