Many ideas have been proposed to reduce traffic congestion. Driving a platoon of vehicles with constant spacing seems to be a promising idea as it increases traffic density. But keeping constant inter-vehicle spacing requires very reliable communication. Another control policy is to drive the platoon with a time headway between vehicles. It is a robust and well known policy but large inter-vehicle distances in addition to weak stability (unity error gain) near low frequencies make it less practical. We have proposed in [1], [2] a modification of the Constant Time Headway policy (CTH). This modification largely reduces the inter-vehicle distances using only one information shared between all vehicles. In this work, we propose an additional modification of our control law. This modification makes our control law similar, in form, to the classical constant spacing policy, but it requires to share only one information between the vehicles. This modification improves the stability of the platoon and removes the weak stability of the CTH near low frequencies. We prove the robustness of the control law in the presence of actuating lags, sensing and communication delays. This proof can also be used to prove the stability of the classical constant spacing policy in the presence of all previous delays, which makes our result more general than those established in the literature. Safety is also discussed and the maximum acceptable communication delay without losing safety is determined. Simulations have been done in many critical scenarios.