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Predictive velocity control can be used to enable efficient driving regarding fuel efficiency and driving time. Commonly, velocity optimization algorithms only take static information, like road slope and curvature, into account and neglect dynamic information, like traffic lights and other traffic participants, although the information is available through sensors or could be made available by vehicle-tovehicle or vehicle-to-infrastructure communication. Thus, static optimization algorithms do not provide optimal solutions in dynamic environments, caused by driver or assistance systems intervention. Because the incorporation of dynamic information increases the complexity of the problem to find an optimal control policy, its use in real-time applications is often prohibited. An algorithm is presented which allows a fast computation of all optimal speed profiles with regard to time and fuel consumption.