In the longitudinal control problem for automated heavy-duty vehicles, an important control objective is string stability, which ensures that errors decrease as they propagate upstream through the platoon. It is well known that when vehicles operate autonomously, string stability can he achieved by using speed-dependent spacing with constant time headway. However, this results in large steady-state intervehicle spacings, hence, decreased traffic throughput. This disadvantage is even more pronounced in heavy-duty vehicles, which require larger time headways due to their low actuation-to-weight ratio. In this paper, we develop two new nonlinear spacing policies-variable time headway and variable separation error gait-which all but eliminate this undesirable side effect. The first policy significantly reduces the transient errors and allows us to use much smaller spacings in autonomous platoon operation, while the second one results in smoother and more robust longitudinal control. Furthermore, the two can be combined to yield even better robustness, as is shown through our qualitative analysis.