Concurrent mental workload degrades some aspects of driving performance, but drivers might be able to modify their behaviour adaptively to accommodate cognitive impairments. For example, they might maintain longer vehicle headway in dual-task conditions to compensate for slowed response times. Studies documenting such adaptive behaviours typically use steady-state driving scenarios such as car following. Yet, driving often involves tactical control situations in which drivers need to monitor multiple aspects of their traffic environment and to accommodate changing goals. In two simulator experiments, this study examined the impact of mental workload on safety margins (distances) that drivers keep when engaged in a tactical control task: passing other vehicles. Although drivers did increase their headway adaptively when engaged in steady-state car following (experiment 2), they did not adapt their behaviour to accommodate cognitive load when performing tactical control manoeuvres. Implications of this difference between steady-state and tactical control driving contexts, both for driving research and for driving safety, are discussed.