This paper studies the planning of conflict-free and efficient crossings of antagonistic vehicles’ movements at lightless intersections. A fully automated infrastructure environment is considered, where all vehicles that enter the intersection area are connected and automated (CAVs), i.e., they are equipped with advanced communication and automation technologies. In such a futuristic environment, traffic lights that regulate the right-of-way of different traffic streams are obsolete because of vehicle communication capabilities. The connectivity is utilized to derive vehicle trajectories such that a safe and efficient crossing of lightless intersections is possible. So far, published studies lack the application to complex intersection layouts. To fill this gap, we introduce a control method for CAV pairing allowing for the safe, collision-free crossing of the intersecting area and optimize traffic conditions, i.e., total delays of the system. Simulation results demonstrate the feasibility and applicability of the presented approach, given that all the technical specifications (e.g., communications, velocity actuators) are present. Finally, we conduct a sensitivity analysis for the algorithm’s main parameters, which provides practical insights for the studied experimental scenarios and other existing algorithms in the literature that tackle this problem.