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Recent research has demonstrated the potential benefits of connected, autonomous vehicles (CAVs) to the performance of urban networks. Specifically, several proposals have been made for policies and related technologies that either perform more efficiently when the proportion of CAVs is relatively high or that exclude human driven vehicles (HDVs) altogether. This same body of research has also identified several challenges faced by such networks, especially in the context of shared autonomous vehicles (SAVs). We propose a lane-use policy for networks of exclusively CAVs with the goal of preserving priority within any two-class, arbitrary priority assignment regime. We investigate the merits of such a policy by adopting a simple occupancy based, two-class priority scheme in a network of SAVs. We will demonstrate that by granting and preserving priority for occupied vehicles, average travel times and speeds for passengers are improved with limited degradation in these measures for other, i.e. unoccupied, vehicles. The proposed lane-use policy is developed on realistic physical limitations of the street network and without the need for trajectory reservations.