Network routing games are used to understand the impact of individual users' decisions on network efficiency. Prior work on routing games uses a simplified model of network flow where all flow exists simultaneously. In our work, we examine routing games in a flow-over-time model. We show that by reducing network capacity judiciously, the network owner can ensure that the equilibrium is no worse than a small constant times the optimal in the original network, for two natural measures of optimality. These are the first upper bounds on the price of anarchy in the flow-over-time model for general networks.