A vehicle-actuated traffic light controls two intersecting traffic streams keeping the light green for lane i, i = 1 or 2 until any existing queue has been discharged and a headway of duration at least βı, is detected in the subsequent arrivals. The object of this paper is to investigate how one should choose the βi so as to minimize the average delay per vehicle at the intersection. A model is considered in which the arrival headways are exponentially distributed random variables, departure headways have any specified distribution, and there is a random lost time for each switch of the traffic light. Formulas are derived for the moments of the cycle times, the average wait per vehicle, and the optimal βi.